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Communications in Asteroseismology Volume 150 June, 2007 Proceedings of the Vienna Workshop on the Future of Asteroseismology Vienna, 20 – 22 September, 2006 edited by Gerald Handler & Günter Houdek Austrian Academy of Sciences Press Vienna 2007 Editor: Michel Breger, Türkenschanzstraße 17, A - 1180 Wien, Austria Layout and Production (this issue): Gerald Handler Editorial Board: Gerald Handler, Don Kurtz, Jaymie Matthews, Ennio Poretti http://www.univie.ac.at/tops/ British Library Cataloguing in Publication data. A Catalogue record for this book is available from the British Library. All rights reserved ISBN 978-3-7001-3916-4 ISSN 1021-2043 c 2007 by Copyright Austrian Academy of Sciences Vienna Austrian Academy of Sciences Press A-1011 Wien, Postfach 471, Postgasse 7/4 Tel. +43-1-515 81/DW 3402-3406, +43-1-512 9050 Fax +43-1-515 81/DW 3400 http://verlag.oeaw.ac.at, e-mail: [email protected] Preface by G. Handler and G. Houdek, Proceedings Editors 10 An overview of Michel Breger’s career by D. W. Kurtz and W. W. Weiss 11 Delta Scuti and roAp stars Delta Scuti stars: Observational aspects by M. Breger 25 Approaching asteroseismology of δ Scuti stars: problems and prospects by J. Daszyńska-Daszkiewicz 32 Observations of pulsations in roAp stars by O. Kochukhov 39 Theory of rapidly oscillating Ap stars by M. S. Cunha 48 SX Phe stars in the Fornax dSph galaxy by E. Poretti et al. 55 REM observations of the Herbig Ae stars V346 Ori and PDS2 by S. Bernabei et al. 57 Asteroseismology and mode driving of the Herbig Ae star HD 104237 by M.-A. Dupret et al. 59 Asteroseismology of the extreme metal-deficient field high-amplitude SX Phe variable BL Cam by E. Rodrı́guez et al. 61 δ Sct stars in eclipsing binaries: the case of Y Cam by E. Rodrı́guez et al. 63 Strömgren photometry of the δ Sct star V402 Cep by V. Costa et al. 65 New pulsation pattern of RZ Cas observed spectroscopically in 2006 by H. Lehmann, D.E. Mkrtichian 67 Physical properties of the oEA star IV Cas by S.-L. Kim, C.-U. Lee, J. W. Lee, J.-H. Youn 69 Pulsating components of eclipsing binaries from the ASAS-3 data by G. Michalska and A. Pigulski 71 A theoretical scenario for PMS δ Scuti stars by A. Ruoppo et al. 73 44 Tau: Discrimination between MS and post-MS models by P. Lenz, A. A. Pamyatnykh, M. Breger, V. Antoci 75 An asteroseismic Main Sequence model for the δ Scuti star 44 Tau by R. Garrido et al. 77 The Nainital-Cape Survey: contributions to asteroseismology of CP stars by S. Joshi et al. 79 Vertical structure of pulsations in roAp stars by M. Sachkov et al. 81 Non-LTE line formation in the atmospheres of Ap stars: importance for pulsational analysis of roAp stars by T. Ryabchikova, L. Mashonkina, A. Ryabtsev, R. Kildiyarova, M. Khristoforova 83 First Magnetic Doppler Images of a roAp star by T. Lüftinger, O. Kochukhov, T. Ryabchikova, W. W. Weiss, I. Ilyin 85 Discussion on δ Scuti and roAp stars led by D. W. Kurtz 87 Gamma Doradus stars and solar-like oscillators Asteroseismology of γ Doradus Variables: Past, Present, and Future by A. B. Kaye 91 Theoretical aspects of g-mode pulsations in γ Doradus stars by M.-A. Dupret et al. 98 Observations of solar-like oscillations by T. R. Bedding and H. Kjeldsen 106 Stellar Oscillations in Giant Stars by A. P. Hatzes, M. P. Döllinger and M. Endl 115 Theoretical asteroseismology of solar-like oscillations by G. Houdek 122 λ Boo stars among the γ Dor-type pulsators: the cases of HD 218427 and HD 239276 by E. Rodrı́guez et al. 131 Coordinated observational campaigns for non-radially pulsating objects by K. R. Pollard et al. 133 Analysis tools for non-radially pulsating objects by D. J. Wright, K. R. Pollard, P. L. Cottrell 135 The convective envelope in γ Doradus stars: theoretical uncertainties by J. Montalbán, A. Miglio, S. Théado 137 A search for solar-type oscillations in K giants in M4 by S. Frandsen et al. 139 Rotation and small separations of α Cen A by M. Bazot et al. 141 Solar-like Oscillations with Kepler by J. Molenda-Żakowicz, T. Arentoft, H. Kjeldsen, M. Vaňko 143 High-frequency interference peaks in solar-like stars by C. Karoff 145 Detection of p-mode oscillations in β Hydri from photometric observations with WIRE by C. Karoff, H. Bruntt, H. Kjeldsen, T. Bedding, D. L. Buzasi 147 Solar-like oscillations in open cluster stars by D. Stello et al. 149 Core modes as a seismic probe of mixing beyond the convective core by B. L. Popielski 151 Two-scale mass-flux closure models for turbulence: p-mode amplitudes in solar-like stars by K. Belkacem et al. 153 Discussion on solar-like oscillators and γ Doradus stars led by D. O. Gough 155 Beta Cephei and Slowly Pulsating B stars The present day of asteroseismology of β Cephei stars: observations by A. Pigulski 159 Observational Asteroseismology of slowly pulsating B stars by P. De Cat 167 Oscillations in main sequence B-type stars - challenges to theory by W. A. Dziembowski 175 Candidate SPB and γ Doradus stars from microlensing surveys by A. Narwid, Z. Kolaczkowski, A. Pigulski 181 An abundance analysis of slowly pulsating B stars by M. Briquet and T. Morel 183 Temperature gradients in the core overshooting region by M. Godart 185 A comparative study of B-type pulsators and non-pulsating chemically peculiar Bp stars by M. Briquet et al. 187 Mode identification of multi-periodic Slowly Pulsating B-stars: results and problems by W. Zima, P. De Cat, C. Aerts 189 The ongoing 2005 – 2006 campaign on β Cephei stars in NGC 6910 and χ Persei (NGC 884) by A. Pigulski et al. 191 Pulsating variables in NGC 3293, the open cluster with the most β Cephei stars known by G. Handler et al. 193 A spectroscopic study of the β Cephei star 12 (DD) Lacertae by M. Desmet et al. 195 Asteroseismology of the β Cephei star KP Per by S. Saesen et al. 197 Nitrogen excess in slowly-rotating β Cephei stars: deep mixing or diffusion? by T. Morel et al. 199 An abundance study of the B-type targets for the asteroseismology programme of the CoRoT mission by T. Morel and C. Aerts 201 Effects of diffusion in β Cephei stars by P.-O. Bourge, S. Théado, A. Thoul 203 Amplitude Saturation in β Cephei Models - Preliminary Results by R. Smolec and P. Moskalik 205 The β Cephei instability domain for the new solar composition and with new OP opacities by A. A. Pamyatnykh and W. Ziomek 207 Instability strips of main sequence B stars: a parametric study of iron enhancement by A. Miglio, P.-O. Bourge, J. Montalbán, M.-A. Dupret 209 Asteroseismology of the β Cephei star ν Eridani using differentially-rotating models by J. C. Suárez, R. Garrido, M. J. Goupil 211 Interpretation of the Be star HD 163868 oscillation spectrum based on the MOST observations by W. A. Dziembowski, J. Daszyńska-Daszkiewicz, A. A. Pamyatnykh 213 g-modes in the late-type Be star β CMi detected by the MOST satellite by H. Saio et al. 215 Discussion on β Cephei and SPB stars led by C. Aerts 217 Pulsating white dwarf and sdB stars Observational white dwarf seismology by S. O. Kepler 221 The Future of Computational Asteroseismology by T. S. Metcalfe 227 Pulsating Hot Subdwarfs – An Observational Review by D. Kilkenny 234 Ten years of asteroseismic modelling of pulsating B subdwarf stars: achievements, challenges, and prospects by S. Charpinet et al. 241 The Red Edge of GW Virginis stars by P.-O. Quirion, G. Fontaine, P. Brassard 247 Doubling the number of DBVs and a closer look at their Instability Strip by A. Nitta et al. 249 GD 99 - an unusual, rarely observed DAV white dwarf by Zs. Bognár et al. 251 Mapping Convection using Pulsating White Dwarf Stars by M. H. Montgomery 253 Towards Asteroseismology of Long-Period Variable Subdwarf B Stars by S. K. Randall, G. Fontaine, P. Brassard, E. M. Green 255 An old puzzle in a new light: PG 1336−018 by M. Vučković et al. 257 Time resolved spectroscopy of the multiperiodic pulsating subdwarf B star PG 1605+072 by A. Tillich, U. Heber, S. J. O’Toole 259 Change of splittings in Balloon 090100001 by A. Baran et al. 261 Mode identification in the pulsating subdwarf Balloon 090100001 by means of the spectrophotometric method by A. Baran et al. 263 Time resolved spectroscopy of Balloon 090100001 by R. Østensen, J. Telting and U. Heber 265 The frequency distribution of PG 1657+416, a rapidly pulsating sdB star by R. Oreiro et al. 267 Observations of 23 EC 14026-type pulsating subdwarf B stars by M. D. Reed et al. 269 Time-Series Spectroscopy of the subdwarf B Star PG 1219+534 by J. R. Eggen et al. 271 Stability analysis of sdO equilibrium models by C. Rodrı́guez-López, R. Garrido, A. Moya, J. MacDonald, A. Ulla 273 Discussion on pulsating white dwarf and sdB stars led by D. E. Winget 275 Asteroseismology: Lessons From the Past and Prospects for the Future by S. D. Kawaler 279 Ground-based asteroseismology The Network Activities in HELAS by M. Roth 287 The Delaware Asteroseismic Research Center: Convection in Pulsating White Dwarfs by J. L. Provencal, H. L. Shipman and the WET TEAM 293 Stellar Oscillations Network Group by F. Grundahl et al. 300 Asteroseismology at Dome C in Antarctica by E. Fossat 307 A Fourier Tachometer at Dome C in Antarctica by B. Mosser and the SIAMOIS team 309 Use of NIR spectroscopy for the study of pulsating stars by P. J. Amado et al. 311 Jovian seismology: preliminary results of the SYMPA instrument by P. Gaulme et al. 313 Small IRAIT Telescope: photometry and asteroseismology at Dome C by G. Tosti et al. 315 MONET, HET and SALT and asteroseismological observations and theory in Göttingen by S. Schuh et al. 317 A New Slovak Observatory 500 km from Vienna by I. Kudzej et al. 319 Reflections on some aspects of ground-based observations for asteroseismology by C. Sterken 321 Discussion on ground-based asteroseismology led by C. Sterken 323 Space-based asteroseismology Asteroseismology with the WIRE satellite by H. Bruntt 326 One small satellite, so many light curves: Examples of δ Scuti asteroseismology from the MOST space mission by J. M. Matthews and the MOST Science Team 333 CoRoT data contribution to stellar seismology by E. Michel, A. Baglin, R. Samadi, F. Baudin, M. Auvergne 341 Microsatellites by W. W. Weiss 349 Asteroseismology with the Kepler mission by J. Christensen-Dalsgaard et al. 350 The PLATO mission concept by I. Roxburgh, C. Catala and the PLATO team 357 Dynamos, Asteroseismology, and the Stellar Imager by C. J. Schrijver, K. G. Carpenter, M. Karovska 364 The ground-based counterpart of the CoRoT asteroseismic observations from space by K. Uytterhoeven et al. 371 Discussion on space-based asteroseismology led by A. Baglin 373 Other types of pulsators Indication of pulsation in young Brown Dwarfs by M. Marconi et al. 377 RR Lyrae stars: The changing light curve shape during the Blazhko cycle by E. Guggenberger and K. Kolenberg 379 Photometric campaigns for the Blazhko Project by K. Kolenberg and E. Guggenberger 381 RR Lyrae stars in M4 by G. Kopacki and S. Frandsen 383 Physical parameter determination of seven RR Lyrae stars in Bootes by J. H. Peña, A. Arellano, J. P. Sareyan, R. Peña, M. Alvarez List of participants 385 387 Comm. in Asteroseismology Vol. 150, 2007 Preface When first hearing about the Vienna Workshop on the Future of Asteroseismology, many of you will have asked yourself the same questions: Why discuss the future now, when only the first results from space asteroseismology are available? Isn’t it odd to celebrate the 65th birthday of a renowned asteroseismologist who is far from retirement at this point? The answer to the first question is easy: at the outset of this meeting, MOST was already in space and COROT was soon to be. Therefore, the next projects must already be thought about in order not to lose valuable time. The answer to the second question, however, is hidden in a rather long story which the participants of this workshop have now been told. In short, a long chain of events made one of the organizers make a joke, resulting in a full hall of variable-star researchers singing Happy Birthday for Michel Breger’s 65th birthday when in reality it was only his 58th . So, at his real 65th birthday, it was time to make up to Michel. Most of us attend meetings with lots of scientific ideas, and come back filled with many more, inspired by the discussions with fellow scientists. Moreover, such discussions do obviously contribute to shaping the future of asteroseismology, and because Michel loves discussions it seemed only logical to focus this meeting on discussions. Consequently, this workshop was not organized in the traditional manner, with several review talks followed by large numbers of contributed scientific presentations that leave little or no time for reflection, but rather by trying to address the big questions and hence draw the big picture. Therefore, these proceedings also contain transcripts of all the discussions, in an attempt to reflect the positive and friendly spirit of this meeting and its lively atmosphere. Michel Breger’s enormous reputation in asteroseismology is demonstrated by the fact that in response to the SOC trying to collect as many big names in the field as possible you all came. Our first and foremost thanks therefore go to the participants of this meeting who came to celebrate Michel. The LOC did a wonderful job running this workshop, with many of them going much further with their help than was asked. These proceedings benefited both from the contributions of many referees, conference participants and external specialists, who provided insightful comments, and from the help of the previous and present production editors, Wolfgang Zima and Paul Beck. The photographs included in these proceedings were kindly provided by Katrien Kolenberg, Konstanze Zwintz, Tony Kaye, Dennis Stello and by Victoria Antoci, who also helped with their processing. And finally, this conference could not have been organized without the support of several sponsors, most notably HELAS, and some donations by Erste Bank, Ströck Brot and Okto TV. Gerald Handler and Günter Houdek Proceedings Editors Comm. in Asteroseismology Vol. 150, 2007 An overview of Michel Breger’s career D. W. Kurtz,1 W. W. Weiss 2 1 Centre for Astrophysics, University of Central Lancashire, Preston PR1 2HE, UK 2 Institute of Astronomy, University of Vienna, 1180 Vienna, Austria Who is Michel Breger? You can find him on the Austrian Academy of Science’s website as: Mag. rer. soc. nat., Dr. phil., B. Sc., M.A., o. Prof. Michel Breger and that is impressive! (Although few of us have much idea what it all means.) He was born Michel (as pronounced in German with a guttural “ch”) and still is Michel to his university administration and to the Austrian Academy of Sciences; he is Mike (from his South African and American nick-name) to his many students past and present, and to most of the international astronomical community – this is even occasionally Anglicized to Michael; he is even “Mi-shell Brezhair” in France and Quebec! Mike is a man of many names, but for his more than 35 postgraduate students and many others he is also known as “mentor”, and all of us know him as “friend” and “colleague”. I (DWK) was Mike’s first PhD student at the University of Texas over 30 years ago. When I say that today to his current students and postdocs, I get a look of utter disbelief! I can see in their eyes that they are thinking, “But Mike Breger is so young; how could he have supervised an old guy like you?” Well, Mike is 8 years older than I am, although he appears not to age. I can assure you that he does - just at a much slower rate than most of the rest of us – and Fig. 1 proves this. Mike went to school in East Germany following the war; Fig. 8 shows him in a school picture at age 8 in 1949. Then in 1952 his family moved to Swakopmund, Namibia (then South West Africa) which at the time was an officially tri-lingual country where there was good German-language schooling. When it came time to go to university, Mike looked to the best university in Africa – the University of Cape Town (UCT) – where he studied mathematics and physics from 1960 − 1964. Fig. 2 shows his graduation picture. Mike was searching for an honour’s project for his final year at UCT, and a friend, Tony Fairall (now professor of astronomy at UCT), made a fateful suggestion. According to Tony: “We were both students in Driekoppen Res, though Mike was about 2 years senior to me. When he expressed an interest in astronomy, I volunteered to take him to the Royal Observatory. I rode on the back of Mike’s Vespa scooter, introduced him to Dick Stoy and David Evans, and the rest is history!” Mike was impressed particularly with Stoy, who was then the director of the observatory. He found, as he puts it, “Dick Stoy put students at the telescope!” And that lesson stuck. Mike Breger throughout his career with the many students he has supervised “puts students at the telescope”. That is still true today at a time when this is becoming harder as astronomers work in ever larger groups and much observing is service observing on large telescopes. During Mike’s honours year at UCT he not only got to observe, but he clearly showed that he likes to write and he likes to publish – four papers in the Monthly Notes of the Astronomical Society of South Africa (MNASSA) appeared in his final undergraduate year: 1. Breger M., 1964, MNASSA, 23, 41: A Note on the Relation between the Radial Velocity and Variation for RR Lyrae Stars 2. Breger M., 1964, MNASSA, 23, 64: Photoelectric Observations of HH Pup 12 An overview of Michel Breger’s career Figure 1: Mike Breger was born 8 August 1941 in Oberhausen, Germany. 3. Breger M., 1964, MNASSA, 23, 112: Provisional Radial Velocities for 9 RR Lyrae Stars 4. Breger M., 1964, MNASSA, 23, 117: A Note on the Mean Luminosity of RR Lyrae Stars At the end of his undergraduate years Mike got a job for a short while as a Radcliffe Observatory Assistant at the 74-inch (1.9-m) telescope in Pretoria (now at the Sutherland station of the South African Astronomical Observatory – SAAO). There he learnt spectroscopy, but this was at a time when the detector was a photographic plate. The observer had to spend his afternoons cutting photographic plates in pitch darkness to the correct size of the plate holder. This was done with a diamond blade and by feel. You could tell which side of the plate the emulsion was on by touching it lightly with your tongue! The emulsion side was slightly sticky and a little bit sweet; the other side was just smooth glass. Then the observer spent the night at the eyepiece guiding the star up and down the slit by eye to broaden the spectra for better signal-to-noise, and then finished in the morning developing the plates by feel in the dark (or at best under very dim red light for blue plates): developer, wash, fixer, clearing agent, drying rack. Finally, the day was spent measuring the spectra. Sleep? What is that? Mike observed all night and almost went blind measuring tiny spectra in a dark room all day. He then changed back to photometry fast! (Even though it only paid $ 16 a month.) Thus he was led (driven?) to a career in photometry. On finishing his undergraduate degree, Mike wanted to go to graduate school in astronomy and sought advice. Everyone said the same thing: Go to the best university. For his undergraduate training that is what he had done while staying relatively close to home (it is “only” about 1600 km and four days and three nights by train from Swakopmund to Cape Town). For graduate school he chose the University of California at Berkeley on San Francisco D. W. Kurtz and W. W. Weiss 13 Figure 2: Mike - on the right with two friends - on “Jammie” (Jameson Hall) steps at the University of Cape Town in 1964. Bay in the USA. He arrived there in 1965 into the height and heart of the “hippie” era, the free-speech movement, the free-love movement, and the anti-Viet Nam War demonstrations. In the last few generations there can be no more evocative time and place to have been a student than at Berkeley in the 1960s. Mike quickly discovered a talent for organization. His first demonstration had already been organized in Cape Town to protest against the high price of food in the student cafeteria; Fig. 3 shows him and his fellow students cooking on camp stoves in the cafeteria to undercut the official prices. In California, he joined the committee to save Haight-Ashbury. This is a neighbourhood of beautiful Victorian San Franciscan mansions centred on the corners of Haight and Ashbury streets which was run-down in the 1960s and inhabited by hippies, students, and other young people, “drop-outs”, and, of course, drug-users – although this mostly meant relatively soft drugs such as marijuana and LSD at the time – as well as being a centre of rock music. It was a time of the Grateful Dead, Timothy Leary, Ken Kesey, Joan Baez, be-ins and love-ins. Mike grew his hair down to his waist (although, unfortunately, we have no pictures to prove this!) - quite a change from the tie-wearing arrival in 1965 seen in Fig. 3. It was during these grad student years that Mike gave his first trembling talk at an American Astronomical Society meeting where he presented the results of the millimag photometry he had been doing and some of his first small-amplitude δ Scuti star light curves. (At the time 0.01 mag precision was considered to be good photometry, so Mike had increased the precision by a factor of 10.) At the end of his talk two famous photometry pundits, who will remain unnamed, got up and stated their doubts that such precision could be obtained at all. Two theoreticians (Martin Schwarzschild and John Cox) replied that all of his results were quite logical and that the constancy of the comparison stars proved the reality of the small-amplitude light variations. As Mike says, “It just goes to show that theoreticians can be kind to frightened graduate students.” 14 An overview of Michel Breger’s career Figure 3: Mike and his fellows cooking and selling food in the Cape Town student cafeteria in 1962 in protest against high prices. Mike discovered a talent for, and love of, organization at this time. It was also at this time that Mike was offered his first job with a company in the Bay area working on satellite guidance using stars. He declined the job, and it turned out to be a good thing he did, as the project was working on a spy satellite and it is doubtful whether a hippie-protest-organizer was the person they were looking for. With the pattern set at UCT in his undergraduate honours’ year, Mike continued with the discoveries and publications. The years 1965 − 1969 were the years of discovery in δ Scuti stars, and the time when a new standard of photometric precision was set: 1. Breger Michel, 1969, PhDT: Variability Near the Instability Strip in the Delta Scuti Region. 2. Breger M.; Sanwal N. B., 1968, ApL, 1, 103: Short Period Variability of B, A and F Stars. I. A Coma Cluster Delta-Scuti Type Variable 3. Breger M., 1969, AJ, 74, 166: Short-period variability of B, A and F stars. II. Photometry of new Delta Scuti stars. 4. Breger Michel, 1969, ApJS, 19, 79: Short-Period Variability of B, A, and F Stars. III. a Survey of Delta Scuti Variable Stars 5. Breger Michel, 1969, ApJS, 19, 99: Short-Period Variability of B, A, and F Stars. IV. Variability in the Lower Hertzsprung Gap 6. Breger M., 1969, ApL, 3, 67: Short-Period Variability of B, A and F Stars. V. The Coma Cluster and NGC 752 D. W. Kurtz and W. W. Weiss 15 The bright star δ Scuti was discovered to have radial velocity variations as early as 1900 (Campbell & Wright 1900). In 1935 two papers in PASP noted the character of the variability of δ Scuti (Colacevich 1935, Fath 1935). They were short notes by A. Colacevich and E. A. Fath who noted: “the radial velocity is variable with a period of ... 4hr 38.m 9 ... The short period and small amplitude, together with the light variation ..., show that this star is in all likelihood not a real spectroscopic binary.” The time span from that report – a time when the pulsating nature of δ Scuti was still a mystery – to Mike Breger’s PhD thesis at Berkeley was only 30 years. There had been progress in the study of δ Scuti stars in those 30 years, and they were by 1965 recognized as a class of pulsating variable star, but the real advances in the field date from Mike’s seminal PhD work and the five papers listed above. The state of the art now is still defined by work that has been led by Mike Breger, as can be seen in the selection of just some of the light curves obtained by the Delta Scuti Network (DSN) seen in Fig. 4. One of the problems of such high precision photometric work is that it is now difficult to find truly constant comparison stars! In Mike’s opinion: “Constant stars are awful!” From 1969 to 1972 Mike was a postdoc at the State University of New York at Stony Brook on Long Island where he worked with Steve Strom studying the polarization of pre-main sequence stars. It was at that time that he began his interest in high precision polarimetry, going on, as usual, to develop ways of getting higher precision observations that had been previously possible. He was also thinking about the possibility of pulsation in pre-main sequence stars, but was mentally fixed on T Tauri stars, and they cannot be seen directly because of their thick circumstellar envelopes. Steve said, “Well, why don’t you look at Herbig Ae/Be stars?”, and Mike thought, “Of course. Why not look at A stars? How obvious!” The result was the discovery of the first pre-main sequence δ Scuti stars. The study of pulsation in such stars and the ultimate goal of distinguishing their structural differences from post-main sequence δ Scuti stars is now a field in its own right. It started with these papers from Mike at Stony Brook: 1. Breger Michel, 1972, ApJ, 171, 539: Pre-main sequence stars. I. Light Variability, Shells, and Pulsation in NGC 2264 2. Breger Michel, Dyck H. Melvin, 1972, ApJ, 175, 127: Pre-main sequence stars. II. Stellar Polarization in NGC 2264 and the Nature of Circumstellar Shells 3. Breger Michel, 1974, ApJ, 188, 53: Pre-main-sequence stars. III. Herbig Be/Ae stars and other selected objects Mike had a request from Ed Burke in 1972 to help him figure out the variability of an F star, but it refused to yield its mystery at that time. Thus the γ Dor stars waited many more years to be discovered. You don’t win them all. Mike had been observing at Kitt Peak and made friends with many people there. He got a phone call one night asking him if he knew that his supervisor, Steve Strom, had taken a new position at Kitt Peak. As such job moves often happen, this rumour got back to him before Steve had had the chance to tell him himself. It meant that Mike was back in the job market and there was a good one advertised at the growing Department of Astronomy at the University of Texas at Austin. Both Mike and his good friend Myron Smith applied for the job with Mike advising Texas that Myron is “an excellent spectroscopist” and they should hire him, and Myron advising Texas that Mike is “an excellent photometrist” and they should hire him! In the end Texas created another position and hired them both! (See Fig. 5.) 16 An overview of Michel Breger’s career -5 0 -1 00 -50 0 0 50 65 7.0 66 7 .8 6 6 7.9 66 8 .0 66 8 .9 66 9 .0 67 0 .8 67 0 .9 67 1 .0 6 71 .65 6 73 .8 6 7 3.9 6 74 .0 6 7 4.6 67 4.7 67 5 .7 -1 00 -50 0 -50 50 0 50 6 7 6.7 67 7 .8 67 7 .9 68 6 .8 0 69 2 .8 69 2 .9 6 93 .0 6 9 3.9 6 9 4.0 7 00 .0 7 0 3.8 70 6.7 7 06 .8 7 06 .9 -50 -1 00 -50 0 50 0 50 7 09 .7 70 9 .8 70 9.9 7 10 .0 7 10 .7 71 0 .8 71 0.9 7 11 .0 71 1.7 7 11 .8 7 11 .9 7 12 .7 7 13 .7 7 13 .8 7 14 .5 -1 00 -5 0 -50 0 0 50 50 7 19 .8 71 9 .9 72 0 .0 7 20 .1 7 20 .9 72 1 .0 72 1.1 7 21 .2 72 1 .7 7 2 1.8 7 21 .9 72 2 .7 7 2 2.8 7 2 2.9 72 3 .0 -50 -1 00 -50 0 50 0 50 7 23 .1 7 23 .2 72 3 .8 72 3.9 7 24 .7 72 4 .8 72 4.9 7 25 .8 7 25 .9 7 2 6.8 7 26 .9 7 27 .7 7 27 .8 72 7.9 -1 00 -5 0 0 -50 0 50 50 7 29 .7 7 2 9.8 7 2 9.9 7 30 .0 7 30 .7 7 30 .8 73 0 .9 7 3 3.7 7 3 3.8 7 33 .9 7 34 .7 7 34 .8 73 4.9 -1 00 -5 0 -50 0 50 0 50 73 5.6 7 35 .7 73 5 .8 7 35 .9 73 6.0 73 6 .6 7 3 6.7 7 36 .8 7 3 6.9 73 7 .0 73 7 .7 73 7 .8 7 37 .9 73 8 .7 7 38 .8 -50 -100 0 -50 50 6y [mmag] 0 50 740.7 740.8 740.9 744.0 744.1 744.2 744.3 744.4 744.5 745.3 745.9 746.0 746.1 747.1 747.2 -50 -100 0 -50 50 0 50 747.7 747.8 747.9 748.0 748.1 748.3 748.4 748.7 748.8 748.9 749.0 749.3 749.4 749.5 -50 -100 0 -50 50 0 50 749.7 749.8 749.9 750.0 750.1 750.2 750.3 750.4 750.7 750.8 750.9 751.0 751.1 751.4 -50 -100 0 -50 50 0 50 751.9 752.0 752.9 753.0 753.2 753.3 753.4 753.5 753.6 753.7 753.8 753.9 754.3 754.4 754.5 -50 -100 0 -50 50 0 50 754.7 754.8 754.9 755.3 755.0 755.4 755.7 755.8 756.3 756.4 757.7 757.8 -100 -50 -50 0 0 50 50 758.7 758.8 759.0 759.1 759.7 759.8 759.9 760.0 760.4 760.5 760.7 760.8 760.9 761.0 761.1 -100 -50 -50 0 0 50 761.1 -100 50 761.7 761.8 761.9 762.0 762.4 762.5 762.6 762.7 762.8 762.9 763.0 763.1 763.4 763.5 -50 -50 0 50 0 50 764.7 764.8 765.7 765.8 766.8 768.05 768.7 768.8 769.4 769.5 769.9 770.4 771.1 775.7 775.8 -100 -50 0 -50 50 0 50 6v [mmag] 50 776.7 776.8 777.8 778.7 778.8 779.7 779.8 781.7 781.8 784.7 HJD 245 2000+ APT ^ SAAO OSN 784.8 785.7 785.8 785.9 786.0 SSO Figure 4: Light curves of the δ Scuti star FG Vir from which over 75 pulsation frequencies were found. From Breger et al. (2005). D. W. Kurtz and W. W. Weiss 17 Figure 5: Mike Breger and Myron Smith in 1972 at the time they went to Texas. For the occasion of this conference in honour of Mike’s 65th birthday, Myron sent the following letter: Dear Mike – The picture of you from 1974 [Fig. 6] captures your outgoing friendliness then as now. Recall what a unique history you and I have had – lay aside astronomy for a moment. We met while we were students folk-dancing. You had come to Tucson to observe at Kitt Peak. In the years that followed in Austin, we folk-danced for several years in the same groups (plural!), and this became so much of our social lives. When you would go off on conferences or trips, you would come to my apartment and I would go through the steps that you had missed! Later, in 1975, you were the best man at my wedding. In the Texas astronomy department, we became the mirrored images of instruction for photometry and spectroscopy. I think one of our better accomplishments was the summer hands-on course for grad students for observing techniques at McDonald Observatory. Look at the students that went through the system to later become a who’s who of observational stellar astronomy, going on such diverse careers as being responsible for spectroscopic instrumentation at the Keck, to leaders in asteroseismology, to the exchange of astronomical FITS files and “serialization” for the Virtual Observatory. I do an injustice to leave out so many others! Those days were not always carefree 18 An overview of Michel Breger’s career Figure 6: Mike Breger in 1974. – remember the discussions of those other folk (theoreticians, women) and of drama over tenure. I remember that win or lose, you were always there with a helping hand to me and with your adage: “things are never as good or as bad as they seem.” How true that was for the unfolding events to follow those, sometimes of insignificance and other times of lasting importance. What is clear to me from the States is that your decision to leave Texas for Vienna had lasting and wonderful consequences, and your present conference is just a part of it. As ever, all best wishes – Myron You may have gathered from Myron’s story that Mike is an accomplished dancer, and even was for many years a dance instructor. This second professional career continued when Mike moved to Austria in 1984 and he acted for many years as a Lecturer for International Folk Dancing at the University of Vienna Sports Institute! So why did he decide to give up a very promising job at one of the most prominent observatories in the US? Again, strange variable stars with controversial properties played a role. In particular, it was the chemically peculiar star 21 Com for which he had reported in a publication in 1969 light variations with periods of about 40 min. A group at the Institute for Astronomy of the University of Vienna was working at this time on CP stars and I (WWW) applied in 1979 for telescope time at McDonald Observatory to obtain high time resolution Hα and Hβ line profiles with the Coude spectrograph. It came naturally that the visitor from Vienna met Michel Breger in Austin and we quickly discovered many scientific interests in common. It did not need much effort to convince Mike to spend his sabbatical in Austria, thus he spent the spring of 1979 in Vienna. Obviously, the climate at the institute – young staff members, each of them expert in his field, all collaborating and interested in science – D. W. Kurtz and W. W. Weiss 19 and nice groups of folk dancers made Mike “home-sick”, because he returned in 1982 for half a year to Vienna. At that time he was mainly interested in polarimetry and Quasars, but still had an eye on his beloved δ Scuti stars. Period determination was a tricky problem and Mike developed a Fortran code, running at our Digital Equipment VAX computer and which he called PERDET . He published a description of this software package in Volume 82/2 of the Vienna Internal Reports and a full chapter was devoted to “a possible scheme to find three periods”. Nowadays this does not appear as a big achievement, but in the 1970s it certainly was. At that time the trend was also towards analysing many stars and use statistical means to understand the group properties. Mike’s intentions were the opposite: investigate few, but well-selected samples of stars with all available tools and try to understand individual targets in detail. 4 CVn and FG Vir are perfect examples for which he collected data during several decades! PERDET was very successfully used by Mike and his international collaborators so that he decided to add new features and in particular a user friendly graphical interface what developed to PERIOD with its various improvements and versions. PERIOD is a Windowsbased highly efficient tool for analysing complex light curves and is heavily used world wide in the pulsating star community. Identifying more than 80 frequencies in the δ Scuti star FG Vir would be impossible without this tool! Unfortunately, “period” is not an adequate keyword for determining the number of references to this software tool via ADS (432736 articles were selected and retrieved), but a crude personal guess would be that several 100 papers have used PERIOD, not mentioning unpublished research and work in student labs. Meanwhile, Mike moved in 1982 as full professor to Vienna and succeeded Prof. Joseph Meurers, the former Director of the Observatory which became the Department of Astronomy of the University of Vienna after merging with the Institute for Theoretical Astronomy. From 1984 to 1986 and 1994 to 2005 he acted as chairman of the department, from 2000 to 2004 as Associated Dean and Dean of Studies and since 2004 as Associated Dean of the Faculty of Geological Sciences, Geography and Astronomy of the University of Vienna. Mike became involved in administrative University business in a critical time. About every 8 years politicians felt (and they still do!) the need to re-organize our University. In hindsight the effect is that inefficient people become marginalized (but they do not disappear and hence still slow down the system) and strong personalities try to take over. This process involves lots of time-consuming activities that are generally unrelated to science. It is to Mike’s credit to have governed the institute through turbulent waters without serious loss. On the contrary, he was able to recover staff positions which were already lost earlier and to secure a strong and independent position of the institute. What is truly remarkable is the fact that Mike succeeded as an administrator without giving up producing top level science! New and powerful methods for data analyses soon brought to light problems of inadequate observations. Consequently, Mike created a global network of observatories such that program stars could be monitored continuously for 24 hours and for many days or weeks in a row. The first Delta Scuti Network (DSN) campaign in 1982 was devoted to θ 2 Tau and since then, 29 (!) DSN campaigns have been organized by him (Table 1). That truly is a success story. These long stretches of high quality data allowed Mike to study for the first time on secure grounds amplitude variations (e.g., 4 CVn), period changes of δ Scuti stars as indicators of stellar evolution (which they turned out not to be), and strange cyclic effects in the pulsation properties which indicate the presence of closely spaced frequencies (Delta Scuti Network campaigns needed!). The richness of observed pulsation frequency spectra also indicated early in Mike’s career as δ Scuti star-guru that non-radial pulsation (NRP) plays a significant role. Actually, in part thanks to his involvement, Europe became the leader in investigating NRP. A consequence was the need for reliable mode identifications which still is not an easy task and Mike successfully applied photometric and spectroscopic tools to solve controversies. Bringing together many δ Scuti star researchers who are distributed all over the continents required an efficient medium for communication. Mike realized this need and he founded in 20 An overview of Michel Breger’s career Figure 7: Mike enjoying the Vienna Workshop on the Future of Asteroseismology 1989 the Delta Scuti Star Newsletter. Obviously he had filled a much-felt gap, because this Newsletter quickly became very popular in the pulsating-star community. Mike was so successful that he decided to do the next step and to found Communications in Asteroseismology which is published by the Austrian Academy of Sciences as a refereed journal and which is meanwhile also referenced by SIMBAD and ADS. You are holding the most recent volume in your hands! Parallel to all his scientific work on pulsating stars in the classical instability strip he acted from 1985 to 1988 as vice president and from 1988 to 1991 as president of IAU Commission 27, Variable Stars, was elected in 1996 as corresponding member of the Austrian Academy of Sciences and served since 1997 as member of the board of directors for the journal Astronomy & Astrophysics and since 2000 as member of the governing board of the Space Research Institute of the Austrian Academy of Sciences. Circling our Sun 65 times, most of it devoted to Astronomy and with outstanding results in science as well as in academic administration surely is a strong reason for a celebration. That is why the Vienna Workshop on the Future of Asteroseismology was initiated in his honour. It obviously did not only please the participants who arrived from all over the world, but also our guest of honour: Michel Breger. 21 D. W. Kurtz and W. W. Weiss Table 1: Delta Scuti Network campaigns until 2005 DSN 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 target θ 2 Tau 4 CVn θ 2 Tau HR 729 BU Cnc & EP Cnc 63 Her HN CMa CD-24 7599 FG Vir IC 418 CD-24 7599 θ 2 Tau IC 418 FG Vir 4 CVn DSN 1983 1984 1986 1988 1989 1990 1990 1992 1993 1993 1994 1994 1994 1995 1996 16 17 18 19 20 21 22 23 24 25 26 27 28 29 target 4 CVn CD-24 7599 BI CMi BI CMi 44 Tau 44 Tau FG Vir FG Vir 44 Tau FG Vir 44 Tau HD 210111 & AS Eri UV Oct & SS For 44 Tau 1997 1998 1998 1999 2000 2001 2002 2003 2003 2004 2004 2005 2005 2005 Acknowledgments. Our sincere thanks go to: Eva Breger, for smuggling the family photo collection from home to a conspirative meeting; Myron Smith, for digging in his and his sister’s private photo archive, and Victoria Antoci, for improving ancient photos. References Breger M., Lenz P., Antoci V., et al., 2005, A&A, 435, 955 Colacevich A., 1935, PASP, 47, 231 Fath E. A., 1935, PASP, 47, 232 Campbell W. W., Wright W. H., 1900, ApJ, 12, 254 22 An overview of Michel Breger’s career Figure 8: A school class picture from 1949 when Mike was 8 years old. Can you find him? He is the boy with the “professorial” look third from the left in the back row. Delta Scuti and roAp stars 24 An overview of Michel Breger’s career Douglas Gough and Don Kurtz in friendly discussion at the conference dinner. Patrick Lenz and Alosha Pamyatnykh thinking about the next models to compute. Comm. in Asteroseismology Vol. 150, 2007 Delta Scuti stars: Observational aspects M. Breger Institute of Astronomy, University of Vienna, 1180 Vienna, Austria Abstract The review concentrates on several important aspects of observational studies of δ Scuti stars. After a discussion of promising astrophysical questions we examine • the extreme amplitude variability of the evolved star 4 CVn • the role of rotation in determining the amplitudes of radial and nonradial modes • the lack of constancy at the millimag level of the comparison stars: we propose that up to four photometric comparison stars are used • the very high accuracy to which frequency values can be determined • the problem with the sufficient frequency resolution required for the detection of close frequencies. δ Scuti stars as astrophysical tools The δ Scuti variables are stars of spectral type A and F in the main-sequence or immediate post-main-sequence stage of evolution. They are situated in the classical instability strip with the instability caused mainly by the Heii ionization zone. In general, the period range is limited to between 0.02 d and 0.25 d. Longer periods (gravity modes) may also be present. The stars generally pulsate with a large number of simultaneously excited radial and nonradial modes. This makes them well-suited for asteroseismological studies. The photometric amplitudes of the dominant modes in the typical δ Scuti star are only a few millimag. It is now possible to detect a large number of simultaneously excited modes with sub-millimag amplitudes in stars other than the Sun using ground-based telescopes as well as satellites. An extensive review of δ Scuti stars is available (Breger 2000) and here we concentrate on a few topics of interest. At present, the best observed star is FG Vir, for which more than 2000 hours of highprecision photometry have revealed 75+ frequencies of pulsation (Breger et al. 2005). As in most well-studied δ Scuti stars, the excited modes are both radial and nonradial. The combination of spectroscopic and photometric techniques as well as pulsation modelling has made it possible to identify the nature of the major pulsation modes (Daszyńska-Daszkiewicz et al. 2005). Probably the main aspect of the present asteroseismological research on the δ Scuti stars is concerned with concentrating on the observed pulsation frequencies of a few chosen pulsators in order to improve the models of stellar structure, evolution, convection and pulsation to agree with more and more detailed observations. Modes ranging from = 0 to very high values (12+) are excited in these stars, but the mode selection mechanism is not clear. The observational problem is the following: since the number of detected modes increases dramatically as the observational threshold decreases (see FG Vir or some of the MOST results), what causes a star to select some low-degree modes to have photometric amplitudes of several hundredths of a magnitude instead of a 0.0001 mag or less? How can we determine that a particular mode is not excited, rather than present with an undetectable amplitude? For mode selection, stellar rotation (see below) is important, but can only be one of many factors. δ Scuti pulsation also occurs among pre-main-sequence stars, e.g., eight pre-main-sequence stars were found in the clusters IC 4996 and NGC 6530 (Zwintz & Weiss 2006). The internal 26 Delta Scuti stars: Observational aspects structure of pre-main-sequence stars differs substantially from that of post-main-sequence stars of similar luminosity and temperature. The difference should show up in the nonradial pulsation spectrum, especially when modes of different values are compared with each other. The important detection of the differences requires very detailed pulsation studies of selected pre-main-sequence stars. Another interesting application of asteroseismology concerns the chemically peculiar stars inside the instability strip. An example is provided by the λ Boo stars, which show surface underabundances of most Fe-peak elements and solar abundances of the lighter elements (C, N, O, and S). Different theories to explain the spectra of these stars include accretion of interstellar matter, diffusion, mass loss or composite spectra of spectroscopic double stars. These effects should lead to different pulsation spectra. Paunzen et al. (2002) have reported that the average pulsation of λ Bootis stars differs from that of the average δ Scuti star in two ways: incidence and radial order of the pulsation modes. A more extensive study of the λ Boo star, HD 210111, by Breger et al. (2006) revealed no unusual pulsational behaviour. Probably both studies were not extensive enough to answer the question of possible differences between ’normal’ and λ Boo-type δ Scuti stars. A number of δ Scuti pulsators are also found in semi-detached Algol systems. This raises the question whether their pulsation is different. Some of these stars have unusually short pulsation periods, e.g., the 22-minute period of RZ Cas (Rodrı́guez et al. 2004). In fact, RZ Cas also shows a λ Boo-type abundance pattern (Narusawa et al. 2006). Additional studies of these close systems are very promising. Amplitude variability A presently unsolved problem concerns the origin of the amplitude and phase variability found in δ Scuti (as well as other) pulsators. This is demonstrated for an extreme case, 4 CVn, in Fig. 1. It turns out that the small-amplitude δ Scuti stars are an ideal group to search for the cause of the variability, since (unlike RR Lyrae stars and Cepheids) their light curves are sinusoidal and the nonlinear effects are considerably reduced. For the stars BI CMi and FG Vir, it could be shown that the amplitude and phase variability is caused by beating between two modes of almost identical frequencies (Breger & Pamyatnykh 2006). Radial and nonradial modes: the role of rotation At the present time the size of the amplitudes of δ Scuti stars cannot be predicted accurately from theory. However, from observations we can show that the most important parameter determining the size of the amplitudes is stellar rotation. This is demonstrated in Fig. 2. The picture, however, is more complex than appears at first sight, since the stars are multifrequency pulsators. Not surprisingly, the first δ Scuti stars to be discovered were the variables with large amplitudes of AV ≥ 0.3 mag. These stars are now known as high-amplitude δ Scuti stars (HADS) and were in earlier times also called Dwarf Cepheids. It was only during systematic, high-precision variability surveys that it was discovered that the HADS were not typical for the stars in the Lower Instability Strip, but that most of the stars near the main sequence have small, almost undetectable amplitudes. HADS generally rotate slowly with v sin i ≤ 30 km/s. This is in contrast to an average rotation ∼150 km/s in this part of the Hertzsprung-Russell Diagram. The assumption that the large-amplitude modes of the HADS are radial modes was confirmed by the period ratios between the radial fundamental and first overtone modes of the double-mode HADS. However, recent analyses have revealed that low-amplitude nonradial modes may also be present (e.g., V974 Oph, Poretti 2003), but not in all HADS (e.g., GSC 00144-03031, Poretti et al. 2005). 27 Michel Breger 4 CVn: 1966 - 1970 Power in parts per million 500 0 4 CVn: 1974 500 0 4 CVn: 1996 500 0 60 80 100 120 140 Frequency (+Hz) Figure 1: The power spectrum of 4 CVn in three different time periods. Arrows denote the intrinsic frequencies. The diagram shows that due to amplitude variations the same star may look like different stars in different years. The pulsation spectrum of the 2005 data (not shown here) indicates that all the peaks are still present, and no modes have disappeared but have different amplitudes. The typical δ Scuti variable does not rotate slowly, has very low amplitudes and pulsates with mainly nonradial modes. If radial modes are detectable at all, they have very low amplitudes. An excellent example is the star FG Vir, where the radial fundamental mode at 12.15 c/d has a much smaller amplitude than the dominant =1 mode at 12.72 c/d. The following hypothesis summarizes the present situation: (i) Radial as well as nonradial pulsation can occur in all δ Scuti stars, irrespective of whether the star rotates quickly or slowly. (ii) The radial modes are strongly affected by stellar rotation. They reach large amplitudes up to a magnitude only if the star rotates slowly. These stars are known as HADS and resemble the classical variables in the instability strip such as Cepheids and RR Lyrae stars. (iii) Stars rotating faster than ∼30 km/s have low amplitudes of pulsation and pulsate with a multitude of mostly nonradial modes. If radial modes can be detected photometrically at all, they have low amplitudes. An example is the star FG Vir, where the radial mode at 12.15 c/d has an amplitude of 0.004 mag in V , while the dominant = 1 mode at 12.72 c/d reaches 0.022 mag. (iv) There exists a region with stars in which both = 0 (radial) and = 1 (nonradial) modes may reach amplitudes in excess of 0.05 mag (peak-to-peak). Examples are stars such as 1 Mon and 44 Tau (projected rotational velocities of 14 and 2 km s−1 , respectively), which are both studied by the Delta Scuti Network at the present time. 28 Delta Scuti stars: Observational aspects 1.0 0.9 V Amplitude in mag 0.8 0.7 HADS (high-amplitude Delta Scuti stars) 0.6 0.5 0.4 0.3 Intermediate region includes 44 Tau and 1 Mon 0.2 Low-amplitude Delta Scuti stars 0.1 0.0 0 50 100 150 200 250 300 Rotational velocity, v sin i, in km/s Figure 2: Relationship between the measured projected rotational velocity, v sin i, and amplitude of pulsation. The diagram shows that large amplitudes (mostly radial modes) require slow rotation. However, nonradial modes with small amplitudes are detected in δ Scuti stars of all rotational velocities. An observational necessity: comparison stars In order to study variability on the millimag level of photometric accuracy, it is necessary to also observe comparison stars. This holds for ground-based photomultiplier and CCD photometry, and also for satellite measurements. Because of observational limitations, the choice of comparison stars is limited. Recent extensive photometric campaigns by the Delta Scuti Network have corroborated the suspicion that constant comparison stars are very rare, especially at the millimag level. This can be demonstrated by the results for the δ Scuti star 44 Tau. Two of the four carefully chosen comparison stars of spectral type F were detected to be variable with long periods (see Fig. 3). This demonstrates that great care needs to be taken in choosing constant comparison stars. The popular techniques of avoiding A stars (since they probably also are δ Scuti variables) and choosing F stars is a good one. Nevertheless, most of the F stars studied by us show low-frequency peaks and may be γ Dor variables, whose instability strip extends to somewhat lower temperatures than previously known. We advise that campaigns should choose more than two comparison stars. Frequency precision vs. frequency resolution The knowledge to what precision a frequency can be determined is important. It is required to interpret measured period changes, possibly of evolutionary nature. Also, many amplitude variations are actually caused by the beating of close frequencies: consequently, knowledge of the frequency resolution is required. Michel Breger 29 Figure 3: The problem with small-amplitude variability of comparison stars is demonstrated by examining four (!) comparison stars used for the study of 44 Tau. The panels show the power spectra of the difference between two comparison stars in the 0.8 to 1.0 c/d frequency region. The top two left panels indicate that the 0.936 c/d peak is present in both (C1-C3) and (C1-C4), but absent in (C3-C4). This shows that the peak originates in C1. Similarly, the 0.885 c/d peak originates in C2. Stars C3 and C4 appear to be constant most of the time. The frequency precision is sometimes estimated to be 1/ΔT, where ΔT is the length of observation. This is incorrect: under many conditions the precision is much higher. If we fit a sine curve p to the data, then the uncertainty can be computed in the standard manner, viz., σ(f) = 6/N σ(m)/(ΠaΔT), where m is the brightness in mag, a is the amplitude, N is the number of observations. There are some hidden assumptions here that there is only white noise, essentially no aliasing, multiple frequencies do not affect each other, and that there exists little or no amplitude variation. These assumptions are not always met. The calculation of the frequency precision can be improved by Monte Carlo simulations to the data, e.g., as performed in our statistical package PERIOD04 (Lenz & Breger 2005). Let us apply the Monte Carlo simulations to the 80 frequencies of FG Vir and the 1992 – 2004 data (Breger et al. 2005). We note that 80 frequencies take up 241 degrees of freedom (80 frequencies, 80 amplitudes, 80 phases and 1 zero-point). This presents no problem, since there are more than 10 000 independent data points in the sample. For the dominant frequency of FG Vir at 12.72 c/d, the Monte Carlo simulations result in σ(f) = 1.678 x 10−7 c/d, (or 1.9 pHz, or one part in 10−8 ). This value is only slightly higher than that given by the standard formula, but a factor of a thousand better than given by 1/ΔT. The conditions to obtain this precision were listed above. If the star has close frequency doublets, the conditions are not met and the precision is lowered significantly due to the ’interaction’ between the two frequencies. Now the frequency resolution becomes important. It is also not quite correct to state that the frequency resolution is given by 1/ΔT. In fact, Loumos & Deeming (1978) showed that the frequency resolution is only 1.5/ΔT! For a twomonth observing run, the detectable frequency separation would be larger than 0.025 c/d. A typical ground-based observing campaign by the Delta Scuti Network covers several years or decades: for a three-season campaign with ΔT ∼ 30 months, the frequency resolution by the Loumos & Deeming criterion would be would be 0.0017 c/d or 19 nHz. The situation may, in fact, be better than this, since the quality of the measurements during the time ΔT as well as the amplitudes of two close frequencies need to be considered. After all, if the measurements were continuous and error-free (infinite signal/noise ratio), two 30 Delta Scuti stars: Observational aspects independent frequencies of any separation could hypothetically be determined. Consequently, the question of what is meant by frequency resolution becomes important. Numerical simulations with realistic data are required to determine the probability of a correct discovery and determination of the frequency doublet. In particular, effects such as aliasing, non-white noise and the presence of additional frequencies need to be considered. Our experience with proving that close frequency pairs in FG Vir exist (Breger & Pamyatnykh 2006) advises caution: we only solved the problem by obtaining a coverage much longer than required by statistical predictions. Conclusions In the paper we have highlighted several aspects of δ Scuti star research with considerable asteroseismological potential. We also examined several observational problems which may not be generally known. The difficulties can be overcome in the planning stages of future observational campaigns. Acknowledgments. This investigation has been supported by the Austrian Fonds zur Förderung der Wissenschaft. We are grateful to P. Reegen for assistance with the APT measurements of 44 Tau and its four comparison stars and W. Weiss as well as T. Kallinger for interesting discussions. References Breger M., 2000, in Breger M., Montgomery M. H., eds, ASP Conf. Ser. Vol. 210, Delta Scuti and Related Stars. Astron. Soc. Pac., San Francisco, p. 3 Breger M., Pamyatnykh A. A., 2006, MNRAS, 368, 571 Breger M., Lenz P., Antoci V., et al., 2005, A&A, 435, 955 Breger M., Beck P., Lenz P., et al., 2006, A&A, 455, 673 Daszyńska-Daszkiewicz J., Dziembowski W. A., Pamyatnykh A. A., et al., 2005, A&A, 438, 653 Lenz P., Breger M., 2005, Comm. Asteroseis., 146, 53 Loumos G. L., Deeming T. J., 1978, Ap&SS, 56, 285 Narusawa S. Y., Ozaki S., Kambe E., Sadakane K., 2006, PASJ, 58, 617 Paunzen E., Handler G., Weiss W. W., et al., 2002, A&A, 392, 515 Poretti E., 2003, A&A, 409, 1031 Poretti E., Suárez J. C., Niarchos P. G., et al., 2005, A&A, 440, 1097 Rodrı́guez E., Garcı́a J. M., Mkrtichian D. E., et al., 2004, MNRAS, 347, 1317 Zwintz K., Weiss W. W., 2006, A&A, 457, 237 Michel Breger 31 DISCUSSION Dziembowski: The correlation between the rotational velocities and amplitudes of the δ Scuti stars has a common cause. The large-amplitude stars are all evolved objects and they rotate more slowly. But there may be another connection, namely that the amplitudes have to do with resonances. Rotation gives you more options for radial modes to undergo resonances and therefore you can estimate that there is a significant influence of rotation. Breger: I think your point about the evolutionary status is a very good one. I have repeated this diagram for stars near the ZAMS and for evolved stars. One expects that main sequence stars have smaller amplitudes and evolved stars larger ones. But ”fortunately” the correlation still exists, even if you only plot evolved objects. Kepler: Are the amplitude variations you see due to close frequencies or are they intrinsic amplitude modulations? Breger: Whereever there exist enough data to distinguish between the two explanations, for δ Scuti stars the amplitude variations are caused by the beating of close frequencies. Michel Breger and Chris Sterken taking a deserved break. Comm. in Asteroseismology Vol. 150, 2007 Approaching asteroseismology of δ Scuti stars: problems and prospects Jadwiga Daszyńska-Daszkiewicz Instytut Astronomiczny, Uniwersytet Wroclawski, ul. Kopernika 11, Poland Abstract The main obstacle in exploiting the frequency data of δ Sct stars is the difficulty in mode identification. The δ Sct oscillation spectra, unlike those of the Sun or white dwarfs, do not exhibit very regular patterns. Thus, the mode identification must rely on sophisticated methods, which involve combined multi-passband photometry and radial velocity data, with an unavoidable theoretical input from stellar atmosphere models. Moreover, there are serious uncertainties in theory of δ Sct stars that have to be solved. Mode identification and determination of global and internal structure parameters for δ Sct stars has to be done simultaneously. I describe in some detail the methodology and present some recent results we obtained concerning degrees of excited modes, global stellar parameters, and constraints on models of subphotospheric convection, as well as effect of rotational mode coupling. Introduction δ Scuti stars are one of the most intensively studied group of pulsating variables. In the HR diagram, they are located at the intersection of the classical instability strip with the main sequence, and somewhat above it. It was recognized many years ago that the pulsations of these objects, as other classical variables, are driven by the κ-mechanism acting in the Heii ionization zone. Excited are low-order p- and g-modes with periods ranging from 0.02 d to 0.3 d. Over the last 20 years, many multisite observations of these stars were carried out by networks like DSN and WET. These campaigns have resulted in a growing number of detected oscillation frequencies. On the basis of these data several attempts were made towards construction of asteroseismic models of certain multimodal pulsators. One of such objects was XX Pyx, for which Pamyatnykh et al. (1998) tried to construct a seismic model without an identification from photometry or spectroscopy. Another example, θ 2 Tau, is a binary system consisting of an evolved (primary) and a main sequence A-type (secondary) star (Breger et al. 2002), both inside the instability strip. The most multimodal and most promising object for asteroseismology of δ Sct stars is FG Vir. This star was studied by Guzik & Bradley (1995), Viskum et al. (1998), Breger et al. (1999) and Templeton et al. (2001). Recent large photometric and spectroscopic campaigns, organized in the years 2002-2004 by Breger et al. (2005) and Zima et al. (2006), increased the number of known independent oscillation frequencies of FG Vir to 67. In spite of all these efforts we still do not have a good seismic model for any δ Sct star. So far, not much has been learnt from these rich oscillation spectra. There are still problems with the identification of excited modes as well as large uncertainties in modelling δ Sct pulsation to exploit the frequency data for constraining stellar models. The most important aspects are: turbulent convection-pulsation interaction, effects of rotation, mechanism of mode selection, diffusion. In this paper, I outline the method which gives simultaneously mode identification and constraints on stellar parameters and convection. I discuss also effects of uncertainties arising from the atmospheric models and, briefly, effects of rotational mode coupling on mode identification. Jadwiga Daszyńska-Daszkiewicz 33 Mode identification In the case of main sequence pulsators, the most widely used tools for mode identification are pulsation amplitudes and phases derived from observed variations in photometric passbands and in radial velocity. If effects of rotation can be neglected, the amplitude ratio vs. phase difference diagrams can lead to the degree determination, and they are independent of the azimuthal order m and the inclination angle. As was shown by Daszyńska-Daszkiewicz, Dziembowski & Pamyatnykh (2003) (Paper I), in the case of δ Sct variables the photometric amplitudes and phases are very sensitive to the treatment of convection in the outer layers. This is because in calculating these observables one has to make use of the complex parameter f, giving the ratio of the local flux variation to the radial displacement at the photosphere. The f parameter is obtained in the framework of linear nonadiabatic theory of stellar oscillation and, in the case of δ Sct stars, exhibits strong dependence on convection, as was already emphasized by Balona & Evers (1999). To avoid this problem, in Paper I we invented a method of simultaneous determination of the degree and f parameter from multi-colour photometry and radial velocity data. The procedure consists of solving the set of observational equations for complex photometric amplitudes in a number of passbands, λ, Dλ (ε̃f ) + Eλ ε̃ = Aλ , (1) where ε̃ = εYm (i , 0), 1 λ ∂ log(Fλ |bλ |) b 4 ∂ log Teff # " « „ 2 3 ∂ log(Fλ |bλ |) ω R = bλ (2 + )(1 − ) − +2 . GM ∂ log g Dλ = Eλ Derivatives of the monochromatic flux, Fλ (Teff , log g ), are calculated from static atmosphere models (Kurucz: Kurucz 2004, NEMO2003: Nendwich et al. 2004, Phoenix: Hauschildt et al. 1997). In general, they depend also on the metallicity parameter [m/H] and microturbulence velocity ξt . If the spectroscopic data exist, the above set of equations can be supplemented with the expression for the radial velocity (the first moment of line profile, Mλ 1 ), « „ GM (2) iωR uλ + 3 2 vλ ε̃ = Mλ 1. R ω In the above expressions, ε is the intrinsic mode amplitude, i is the inclination angle and bλ , uλ , vλ are disc-averaging factors weighted by limb-darkening hλ (Teff , log g ). For the limb-darkening law we use the Claret nonlinear formula. Each passband, λ, yields the righthand side. of Eq. (1). The radial velocity data yield the right-hand side of Eq. (2). Then, the system is solved by the least square method assuming trial values of . The identification is based on χ2 ( ) minimization and the quantities to be determined are: ε̃ and (ε̃f ). In Paper I we applied our method to three δ Sct stars: β Cas, 20 CVn and AB Cas, for their dominant frequencies. To this end we used amplitudes and phases in four Strömgren passbands. In all cases the identification of was unique. As an example, in Fig. 1 we plot the χ2 ( ) dependence for one frequency observed in β Cas. In the two panels, the effect of using atmospheric models from different sources is shown. In the left panel, χ2 ( ) was obtained adopting the Kurucz models, whereas in the right one, adopting the Vienna models (NEMO2003). The method works also in the case of multiperiodic pulsators. In Daszyńska-Daszkiewicz et al. (2005) (Paper II) we applied the method to the most multiperiodic δ Sct star FG Vir. Combining the Strömgren vy photometry and radial velocity data for twelve modes, we arrived at a unique identification of in six cases, and we obtained the constraint ≤ 2 in the other six. 34 Approaching asteroseismology of δ Scuti stars: problems and prospects Figure 1: Values of χ2 as a function of for the 9.897 d−1 frequency excited in β Cas, for M = 1.95M and three effective temperatures. In the left panel, χ2 was calculated with the Kurucz models and in the right panel with the NEMO2003 models. The most important property of our method is that the identification of the spherical harmonic degree, , is independent of any input from nonadiabatic pulsation calculations. Moreover, the method uses simultaneously photometry and spectroscopy by combining these data into the system of observational equations. For more details we refer the readers to Papers I and II. Constraints on convection The method outlined above constitutes also a way of inferring f from observations. The value of f, describing the bolometric flux perturbation, is determined in the pulsation driving zone, where the thermal time scale is comparable with the pulsation period. It means that this parameter is sensitive to properties of subphotospheric layers which are poorly probed by the oscillation modes. In general, the f parameter depends on: mean stellar parameters, chemical composition, stellar convection and opacities. Thus, the strong sensitivity of the f parameter on convection in the case of δ Sct pulsators may be considered as an advantage. Once we know the empirical f values, we can compare them with their theoretical counterparts, and obtain valuable constraints on convection in subphotospheric layers. In Paper I, we succeeded in extracting the f parameter from photometric observations for all studied δ Sct stars: β Cas, 20 CVn and AB Cas. We adopted Kurucz models of stellar atmospheres. The pulsation calculations were made assuming a simplistic approach: the mixing-length theory and the convective flux freezing approximation. In the comparison of empirical f values with the theoretical ones calculated with various values of the MLT parameter α, we met a problem in reproducing both the real and imaginary part of f with the same value of α. The general result was that the observed values of fR were close to those calculated with α = 0, whereas the fI preferred higher values of α. The disagreement appeared to be mostly correlated with the uncertainties in the atmospheric models, which I discuss in the next section. In Paper II we applied the method of simultaneous extraction of and f from observations for the most multiperiodic δ Sct star FG Vir. We relied on NEMO2003 atmosphere models. 35 Jadwiga Daszyńska-Daszkiewicz Combining vy Strömgren photometry and radial velocity data, we extracted the f parameter for twelve frequencies and compared them with the theoretical values calculated assuming two different treatments of convection. The first one was the standard mixing-length theory and the convective flux freezing approximation, as in Paper I. As the second one, we considered a non-local time-dependent generalization of MLT by Gough (1977). In the first case the agreement was found for models with α ≈ 0.0, which is evidence that convection in the outer layers of FG Vir is relatively inefficient. In the second case, which includes convection dynamics, the agreement was possible also with larger values of α, but smaller ones (α ≤ 0.5) were still favoured as can be seen from Fig. 2 (taken from Paper II). 10 10 _ = 0.25 _ = 0.50 _ = 1.00 _ = 1.50 5 _ = 0.25 _ = 0.50 _ = 1.00 _ = 1.50 5 0 0 fR-5 fI -5 -10 -10 -15 -15 -20 -20 -25 -25 8 10 12 14 16 18 i [c/d] 20 22 24 26 8 10 12 14 16 18 i [c/d] 20 22 24 26 Figure 2: The empirical f values (dots with error bars) and the theoretical ones calculated for four values of the MLT parameter α, adopting a non-local, time-dependent formulation of MLT. The real and imaginary parts of f are shown in the left and the right panels, respectively. Modelling of δ Sct type pulsation with time-dependent convection treatment can be found also in several other papers, e.g. Grigahcène et al. (2005), Dupret et al. (2005a,b). Uncertainties from atmospheric models To calculate pulsation amplitudes and phases of photometric and radial velocity variations, one needs input from atmospheric models. As mentioned in the previous section, these are the monochromatic flux derivatives over effective temperature, αT , and gravity, αg , as well as the limb-darkening law, hλ . In Fig. 3 we can see how non-smooth derivatives αT , calculated from Kurucz models (left panel) can produce artificial minima of χ2 derived from our method for a dominant mode of FG Vir. Derivatives obtained from NEMO2003 models (right panel) are smooth and only one χ2 minimum appears. In this case, we show also the effect of microturbulence velocity, ξt , on the location of the minimum of χ2 (Teff ). The non-smooth flux derivatives affect also the inferred values of f. This is illustrated in Fig. 4 where empirical f values for β Cas obtained using Kurucz and Vienna models are compared with theoretical ones calculated for five values of the MLT parameter, α. We can see that in the case of Vienna models both real and imaginary parts of f are reproduced with the models assuming inefficient convection (α ≈ 0.0) 36 Approaching asteroseismology of δ Scuti stars: problems and prospects Figure 3: χ2 as a function of effective temperature for a dominant mode of FG Vir derived using Kurucz (left) and Vienna (right) models. The dot with the error bar shows log Teff derived from mean colours. The y-axes on the right-hand side contain the temperature flux derivatives, αT , in the Strömgren vy passbands. In the right panel the effect of the microturbulence velocity on the χ2 minima is also shown. 14 12 14 12 _=0.0 _=0.5 10 fI _=0.0 _=0.5 10 fI 8 8 jt=4 km/s 6 6 _=1.0 4 4 2 2 _=1.6 logTeff= 3.856 0 _=1.0 jt=2 km/s -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 _=1.6 logTeff= 3.856 0 _=2.5 logTeff= 3.846 7 _=2.5 logTeff= 3.846 -7 -6 -5 -4 -3 -2 -1 fR 0 1 2 3 4 5 6 7 fR Figure 4: Comparison of the f values inferred from Strömgren photometry for β Cas with the theoretical ones calculated with various MLT parameters α. The empirical f values were obtained adopting Kurucz models (left panel) and Vienna models (right panel). In the right panel the effect of the microturbulence velocity on the empirical f values is also shown. Rotational mode coupling The most important effect of moderate rotation is mode coupling (Soufi, Goupil & Dziembowski 1998). It takes place if the frequency difference between modes j and k is of the order of the angular velocity of rotation, and if the spherical harmonic indices satisfy the relations: j = k + 2 and mj = mk . As eigenfunctions for individual modes, we have to consider superpositions of all modes satisfying the above conditions. Hence, the photometric amplitude of a coupled mode is given by (Daszyńska-Daszkiewicz et al. 2002) Aλ (i ) = X k ak Aλ,k (i ), Jadwiga Daszyńska-Daszkiewicz 37 where the contribution from modes the in the non-rotating star is determined by the coefficients ak which are solutions from perturbation theory. Now, the location of the mode on the diagnostic diagrams depends on the azimuthal order, m, the inclination angle and the rotational velocity. We considered a stellar model with the following parameters M = 1.8M , log Teff = 3.866 and log L/L = 1.12, and the rotational velocity of about 70 km/s, which are appropriate for FG Vir. As an example, we consider the rotational coupling between = 0 and = 2 axisymmetric modes with frequencies 19.342 and 19.597 d−1 , respectively. In Fig. 5 we show the position for coupled modes on the diagram with the Strömgren y passband and the radial velocity. The left panel refers to the solution dominated by the = 0 component, whereas the right one to the solution dominated by = 2. For discussion of other effects of rotation within the perturbative approach see e.g. Pamyatnykh (2003). Figure 5: The positions of rotationally coupled modes (small open circles) in the AVr /Ay vs. ϕVr − ϕy diagram. We considered coupling between a close = 0 and 2 pair at a rotation velocity of about 70 km/s in a stellar model with M = 1.8M and log Teff = 3.866. Filled symbols indicate the positions of pure = 0, 1, 2 modes. Summary I outlined results obtained in Papers I and II, where we proposed and applied the new method of simultaneous determination of the spherical harmonic degree, , and the nonadiabatic parameter f from multi-colour photometry and radial velocity data. We demonstrated that inferring f values from such observations is possible, thus identification of can be done without a priori knowledge of f. Our method combines photometry and spectroscopy, and it gives the identification at the highest confidence level achieved up to now. Moreover, by comparing empirical and theoretical f values, the method yields constraints on mean stellar parameters and on properties of subphotospheric layers. In the case of δ Sct stars, this is the treatment of convective transport. Inferred values of f are consistent with models calculated assuming rather inefficient convection (α ≤ 0.5). The f parameter constitutes a new asteroseismic tool which is complementary to oscillation frequencies. It is obvious that detecting more and more oscillation frequencies is of great importance, especially in the era of asteroseismic satellite missions. However, it seems that asteroseismology of δ Sct stars will be served better if we focus also on those frequencies for which very accurate and simultaneous ground-based data from photometry and spectroscopy can be obtained. 38 Approaching asteroseismology of δ Scuti stars: problems and prospects Acknowledgments. The author thanks Wojtek Dziembowski and Alosha Pamyatnykh for instructive comments and Mikolaj Jerzykiewicz for carefully reading the manuscript. This work was supported by the Polish MNiI grant No. 1 P03D 021 28 and by the HELAS EU Network No. 026138. References Balona L. A., Evers E. A., 1999, MNRAS, 302, 349 Breger M., Pamyatnykh A. A., Pikall H., Garrido R., 1999, A&A, 341, 151 Breger M., Pamyatnykh A. A., Zima W., et al., 2002, MNRAS, 336, 249 Breger M., Lenz P., Antoci V., et al., 2005, A&A, 435, 955 Daszyńska-Daszkiewicz J., Dziembowski W. A., Pamyantykh A. A., Goupil M.-J., 2002, A&A, 392, 151 Daszyńska-Daszkiewicz J., Dziembowski W. A., Pamyatnykh A. A., 2003, A&A, 407, 999 (Paper I) Daszyńska-Daszkiewicz J., Dziembowski W. A., Pamyatnykh A. A., et al., 2005, A&A, 438, 653 (Paper II) Grigahcène A., Dupret M.-A., Gabriel M., Garrido R., Scuflaire R., 2005, A&A, 434, 1055 Dupret M.-A., Grigahcène A., Garrido R., Gabriel M., Scuflaire R., 2005a, A&A, 435, 927 Dupret M.-A., Grigahcène A., Garrido R., et al., 2005b, MNRAS, 361, 476 Gough D. O., 1977, ApJ, 214, 196 Guzik J. A., Bradley P. A., 1995, Baltic Astron., 4, 482 Hauschildt P. H., Baron E., Allard F., 1997, ApJ, 483, 390 Kurucz R. L., 2004, http://kurucz.harvard.edu Nendwich J., Heiter U., Kupka F., Nesvacil N., Weiss W. W., 2004, Comm. Asteroseis., 144, 43 Pamyatnykh A. A., Dziembowski W. A., Handler G., Pikall H., 1998, A&A, 333, 141 Pamyatnykh A. A., 2003, Ap&SS, 284, 97 Soufi F., Goupil M.-J., Dziembowski W. A., 1998, A&A, 334, 911 Templeton M. R., Basu S., Demarque P., 2001, ApJ, 563, 999 Viskum M., Kjeldsen H., Bedding T. R., et al., 1998, A&A, 335, 549 Zima W., Wright D., Bentley J., et al., 2006, A&A, 455, 235 Comm. in Asteroseismology Vol. 150, 2007 Observations of pulsations in roAp stars O. Kochukhov Department of Astronomy and Space Physics, Uppsala University, Box 515, SE-751 20 Uppsala, Sweden Abstract I review recent results of the observations of magnetoacoustic p-mode oscillations in roAp stars with the focus on time-resolved spectroscopic studies. Time-series spectroscopy of roAp stars reveals unexpected and diverse pulsational behaviour in the spectral lines of different chemical elements. These unique pulsational characteristics arise from an interplay between the short vertical length of pulsation waves and extreme chemical stratification in the atmospheres of peculiar stars. This enables a tomographic reconstruction of the depth-dependence of the chemical composition and pulsation wave properties. The combination of magnetoacoustic tomography with Doppler imaging of the horizontal non-radial pulsation pattern opens the possibility for an unprecedented three-dimensional mapping of roAp star atmospheres. Introduction A significant fraction of the upper main sequence stars of spectral classes between B and F possesses a strong, ordered magnetic field and shows a surface chemical composition strongly deviating from that of the Sun. These chemically peculiar Ap/Bp stars are characterized by unusually slow rotation and they show spectacular variability of the field strength, mean brightness and spectra on the rotation time scale. This is understood to be a result of the rotational modulation of the aspect at which the stable stellar magnetic field geometry and surface chemical inhomogeneities are observed. In addition to their remarkable magnetic and chemical surface characteristics, many cooler Ap stars also exhibit high-overtone non-radial acoustic p-mode pulsations. There are more than 30 such rapidly oscillating Ap (roAp) stars known at the present time (Kurtz & Martinez 2000). These objects oscillate with periods in the range of 6 – 21 min, while their light variation amplitudes rarely exceed 10 mmag in Johnson B. Photometric investigations of roAp stars carried out during the last 25 years have yielded unique asteroseismic information on the internal structure and fundamental parameters of roAp pulsators (e.g., Matthews et al. 1999, Cunha et al. 2003). The observed pulsation amplitudes of roAp stars are modulated according to the visible magnetic field structure, pointing to a defining role played by magnetic fields in exciting the oscillations and shaping the main pulsation properties. Observation of the coincidence of the magnetic field and pulsation amplitude extrema gave rise to the oblique pulsator model (OPM, Kurtz 1982), which attributes the main characteristics of roAp pulsations to an oblique = 1, m = 0 mode, aligned with the axis of a quasi-dipolar magnetic field. The OPM gave a rather successful geometrical explanation of the main features in the roAp frequency spectra. However, subsequent detailed studies of roAp pulsations have revealed that the mode geometry in some stars defies a simple interpretation in terms of a single spherical harmonic (e.g., Kurtz et al. 1997). Several theoretical investigations (Bigot & Dziembowski 2002, Saio & Gautschy 2004, Saio 2005) studied the effects of the distortion of oblique pulsation mode geometry by the global magnetic field and stellar rotation. Bigot & Dziembowski (2002) suggested that the rotational distortion of pulsation eigenmodes is represented by a superposition of non-axisymmetric 40 Observations of pulsations in roAp stars spherical harmonic components, and that there is no alignment of the pulsation axis and the dipolar magnetic field. On the other hand, Saio & Gautschy (2004) and Saio (2005) found an axisymmetric pulsation structure aligned with the magnetic field and predicted that the = 1 mode should be distorted by a dipolar magnetic field in such a way that the pulsation amplitude is strongly confined to the magnetic axis. Sophistication of these theoretical models notwithstanding, it became clear that modelling of the photometric light curves of roAp stars is unable to provide useful tests of magnetoacoustic theories. The information content of the time-resolved photometric observations is small due to averaging of the pulsational disturbances over the visible stellar hemisphere and is also highly uncertain because rapid light variation in roAp stars involves non-linear and non-adiabatic effects that are poorly understood (Medupe & Kurtz 1998). The latter problem explains why no consistent physical picture of the photometric variability of roAp has ever been developed. Instead of deducing the structure of the luminosity perturbations from first principles, all attempts to interpret photometric observations of roAp stars have assumed that the luminosity perturbations are proportional to the pulsational displacement. Therefore, constraints on the pulsation mode geometry obtained from the photometry of roAp stars are inherently indirect, which arguably makes any subsequent inferences about the physics of magnetoacoustic oscillations questionable. Spectroscopic studies of roAp pulsations The investigation of pulsational variations in the spectral line profiles of roAp stars observed at high time and spectral resolution provides much more direct and unprecedentedly rich information about the vertical and horizontal structure of p modes and about their relation to the magnetic field topology, chemical inhomogeneities and anomalous atmospheric structure of Ap stars. Recently major progress in the observational study of roAp stars was achieved by employing time-series spectroscopy. Time-resolved observations of magnetic pulsators revealed a surprising diversity, not observed in any other type of pulsating stars, in oscillations of different lines (e.g., Kanaan & Hatzes 1998). Detailed analysis of the bright roAp star γ Equ (Kochukhov & Ryabchikova 2001a) demonstrated that spectroscopic pulsational variability is dominated by the lines of rare-earth ions, especially those of Pr and Nd. On the other hand, light and iron-peak elements do not pulsate with amplitudes above 50–100 m s−1 . This is at least an order of magnitude lower than the ∼ 1 m s−1 variability observed in the lines of rare-earth elements (REE). Many other roAp stars have been found to show a very similar overall pulsational behaviour (Kochukhov & Ryabchikova 2001b, Balona 2002, Mkrtichian et al. 2003, Ryabchikova et al. 2007a). Magnetoacoustic tomography The peculiar characteristics of p-mode pulsation in roAp stars were clarified by Ryabchikova et al. (2002), who were the first to relate the pulsational variability to vertical stratification of chemical elements. This study of the atmospheric properties of γ Equ showed that the light and iron-peak elements are enhanced in the lower atmospheric layers (log τ5000 ≥ −0.5), whereas REE ions are concentrated in a cloud with a lower boundary at log τ5000 ≤ −4 (Mashonkina et al. 2005). Thus, high-amplitude pulsations observed in REE lines occur in the upper atmosphere, while lines of elements showing no significant variability form in the lower atmosphere. This leads to the following general picture of roAp pulsations: we observe a signature of a magnetoacoustic wave, propagating outwards with increasing amplitude through the chemically stratified atmosphere. 41 O. Kochukhov 1 H_ core Nd lines Pr lines Ca resonance line cores Sr 2 4215 (core) Y lines Saio’s model 300 0.9 0.8 0.7 Pulsation phase Pulsation amplitude, m/s 400 200 0.6 0.5 0.4 0.3 100 0.2 0.1 0 -7 -6 -5 -4 -3 logo5000 -2 -1 0 0 -7 -6 -5 -4 -3 -2 -1 0 logo5000 Figure 1: Reconstruction of the vertical cross-section of pulsation mode in the roAp star HD 24712. Symbols show the observed amplitude (left panel) and phase (right panel) of the radial velocity variation for different spectral lines. The dashed line illustrates the theoretical depth dependence of the pulsation wave properties (H. Saio, private communication). The presence of significant phase shifts between the pulsation radial velocity curves of REEs (Kochukhov & Ryabchikova 2001a), or even between lines of the same element (Mkrtichian et al. 2003), can be attributed chemical stratification effects and, possibly, to the short vertical wavelength of the running magnetoacoustic wave. These unique properties of roAp pulsations, combined with a presence of large vertical abundance gradients in the line-forming region, make it possible to resolve the vertical structure of p modes and to study propagation of pulsation waves at the level of detail previously possible only for the Sun. The study by Ryabchikova et al. (2002) represents the first attempt to use the vertical chemical inhomogeneities as spatial filters which resolve the vertical p-mode structure. The basic idea of this pulsation tomography approach consists of characterizing the pulsational behaviour of a sample of spectral lines and subsequent interpretation of these observations in terms of the pulsation wave propagation. Chemical stratification analysis of REE lines constrains formation depths of pulsating lines, thus allowing one to associate geometrical height with the amplitude and phase of RV pulsations. Figure 1 illustrates results of the pulsation tomography analysis of the roAp star HD 24712. This star was observed simultaneously by the MOST satellite and from the ground, using highresolution spectrographs at several large telescopes, including the ESO VLT. Using these time-series spectra, Ryabchikova et al. (2007a) studied the pulsational variation of more than 600 lines. Pulsation amplitudes and phases for several characteristic lines of light elements, the core of Hα and numerous REE lines are plotted in Fig. 1 as a function of optical depth. Observations are compared with the theoretical p-mode cross-section (H. Saio, private communication). NLTE line formation was taken into account in chemical stratification analysis of REE ions. This modelling reveals a rapid increase of the pulsation amplitude with height and the respective change of the pulsation phase. The oscillation amplitude reaches maximum at log τ5000 ≈ −4.5 and decreases in the higher layers. Preliminary NLTE stratification analysis of Pr (Ryabchikova et al. 2007c) suggests that the formation heights of the Pr iii absorption features are not too different from Nd iii, despite a clear phase offset between the two groups of lines in HD 24712. This phase difference, as well as the amplitude and phase jump between the uppermost layers probed by the Hα core and the location of the REE cloud, may reflect shortcomings of the complicated NLTE analysis. Alternatively, it is possible that we are seeing effects of the inhomogeneous surface distribution of different REEs in HD 24712. Magnetic Doppler images obtained by Lüftinger et al. (2007) show that the horizontal geometry of the Pr and Nd distribution is not the same. This may lead to different pulsational behaviour because the vertical structure of 42 Observations of pulsations in roAp stars magnetoacoustic modes depends on the field strength and orientation (Cunha 2006) and, therefore, may be different at the locations of the Pr and Nd spots in HD 24712. The detailed pulsation tomography analysis based on NLTE chemical stratification modelling is very demanding in terms of the quality of observations, required input data and computer resources. This is why only two roAp stars, γ Equ and HD 24712, were studied with this method up to now. A different approach to the pulsation tomography problem was proposed by Ryabchikova et al. (2007b). They noted that in the framework of the outward propagating magnetoacoustic wave one expects a continuous amplitude vs. phase relation for pulsation modes. The amplitude-phase diagrams offer a possibility to trace the vertical variation in the mode structure without assigning physical depth to pulsation measurements. Ryabchikova et al. (2007b) analysed a sample of ten roAp stars, measuring variations of several hundred lines for each object. The amplitude-phase diagrams were constructed for each star and the resultant vertical mode cross-sections were compared with other pulsational characteristics and with the fundamental stellar parameters. As an outcome of this analysis, it was discovered that the form of pulsational perturbation changes from a predominantly standing to a mainly running wave within the REE line-forming region. It appears that the location of this interesting modification of the pulsation wave properties shifts towards higher layers for cooler roAp stars. Variability of line bisectors In addition to the diversity in the pulsation signatures of different elements and ions, the variation of individual strong REE lines in roAp stars is far from trivial. The most surprising observation is a large change in the amplitude and phase of bisector RV with intensity inside individual lines. In some sharp-lined roAp stars the RV amplitude increases from a few hundred km s−1 to several km s−1 as one moves towards the outer parts of the line profiles. At the same time, the pulsation phase shows complicated trends with bisector intensity, sometimes changing by up to 180o . This remarkable bisector variation was first discovered in γ Equ (Sachkov et al. 2004) and has been demonstrated for other roAp stars (Kurtz et al. 2005, Ryabchikova et al. 2007ab). The rapidly rotating pulsators, such as HD 99563 (Elkin et al. 2005), show an increase of bisector amplitude towards the core – a trend opposite to that of γ Equ. The line core and wings are expected to sample somewhat different parts of the atmosphere and this is why changes in the bisector variation across individual lines are often attributed to height effects. According to this explanation, modification of bisector oscillations indicates a remarkably complex and rapidly changing pulsation mode structure, with several nodes located in the line-forming region. However, this interpretation must be viewed with caution. A rapid change of the pulsation wave properties with height is inconsistent with the welldefined, smooth amplitude and phase depth dependence inferred by pulsation tomography. Theoretical models (Saio & Gautschy 2004, Saio 2005) also predict no nodes in the upper atmosphere. Moreover, the implicit assumption that any deviation from a constant amplitude and phase of the bisector should be interpreted as a height effect is questionable. In fact, no studies looked at the bisector behaviour in normal non-radial pulsators. It appears that at least part of the core-to-wing change of the bisector amplitude may be ascribed to the presence of a high- harmonic contribution in the horizontal pulsation structure. Interpretation of the bisector variability is even more ambiguous for rapidly rotating roAp stars. In these objects the oblique non-radial pulsations are superimposed onto the much larger velocity field due to the stellar rotation. The primary consequence of the dominant rotational broadening of spectral lines is that the mapping between bisector intensity and atmospheric height is no longer valid. Instead, the spectral line wings are formed close to the limb of the visible stellar disk, whereas the line core region is primarily sensitive to the disk centre. Detailed spectrum synthesis calculations demonstrate that in the presence of chemical O. Kochukhov 43 spots one can easily obtain substantial core-to-wing changes of the bisector amplitude and phase without any depth dependence of pulsation wave. Therefore, the interpretation of the bisector variation of rapidly rotating roAp stars in terms of vertical structure of p modes (e.g., Elkin et al. 2005) is probably incorrect. Pulsation Doppler imaging The outstanding pulsational variability of REE lines in rapidly rotating roAp stars permits detailed mapping of the horizontal structure of pulsations. The oblique nature of non-radial oscillations allows pulsational monitoring from different aspect angles, thus facilitating reconstruction of the pulsation pattern. Using this unique geometrical property of roAp pulsations, Kochukhov (2006) has carried out high-resolution spectroscopic monitoring of the prototype roAp star HD 83368 (HR 3831). This star was observed at the ESO 3.6-m telescope during six nights over a period of two weeks. Full rotational phase coverage with the time-resolved spectra was obtained, supplying observational material for the first comprehensive investigation of the pulsational line profile variability (LPV) in a roAp star. The moderately rapid (ve sin i = 33 km s−1 ) rotation of HD 83368 allows to use the Doppler effect in the spectral lines to resolve both the horizontal topology of chemical inhomogeneities and velocity perturbations due to non-radial oscillations. Kochukhov (2004a) extended the principles of Doppler imaging (DI) to the reconstruction of the time-dependent velocity field. In this approach the surface pulsation velocity amplitudes are recovered directly from the observed line profile variability, without a priori constraints on the functional form of pulsation maps. This makes pulsation DI one of few tools suitable for addressing the daring task of inferring non-radial pulsation patterns distorted by a magnetic field and stellar rotation. Applying the pulsation mapping technique to the roAp star HD 83368, Kochukhov (2004b) obtained the first stellar Doppler image of the velocity field. DI analysis of HD 83368 revealed a nearly axisymmetric pulsation geometry and for the first time independently confirmed the alignment of the non-radial pulsation and the magnetic field. Pulsation mapping finds the oblique pulsator geometry as a result of the assumption-free analysis, in contrast to all previous studies of roAp stars which started from the assumption that the OPM is valid. Highresolution maps of pulsations in HD 83368 were used by Kochukhov (2004b) to disentangle different harmonic contributions to the pulsation geometry. It was shown that the oscillations are shaped as suggested by Saio & Gautschy (2004), whereas the non-axisymmetric pulsation components predicted by the theory of Bigot & Dziembowski (2002) cannot be detected. This demonstrates a dominant role of the magnetic perturbation of the p modes and a considerably less important influence of stellar rotation. Rapid line profile variation in sharp-lined roAp stars Despite dramatic progress in understanding the vertical structure of pulsation modes in slowly rotating roAp stars, relatively little attention has been paid to the problem of inferring the horizontal geometry of pulsations. It is often assumed that a horizontal cross-section of non-radial pulsation is given by an oblique axisymmetric mode of low degree, similar to the pulsation geometries found for rapidly rotating roAp stars. Thus, the question of systematic mode identification has not been thoroughly investigated in the case of sharp-lined magnetic pulsators, which represent the majority of roAp stars. Understanding rapid LPV of slowly rotating roAp stars turns out to be a challenging task. The first observation of roAp line profile variability (Kochukhov & Ryabchikova 2001a) demonstrated the presence of unusual blue-to-red running features in the residual spectra of γ Equ. Moreover, a single-wave variability of the REE line width in this star is clearly inconsis- 44 Observations of pulsations in roAp stars Figure 2: Profile variations of the Pr iii 5300 Å line in the spectra of sharp-lined roAp stars. The average spectrum is plotted in the upper part of each panel. The time-series of the difference spectra is shown in the middle. The bottom curve presents the wavelength dependence of the standard deviation. tent with any axisymmetric pulsation geometry described by spherical harmonics (Aerts et al. 1992, Kochukhov 2005). This led Kochukhov & Ryabchikova (2001a) to speculate about the possible presence of non-axisymmetric modes in γ Equ – a suggestion equivalent to stating that the classical OPM is not applicable to this star. Later Shibahashi et al. (2004) argued that the blue-to-red running waves in the residual spectra of γ Equ are inconsistent with spectral variability expected for any, axisymmetric and non-axisymmetric alike, low-degree modes. The puzzle of the pulsational LPV in sharp-lined roAp stars has been solved by Kochukhov et al. (2007). This study presented a comprehensive survey of profile variability in ten roAp stars using observations obtained at the VLT and CFHT telescopes. The variations of the REE lines were investigated in detail and a prominent change of the profile variability pattern with height was discovered for all roAp stars. The profile variability of at least one rare-earth ion in each investigated star is characterized by the blue-to-red moving features, previously discovered in γ Equ. Figure 2 shows an example of this interesting behaviour, common in rapidly rotating non-radial pulsators, but completely inexplicable in the framework of the standard OPM of slowly rotating roAp stars. The analysis of the line profile moments and spectrum synthesis calculations presented by Kochukhov et al. (2007) demonstrates that unusual oscillations in spectral lines of roAp stars arise from the pulsational modulation of line widths. This variation occurs approximately in quadrature with the radial velocity changes, and its amplitude rapidly increases with height in the stellar atmosphere. Kochukhov et al. (2007) proposed that the line width modulation is a consequence of the periodic expansion and compression of turbulent layers in the upper atmospheres of roAp stars. This means that the line profile changes observed in slowly rotating magnetic pulsators should be interpreted as a superposition of two types of variability: the usual time-dependent velocity field due to an oblique low-order pulsation mode and an additional line width modulation, synchronized with the changes of stellar radius. Figure 3 shows that this new OPM correctly reproduces the main features in the observed pulsational variability of line profiles and moments in roAp stars. O. Kochukhov 45 Figure 3: Line profile variations of an oblique non-radial pulsator. a) Spectrum variability for the = 1, m = 0 mode viewed from the pulsation pole. b) Effect of adding harmonic variability of the line width. In each panel the left plot shows the average line profile on top and a time series of the difference spectra below. The right panels illustrate variation of the first (RV, upper plot) and second (line width, lower plot) line profile moments. Conclusions and outlook Recent investigations of the spectroscopic variability of roAp stars revealed an interesting and complex picture. The most prominent effect, distinguishing roAp stars from all other pulsators, is the close interrelation between the chemical stratification and pulsational variability. Magnetoacoustic waves pass through distinct chemical clouds in the upper atmospheric layers, giving rise to depth-dependent amplitude and phase shifts in the radial velocity variation of different elements. The quality of observational material and available computing resources have reached the stage when it becomes feasible to address the task of constructing 3-D dynamical models of pulsating stellar atmospheres. The pulsation Doppler imaging and magnetoacoustic tomography techniques can be combined in a self-consistent remote sensing procedure, aimed at 46 Observations of pulsations in roAp stars the recovery of the 3-D geometry of pulsations and chemical inhomogeneities. This can be achieved by applying the pulsation Doppler imaging method to the time-series observations of spectral lines formed at different heights and then combining the resulting horizontal slices of the pulsation pattern into a 3-D velocity field map. Construction of the empirical maps should be supported by the advanced theoretical modelling of peculiar-star atmospheres and pulsations. In particular, a realistic study of the interaction between pulsations, turbulence and magnetic field in the tenuous outer layers of roAp atmospheres is urgently needed to clarify many puzzling aspects of the spectroscopic variation of roAp stars. Acknowledgments. I thank the organizers of the Vienna Workshop on the Future of Asteroseismology for inviting me to present this review. My participation in the workshop was supported by the grants from the Swedish Kungliga Fysiografiska Sällskapet and the Royal Academy of Sciences. References Aerts C., De Pauw M., Waelkens C., 1992, A&A, 266, 294 Balona L. A., 2002, MNRAS, 337, 1059 Bigot L., Dziembowski W. A., 2002, A&A, 391, 235 Cunha M. S., 2006, MNRAS, 365, 153 Cunha M. S., Fernandes J. M. M. B., Monteiro M. J. P. F. G., 2003, MNRAS, 343, 831 Elkin V. G., Kurtz D. 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P., Kanaan A., 2003, MNRAS, 345, 781 Ryabchikova T., Piskunov N., Kochukhov O., et al., 2002, A&A, 384, 545 Ryabchikova T., Sachkov M., Weiss W. W., et al., 2007a, A&A, 462, 1103 Ryabchikova T., Sachkov M., Kochukhov O., Lyashko D., 2007b, A&A, submitted Ryabchikova T., Mashonkina L., Ryabtsev A., Kildiyarova R., Khristoforova M., 2007c, these proceedings Sachkov M., Ryabchikova T., Kochukhov O., et al., 2004, in Kurtz D. W., Pollard K. R., eds, ASP Conf. Ser. Vol. 310, Variable Stars in the Local Group. San Francisco, p. 208 Saio H., 2005, MNRAS, 360, 1022 Saio H., Gautschy A., 2004, MNRAS, 350, 485 Shibahashi H., Kurtz D. W., Kambe E., Gough D. O., 2004, in Zverko J., Žižňovský J., Adelman S. J., Weiss W. W., eds, IAU Symp. 224, The A-star Puzzle. Cambridge Univ. Press, p. 829 O. Kochukhov 47 DISCUSSION Kepler: The assumption of a single spherical harmonic is wrong in terms of the pulsation, i.e. the real change in the star. You need sums of spherical harmonics or something similar. Kochukhov: Yes, this is precisely what happens. The pulsations are distorted by the magnetic fields and therefore they are not described by a single spherical harmonic, and this is why we are not using spherical harmonics. We are reconstructing the pulsations making no a priori assumptions about horizontal structure, just like in other applications of Doppler imaging. Metcalfe: When you do these reconstructions via Doppler imaging for multiple lines, do you derive the same inclination angles for the magnetic axis? Kochukhov: The magnetic axis is not constrained by the intensity spectra used for pulsation mapping; it is constrained by the analysis of polarimetric stellar measurements. Doppler images discussed here yield inclination of the pulsation axis, which is found to coincide with the orientation of the magnetic axis inferred in the previous studies of the star. As for multiline analysis, it is not yet feasible because the spectra available to us cover only a short wavelength region. Oleg Kochukhov and Mikhail Sachkov concentrating on a discussion. Comm. in Asteroseismology Vol. 150, 2007 Theory of rapidly oscillating Ap stars M. S. Cunha Centro de Astrofı́sica da Universidade do Porto, Portugal and High Altitude Observatory, Boulder, USA Abstract I review recent theoretical work on rapidly oscillating Ap stars and discuss key aspects of the physics of the oscillations observed in this class of pulsators. Introduction Rapidly oscillating Ap stars (hereafter roAp stars) are main-sequence chemically peculiar stars of spectral type A (and sometimes F), which exhibit oscillations with amplitudes of a few mmag and frequencies typically ranging from 1 to 3 mHz. Over 30 stars are presently known to belong to this class of pulsators, the first examples having been discovered almost three decades ago by Kurtz (1982). Moreover, lower-frequency pulsators have been predicted to exist among the more evolved cool Ap stars (Cunha 2002). A first example of the latter has recently been discovered (Elkin et al. 2005), showing that the roAp phenomenon is likely to span a frequency range which is wider than usually considered. In the past few years a number of exciting observational results have motivated the development of theoretical work on roAp stars. In particular, high time- and spectral-resolution spectroscopic observations have unveiled the oscillations in the atmosphere of these stars (Kochukhov 2007), and high duty cycle photometric data, acquired either with the groundbased telescope network WET (Kurtz et al. 2005), or with the Canadian satellite MOST (Matthews 2007), have improved the quality of the observed oscillation spectra of particular members of this class of pulsators. Additional recent observational and theoretical reviews on roAp stars are provided by Kurtz et al. (2004), Cunha (2003, 2005) and Gough (2005). The importance of the magnetic field Ap stars are known to have strong, well organized magnetic fields with typical magnitudes of a few kG (Mathys & Hubrig 1997, Hubrig et al. 2004, 2005, Kochukhov 2006, Ryabchikova et al. 2006). Well below the photosphere the magnetic field is unlikely to play an important role in the dynamics of the oscillations. However, in the outer layers it is expected to influence the oscillations both directly, through the action of an additional restoring force (e.g., Dziembowski & Goode 1996, Cunha & Gough 2000), and indirectly, through the interaction with outer convection (Balmforth et al. 2001). Figure 1 shows schemes of the outer layers of a typical roAp star, where the magnetic field is likely to influence the pulsations, for different magnetic field intensities. In particular, two different regions of influence should be considered: the magnetoacoustic layer, where the magnetic and gas pressures are of the same order of magnitude, and, above it, the magnetically dominated layer, where the former becomes much larger than the latter. These two regions together form what we shall designate the magnetic boundary layer. M. S. Cunha 49 Figure 1: Ratio between magnetic (Pm) and gas (Pg) pressures for different magnetic field intensities. The two horizontal dashed lines bound the region where the magnetic and acoustic pressure are of the same order of magnitude. The continuous line shows the pressure ratio for a magnetic field strength of 1 kG, while the dashed lines show the pressure ratio for fields of magnitude 3 kG, 5 kG and 10 kG, respectively. Direct effect on atmospheric pulsations Over the past few years, exciting results have been derived through the analysis of time-series of high resolution spectroscopic data of roAp stars. These data contain information about the structure of pulsations in the atmosphere of these stars. Here we emphasize some aspects that are likely to be important when interpreting these exciting data. Figure 1 shows that the photosphere of a roAp star (indicated by the change in the slope of the curves) can be located either in the magnetoacoustic, or in the magnetically dominated region, depending on the strength of the magnetic field. Thus, depending on the latter, the structure of the oscillations in the atmosphere of these stars might look significantly different. While in the magnetoacoustic region the restoring force has acoustic and magnetic components of comparable size, in the magnetically dominated region the magnetoacoustic wave decouples, and we may expect to find waves which are essentially magnetic and waves which are essentially acoustic. In the latter regime, the direction of the displacement associated with each of the components is determined by the direction of the perturbed Lorentz force, which, to first order, is perpendicular to the unperturbed magnetic field. Thus, the acoustic and magnetic components will have associated displacements, respectively, along, and perpendicular to the direction of the magnetic field lines. Unless the structure of the atmosphere is very different from that currently accepted, when observed, the acoustic waves are expected to be in the form of running waves, with frequencies larger than the local acoustic cutoff frequency. Since the latter depends on the inclination of the magnetic field (e.g., Dziembowski & Goode 1996), becoming smaller as the inclination of the field in relation to the local vertical increases, one would expect to find these running waves only at particular latitudes, which will depend on the frequency of the oscillation considered. Moreover, since the acoustic displacement is forced to be along the magnetic field lines, its phase, at a given depth and moment in time, is expected to depend on latitude. Hence, when interpreting disk-averaged data it is important to keep in mind that very different displacements might be expected at different latitudes and that aspects such as the surface distribution of the elements are likely to influence significantly what is observed. 50 Theory of rapidly oscillating Ap stars When the magnetic field is sufficiently weak, the photosphere will be located in the magnetoacoustic region and one can no longer describe the displacement there as a simple superposition of magnetic and acoustic components. It is beyond the scope of this paper to analyse how the displacement in this region would be seen in disk-averaged high resolution spectroscopic data. However, it might be enlightening in this context to revisit the study of pulsations in a simple toy model, composed of two adjacent isothermal layers with different characteristic sound speeds (e.g., Balmforth & Gough 1990). If in the top layer the waves are allowed to propagate away, then in the lower layer, which is assumed to have a fully reflected lower boundary, the displacement can be expressed as a sum of a standing wave and a running wave. No matter how small the running wave component might be, if the standing wave component goes through a node at a given depth, at that depth the running wave component will dominate the solution for the displacement. Hence, if one could ’observe’ the waves in the lower layer of this toy model and match the observations to a function of the form Acos(ωt + φ), with ω being the frequency of the oscillation, t the time and φ a phase, one would find φ to be almost constant at all depths, except close to the nodes of the standing component, where the latter would change significantly with depth. Naturally, in the magnetoacoustic layer of roAp stars there are additional elements that need to be kept in mind. In particular, just as in the case of the magnetically dominated region, the depth structure of the displacement is expected to depend on latitude, and any analysis of disk-average data aiming at reconstructing the form of the eigenfunctions in this region must take that dependence into consideration. Direct effect on the global properties of pulsations The magnetic boundary layer influences basic properties of the pulsations such as the oscillation frequencies and eigenfunctions. These effects cannot be neglected when attempting to use common asteroseismic tools, such as large and small separations, to infer information about the properties of the interiors of these stars. On the other hand, these magnetic signatures contain information about properties of the magnetic field, which might be extracted if only we understand the way in which the magnetic field influences the pulsations. Over the past decade several theoretical works have been carried out with the aim of understanding the effect of the magnetic field on the eigenfrequencies and eigenfunctions of roAp stars (Dziembowski & Goode 1996, Bigot et al. 2000, Cunha & Gough 2000, Saio & Gautschy 2004, Saio 2005, Cunha 2006). Two main observational signatures have been given particular attention, namely, the structure of the multiplets and the spacing between consecutive frequencies in the oscillation spectra. Figure 2 shows a schematic view of the oscillation spectra of HR 1217. The asymmetry in the amplitude of the peaks in the multiplets and the strange spacing between frequencies ν6 and ν8 are evident. In the case of roAp stars, the multiplet structures seen in the oscillation spectra are due to the modulation of modes of single azimuthal order m over the rotation of the star (Kurtz 1990). As first shown by Dziembowski & Goode (1996), the direct effect of the magnetic field modifies the eigenfunctions in such a way that they will no longer be well described by a single spherical harmonic. Consequently, the multiplet structure associated with a mode that in the absence of a magnetic field would be described by a single degree , will in general show additional components, associated with other degrees, which are produced by the magnetic distortion of the eigenfunctions. A few examples of how the multiplets are distorted by the magnetic field when the direct effect of rotation on the oscillations is neglected are given by Saio & Gautschy (2004). A comparison between the observed multiplets and the corresponding theoretical expectations can provide information about the inclination between the magnetic field axis and the rotation axis, and between the latter and the line of sight, as well as about the topology of the magnetic field. M. S. Cunha 51 Figure 2: Schematic oscillation spectra of HR 1217, according to the observations obtained during the WET campaign (Kurtz et al. 2005). The average large separation (LS) derived from the spacing of the first six modes of oscillation is shown by arrows positioned at different frequencies. The strange spacing of the last mode and the asymmetry in the amplitudes of the peaks in the multiplets are clearly seen. Another aspect of the observed multiplet structure that has been of concern to theoretical studies is the asymmetry in the multiplet peaks. This asymmetry cannot be explained by the action of the magnetic field on the oscillations, because it can only be produced by an agent, such as the Coriolis force, which can distinguish between the north and south hemisphere (e.g., Bigot & Dziembowski 2002, Gough 2005, Cunha 2005). In this context Bigot & Dziembowski (2002) considered the combined effect of rotation and magnetic field on the oscillations of roAp stars and have shown that if the magnetic and centrifugal effects on the oscillation frequencies are comparable, then the axis of pulsation is no longer aligned with the magnetic axis. Moreover, in this case, even though the Coriolis effect is much smaller than the effects of both the magnetic field and the centrifugal distortion of the star, the former has the important observational consequence of providing a natural explanation for the asymmetry of the peaks in the multiplets. However, in most well studied roAp stars the magnetic field is considerably stronger than that considered by Bigot & Dziembowski (2002). When the magnetic perturbation dominates over the centrifugal perturbation, the pulsation axis is expected to be closely aligned with the magnetic axis, and the asymmetry produced by the Coriolis effect disappears. However, it has been known from the works of Cunha & Gough (2000), Cunha (2006) and Saio & Gautschy (2004) that the magnetic effect on the oscillation frequencies varies in a cyclic way with both magnetic strength and oscillation frequency, alternating between maxima and minima. Thus, even at very strong magnetic fields, if the magnetic effect on the oscillations becomes sufficiently small to be comparable with the perturbation due to centrifugal distortion, it might still be possible to see the effect of the Coriolis force in the structure of the multiplet. The direct effect of the magnetic field on the frequencies of the oscillations has also been the subject of several studies over the past years. Earlier results have shown that the oscillation frequencies, the large, and the small separations are expected to be significantly modified by the action of the magnetic field (Cunha & Gough 2000, Saio & Gautschy 2004), and that anomalies in the frequency spacing such as that observed in the highest frequency mode of HR 1217, might be qualitatively explained by that effect. Moreover, it became clear that mode 52 Theory of rapidly oscillating Ap stars conversion in the magnetic boundary layer leads to energy losses that can be relatively large at particular frequencies (Cunha & Gough 2000), and that this dissipation helps explain the absence of δ-Scuti type pulsations in roAp stars (Saio 2005). More recently, Cunha (2006) has shown that it might be possible to derive, from the observed perturbations, information about the magnetic field properties in the magnetic boundary layer. In particular, this work shows that the oscillation frequencies are influenced by the magnetic field in two distinct ways: firstly the magnetic frequency shifts scale with frequency in a way that depends essentially on the structure of the outer layers and the intensity of the magnetic field; secondly, the amount by which the real part of the frequency shift jumps at well defined frequencies depends essentially on the magnetic field configuration and on the degree of the mode. This separation between the effects of magnetic strength and magnetic topology, diminishes, considerably, the number of models that have to be considered when trying to match the oscillation spectra of a given roAp star. Indirect effect of the magnetic field Besides its direct effect, the magnetic field can also influence the pulsations in an indirect way, in particular through its interaction with envelope convection. Earlier works (Balmforth et al. 2001, Cunha 2002) have shown that if convection is suppressed in the envelope of roAp stars, then high frequency oscillations, with periods similar to those observed, could be excited by the opacity mechanism acting on the hydrogen ionization region. Despite this success, the lack of observed δ-Scuti type pulsations in roAp stars, which were also predicted to be excited in the model with convection suppressed, remained unexplained. Recently, it has been shown by Saio (2005) that the direct effect of the magnetic field on the oscillations could lead to the stabilization of the low radial order δ-Scuti type pulsations in roAp stars, through the dissipation of slow Alfvén waves. Moreover, the effect of diffusion, considered by Théado et al. (2005) and Cunha et al. (2004), is also expected to help such stabilization. In the absence of envelope convection, the helium settles very quickly in the outer layers, leaving hardly any helium in the region where it undergoes its second ionization. Since the δ-Scuti-type pulsations are excited predominantly by the opacity mechanism acting in the region of second helium ionization, the reduced abundance of helium in that region leads, in most models, to the suppression of this type of pulsation. Discussion and expectations for the future From their discovery, roAp stars have been considered to be particularly well suited for asteroseismic studies, due to the high radial order of their oscillations. While over the past decade theoretical studies have shown that the interpretation of the oscillation spectra of roAp stars is not as straightforward as one could naively have thought, the same studies have revealed the potential of using these observations to learn about the magnetic field of these stars. Over the past few years the Canadian satellite MOST has observed four roAp stars, including the well known HR 1217 (Matthews 2007). Through the comparison of these observations and theoretical results obtained with models of roAp stars, we will hopefully improve our understanding of the interaction between the magnetic field and pulsations, and will be able to infer information about the sub-photospheric layers of these stars. Moreover, the French-led mission CoRoT launched in December 2006 is expected to bring new insights into studies of roAp stars. As part of its additional science programme, it is hoped that CoRoT will find new roAp stars, which will help establish the observational instability strip for this class of pulsators and test theoretical predictions made through linear stability analysis (Cunha 2002). Last, but not least, as high resolution spectroscopic observations of roAp stars continue to produce new intriguing results, further theoretical work aimed at understanding the pulsations in their atmospheres is certainly expected. M. S. Cunha 53 Acknowledgments. This work was supported by FCT and FEDER (POCI2010) through the project POCTI/CTE-AST/57610/2004, by FULBRIGHT, through a grant under the Mutual Educational Exchange Program, and by NCAR, through the ECSA and HAO Visiting Scientist Programs. References Balmforth N. J., Cunha M. S., Dolez N., Gough D. O., Vauclair S., 2001, MNRAS, 323, 362 Balmforth N. J., Gough D. O., 1990, ApJ, 362, 256 Bigot L., Provost J., Berthomieu G., Dziembowski W. A., Goode P. 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W., 2004, A&A, 415, 685 Hubrig S., Nesvacil N., Schöller M., et al., 2005, A&A, 440, L37 Kochukhov O., 2006, A&A, 454, 321 Kochukhov O., 2007, these proceedings Kurtz D. W., 1982, MNRAS, 200, 807 Kurtz D. W., 1990, ARA&A, 28, 607 Kurtz D. W., Elkin V. G., Mathys G., et al., 2004, in Zverko J., Ziznovsky J., Adelman S.J., Weiss W. W., eds, IAU Symp. 224, The A-Star Puzzle. Cambridge Univ. Press, UK, p. 343 Kurtz D. W., Cameron C., Cunha M. S., et al., 2005, MNRAS, 358, 651 Matthews J. M., 2007, these proceedings Mathys G., Hubrig S., 1997, A&AS, 124, 475 Ryabchikova T., Kochukhov O., Kudryavtsev D., et al., 2006, A&A, 445, L47 Saio H., Gautschy A., 2004, MNRAS, 350, 485 Saio H., 2005, MNRAS, 360, 1022 Théado S., Vauclair S., Cunha M. S., 2005, A&A, 443, 627 54 Theory of rapidly oscillating Ap stars DISCUSSION Frandsen: It is very fortunate that these stars rotate. For instance, just observing the amplitude of the oscillation at a given rotation phase tells you something about the mode, even if it must be described with a superposition of a number of spherical harmonics. And then we are lucky that the pulsation periods are so short that they can be observed only over a very small fraction of the rotation period. Dziembowski: Oleg said that rotation apparently has no effect on mode geometry. Now you said that in fact rotation is necessary to explain the asymmetry of the sidepeaks. What’s your preferred solution for this dilemma? Kochukhov: The main problem is that the asymmetry we are talking about now is the asymmetry in the photometric data, where you cannot make a direct connection between the horizontal luminosity distribution and the pulsational quantities. Instead, one should consider spectroscopy, which gives direct access to horizontal displacement. However, in the wealth of spectroscopic observables there are some which show no apparent asymmetry of sidepeaks. Cunha: Yes, but you still have to explain the asymmetry in photometry, and the only way I have seen is Wojtek’s explanation in terms of the Coriolis force. Kochukhov: There is certainly a significant discrepancy between photometry and spectroscopy and there is no explanation why. Dziembowski: But wouldn’t you think that theory should explain both photometry and spectroscopy? Kochukhov: We don’t know the actual pulsational displacement. We make a guess that it is a spherical harmonic, but I repeat that this just a guess. I am afraid this is a bit dangerous. Dziembowski: It’s not a matter of a spherical harmonic dependence but only of the axial symmetry. Gough: May I add a short comment related directly to this issue which might clarify the situation: no matter what the distortion of the eigenfunction, and from no matter what source it arises, nonrotating stars don’t know the difference between their left and their right. Left – right is the only property that distinguishes between m = +1 and m = −1, but the latter is a matter of one’s choice of coordinate axis, which a star cannot know. Only when the star is rotating is there a physically real principal axis, an axis which we are forced to adopt for describing eigenmodes; that axis has a well defined directed orientation, and can therefore tell the star which is the left and which is the right. It is quite different from the principal axis of the distortion caused by any other, axisymmetric, force, such as a magnetic field, for example, which has direction, of course, but is not orientated. So if there is an m = +1 – m = −1 asymmetry, whether it be in photometric or in spectroscopic data, it has to be a consequence of rotation. Comm. in Asteroseismology Vol. 150, 2007 SX Phe stars in the Fornax dSph galaxy E. Poretti,1 L. Dell’Arciprete,1,2 C. Greco,3,4 G. Clementini,3 E. V. Held,5 L. E. Pasinetti,2 M. Gullieuszik,5,6 M. Maio,4 L. Rizzi 7 1 INAF-Osservatorio Astronomico di Brera, Merate (LC), Italy 2 Università degli Studi di Milano, Milano, Italy 3 INAF-Osservatorio Astronomico di Bologna, Bologna, Italy 4 Dipartimento di Astronomia, Università di Bologna, Bologna, Italy 5 INAF-Osservatorio Astronomico di Padova, Padova, Italy 6 Dipartimento di Astronomia, Università di Padova, Padova, Italy 7 Institute for Astronomy, University of Hawaii, Honolulu, USA Introduction We started an observational project on the Fornax dSph galaxy to exploit the possibilities offered by the use of pulsating stars as distance indicators. In particular, the driving idea was to search for stars with P <0.20 d, since the size and surface brightness of the Fornax galaxy made it a very suitable target for wide-field monitoring with a middle-class telescope. Following the classification used for galactic variables, short-period pulsators in the Fornax galaxy should be SX Phe variables, since they are expected to be metal-poor stars. Observations To pursue our goal we used the Wide-Field Imager (WFI) at the 2.2 m ESO-MPI telescope; we surveyed the northern part of the Fornax galaxy in November 2001. We obtained dense B-time series (exposure time 700 sec) to perform a reliable frequency analysis and complementary, less continuous V -time series (exposure time 1000 sec) to obtain mean magnitudes and amplitudes in a two-colour system. Preliminary results have been reported by Clementini et al. (2006) and Poretti et al. (2006). We have now completed the reduction of the eight chips of the WFI mosaic, detecting 86 short-period stars and hundreds of RR Lyr variables. We emphasize that the detection of short-period variables was not an easy task. Indeed, the short periods made the regular variability hardly discernible when plotting the points separated by 12 min from each other. Therefore, we carefully applied frequency analysis methods both to the whole time series and to the measurements of a single night. This procedure allowed us to reject spurious candidates (i.e., stars for which the scatter in just one night mimics an apparent variability) and to enhance the real variability. Not all the 86 SX Phe stars belong to the field of the Fornax galaxy. In chip #6 the globular cluster For 3 is resolved into stars, at least in the outer parts, and several RR Lyr stars have been found in the outer regions. Amongst them, two SX Phe variables have also been detected and we suggest that they very probably belong to For 3. The detection of SX Phe variables in a globular cluster in another Local Group galaxy is a remarkable observational result. The distribution of the standard deviations of the least-squares fits ranges between 0.04 and 0.20 mag with an average precision of 0.08 mag. This is a very satisfactory result considering that the variables have mean B-magnitudes between 22.5 and 24.2. The Fornax sample is characterized by short-periods (left panel in Fig. 1): 59% of the stars have a period less than 0.07 d and 81% less than 0.08 d. There is an evident underabundance of stars with P >0.10 d, corroborating the hypothesis that these variables are likely metalpoor stars. The full B amplitudes range in an almost uniform way from 0.20 to 0.90 mag with an isolated peak in the 0.40 – 0.50 mag interval (right panel in Fig. 1). This fact strongly suggests that the majority if not all the variables are radial pulsators. 56 SX Phe stars in the Fornax dSph galaxy Figure 1: Distribution of the periods and amplitudes of SX Phe stars in the Fornax dSph galaxy Acknowledgments. A large part of this work has been made by the student Luca Dell’Arciprete. His supervisor and our colleague, Prof. Laura E. Pasinetti, suddenly died on September 13th, 2006. Several astronomers have been formed under her teaching: we gratefully honour her memory. References Clementini G., Greco C., Held E. V., et al., 2006, Mem. Soc. Astron. Ital., 77, 249 Poretti E., Dell’Arciprete L., Clementini G., et al., 2006, Mem. Soc. Astron. Ital., 77, 219 Comm. in Asteroseismology Vol. 150, 2007 REM observations of the Herbig Ae stars V346 Ori and PDS2 S. Bernabei,1,2 M. Marconi,3 V. Ripepi,3 S. Leccia,3 E. Rodrı́guez,4 T. D. Oswalt,5 M. J. López-González,4 F. J. Aceituno,4 A. Ruoppo,3,6 F. Palla,7 M. J. P. F. G. Monteiro,8 E. Molinari,9 G. Chincarini,9 F. M. Zerbi,9 S. Covino,9 V. Testa,10 G. Tosti,11 F. Vitali,10 L. A. Antonelli,10 P. Conconi,9 G. Malaspina,9 L. Nicastro,12 E. Palazzi 12 1 INAF-OABologna, Via Ranzani 1,40127 Bologna, Italy Univ. de La Laguna, Avda. Astrofisico F. Sánchez sn, 30071 La Laguna, Spain 3 INAF-OACapodimonte,Via Moiariello 16, 80131, Napoli, Italy 4 IAA, CSIC, Apdo. 3004, 18080 Granada, Spain 5 Florida Institute of Technology, 150 W Univ. Blvd., Melbourne, FL 32901-6988, USA 6 Università Federico II, Complesso Monte S. Angelo, 80126, Napoli, Italy 7 INAF-OAAarcetri, Largo E. Fermi, 5, I-50125, Firenze, Italy 8 DMA-Fac. de Ciências and CAUP, Rua das Estrelas, 4150-762 Porto, Portugal 9 INAF-OABrera, Via E. Bianchi 46, 23807, Merate (LC), Italy 10 INAF-OARoma, Via di Frascati, 33, 00040 Monte Porzio Catone (ROMA) Italy 11 Perugia University- Piazza Università, 1, 06100 Perugia, Italy 12 INAF-IASF, Bologna, Via P. Gobetti 101, I-40129 Bologna, Italy 2 Abstract We present preliminary results of a photometric study devoted to the two Herbig Ae stars V346 Ori and PDS 2, based on data from the R.E.M. telescope. As a result, 1) we confirm the multiperiodicity of V346 Ori; 2) we discover δ Scuti-like pulsation in PDS 2. Introduction V346 Ori and PDS 2 are interesting objects: V346 Ori was already suspected to be a multiperiodic PMS δ Scuti star (Pinheiro et al. 2003), whereas PDS 2 was investigated because its spectral type F3V makes it a very good object to constrain the poorly sampled red edge of the PMS δ Scuti instability strip. We studied these two objects by using the 0.6 m R.E.M. telescope (La Silla, Chile, www.rem.inaf.it). Note that present R.E.M. observations for V346 Ori are part of a multisite campaign for which data analysis is ongoing. Results Due to the lack of space, here we only present the periodogram obtained for V346 Ori (see Fig. 1) based on about 94 h of R.E.M. observations. These data allowed us to identify at least 9 significant frequencies (see figure). A similar analysis for PDS 2, (22 h of R.E.M. observations during 7 nights), allowed us to establish that PDS 2 is a multiperiodic pulsating star with at least three significant oscillation frequencies at f1=17.05 c/d, f2=13.77 c/d, f3=24.24 c/d. Thus, PDS 2 is a new member of the PMS δ Scuti class. In the future we will: 1) finalize the analysis for V346 Ori (taking advantage of the photometry from other sites) and for PDS 2; 2) interpret the periodicities found for the two stars in the light of both radial and non-radial pulsation models. References Pinheiro F. J. G., Folha D. F. M., Marconi M., et al., 2003, A&A, 399, 271 58 REM observations of the Herbig Ae stars V346 Ori and PDS2 Figure 1: Periodogram for V346 Ori R.E.M. data. All significant frequencies are indicated and labelled. Comm. in Asteroseismology Vol. 150, 2007 Asteroseismology and mode driving of the Herbig Ae star HD 104237 M.-A. Dupret,1 S. Théado,2 T. Böhm,3 M.-J. Goupil,1 C. Catala,1 A. Grigahcène 4 1 Observatoire de Paris, LESIA, CNRS UMR 8109, 92195 Meudon, France 2 Institut d’astrophysique et de Géophysique, Liège, Belgique 3 Observatoire Midi-Pyrénées, CNRS, 31400 Toulouse, France 4 CRAAG - Algiers Observatory BP 63 Bouzareah 16340, Algiers, Algeria Abstract Eight pulsation frequencies were detected in the Herbig Ae star HD 104237 during two observational campaigns in 1999 – 2000 (Böhm et al. 2004). Moreover, Böhm et al. (in preparation) detected recently in their data two independent signatures of a signal at 95 hr that corresponds probably to rotational modulation. We present here a seismic study of this Pre-Main Sequence star based on these observations. Different possible interpretations of the pulsation spectrum are considered. The driving of the pulsation modes is not explained by standard models, the observed frequencies being too high for δ Scuti-type pulsations. We consider the effect of He accumulation in its partial ionization zones as a possible explanation for this driving. Interpretation of the frequencies There are different determinations of Teff for HD 104237 (see Dupret et al. 2006). The highest degree of confidence can be given to the value Teff 8250 ± 150 K determined by Böhm et al. (in preparation) on the basis of the many spectra obtained during the campaign. As there is no mode identification, we must make some guess for the interpretation of the pulsation frequencies. In a first family of possible solutions, the approximate equidistance found around 2.3 c/d in the observed spectrum is interpreted as the large separation (see Dupret et al. 2006). The problem of this solution is that the required radius is large. Hence, the theoretical luminosity is larger than the observed value (parallax known). In a second family of possible solutions, a multiplet appears as a possible rotational splitting and two radial modes are fitted. Models near the observed Teff and L are found in this case. However, the predicted frequency splitting for solid rotation (95 hr period) is smaller than observations. If we see really a rotational splitting, this could be an indication of differential rotation. Mode driving The driving of the observed pulsation modes of HD 104237 is not explained by standard models. Even if it was inside the classical instability strip (which is not the case with the new determination by Böhm et al.), the frequencies of the predicted unstable modes would be too low compared to observations. We consider here the effects of inhomogeneous He distributions on mode excitation. In HD 104237, a He accumulation could arise in the external layers of the stars, resulting from the combined effects of magnetic field (which might suppress convection), microscopic diffusion and winds. A detailed prescription of these processes is not included in the models presented here: as a first step, we just impose in our models different ad-hoc He accumulation profiles (Fig. 1) parametrized in a similar way as proposed 60 Asteroseismology and mode driving of the Herbig Ae star HD 104237 0.8 0.7 model h 0.5 model 1 model 2 model 3 0.4 model 4 0.6 Y Unstable modes Model h All modes are stables Model 1 p7 26.49 c/d Model 2 p5 - p8 20.69 - 29.46 c/d Model 3 p5 - p9 20.68 - 32.53 c/d 20.72 - 23.64 c/d Model 4 p5 - p6 Observations 28.50 - 35.61 c/d 0.3 0.2 0.1 0 5.4 5.2 5 4.8 4.6 4.4 4.2 4 log T Figure 1: Left: Different He profiles. Right: Ranges of predicted unstable modes as compared with the observed frequency range. by Balmforth et al. (2001). Our models have the same global parameters: M = 2.3M , log Teff = 3.915, log(L/L ) = 1.55, Z = 0.012. The different He profiles of Fig. 1 affect significantly the opacity in the He partial ionization zones. This affects in turn significantly the κ-driving of the modes as shown in the right panel. In model 3, the opacity drop at log T 4.6 is the steepest and as a consequence the largest number of modes are excited, up to frequencies of 32.53 c/d. We do not reach yet the observed upper limit at 35.6 c/d but our results are already encouraging. References Balmforth N. J., Cunha M. S., Dolez N., Gough D. O., Vauclair S., 2001, MNRAS, 323, 362 Böhm T., Catala C., Balona L., Carter B., 2004, A&A, 427, 907 Dupret M.-A., Böhm T., Goupil M.-J., Catala C., Grigahcène A., 2006, Comm. Asteroseis., 147, 72 Comm. in Asteroseismology Vol. 150, 2007 Asteroseismology of the extreme metal-deficient field high-amplitude SX Phe variable BL Cam E. Rodrı́guez,1 S. Fauvaud,2,3 J. A. Farrell,4 A.-Y. Zhou,5 J.-P. Sareyan,6 M. J. López-González,1 G. Klingenberg,7 M. Wolf,8 A. Rolland,1 P. López de Coca,1 P. Van Cauteren,9 P. Lampens,10 M. Helvaci,11 E. G. Hintz,12 L. Král,13 F. Fumagalli,3 J. H. Simonetti,14 B. H. Granslo,7 L. Kotkova,15 G. Santacana,2 J. Michelet,16 H. Kucáková,13 R. Kocián,13 K. Truparová,13 A. Avdibegovic,11 M. Blazek,11 J. Kliner,11 P. Zasche,11 M. Vilásek,13 S. Bartosı́ková,13 O. Trondal 7 1 Instituto de Astrofı́sica de Andalucı́a, CSIC, E-18080 Granada, Spain, E-mail:[email protected] 2 Association AstroQueyras, Le bois de Bardon, Taponnat, La Rochefoucauld, France 3 Groupe Européen d’Observations Stellaires (GEOS), Bailleau l’Evêque, France 4 Sulphur Flats Observatory, Jemez Springs, NM 87025, USA 5 National Astronomical Observatories, Chinese Academy of Sciences, Beijing 100012, China 6 Observatoire de la Côte d’Azur, BP 4229, F-06304 Nice cedex 4, France 7 Variable Star Section, Norwegian Astronomical Society, N-0315 Oslo, Norway 8 Astronomical Institute, Charles University Prague, CZ-180 00 Praha 8, Czech Republic 9 Beersel Hills Observatory, 1650 Beersel, Belgium 10 Koninklijke Sterrenwacht van België, B-1180 Brussel, Belgium 11 Ankara University, Department of Astronomy and Space Sciences, Ankara, Turkey 12 Department of Physics and Astronomy, Brigham Young University, Provo, UT 84602, USA 13 Obs. and Planetarium of Johann Palisa, VSB-Technical University, Ostrava-Poruba, Czech Republic 14 Martin Obs., Physics Dep., Virginia Polytechnic Institute & State Univ., Blacksburg, VA 24061, USA 15 Astronomical Institute, Academy of Sciences, Ondrejov, Czech Republic 16 Club d’Astronomie Lyon Ampére, 37 rue Paul Cazeneuve, Lyon, France Classical pulsating stars displaying large amplitudes in the Lower Instability Strip commonly are pure monoperiodic or double-mode radial pulsators. Only in a very few cases, some additional independent modes have been detected in their light curves which are preponderantly nonradial. BL Cam is suspected to be one of these very few exceptions. This star is an extreme metal-deficient field high-amplitude SX Phe variable in which multiperiodicity has been claimed by different authors (see Fauvaud et al. 2006 for a review) with the secondary peaks displaying very small amplitudes compared to the main periodicity. Thus, this star promised to be a good target for asteroseismic studies. The main aim of this work is to realize a detailed study of this star concerning: (a) its pulsational content and (b) the behaviour of its main periodicity in the O-C diagram. Preliminary results concerning the former point are presented here. The observations were carried out between August, 2005 and March, 2006 from a number of observatories in Europe and America, with observations collected during more than 100 nights and 550 hours. All observations were obtained with CCD cameras and various filters, the majority of them using the Johnson V filter. More than 500 new times of light maximum have been also determined. In particular, at Sierra Nevada Observatory (SNO), the data were sequentially collected in the filters BVI on 13 nights and about 70 hours in each filter (Fig. 1). From this, nearly 300 hours of useful data were used for the frequency analysis following the method described in Rodrı́guez et al. (1998) and Lenz & Breger (2005). The results show very dense pulsational microvariability in this star in addition to the high-amplitude main periodicity (f0 =25.5765 cd−1 , ΔV=153 mmag). In total, 22 secondary peaks, with very small amplitudes (between 7.4 and 1.6 mmag), were found significant, corresponding to 21 independent modes and one combination f0 +f1 . This represents the most complex spectrum ever known in a high-amplitude pulsator in the Lower Instability Strip and opens the possibility to investigate similar microvariability features in other classical high-amplitude objects. Moreover, some additional periodicities are probably still remaining 62 Asteroseismology of the extreme metal-deficient field high-amplitude SX Phe variable BL Cam Figure 1: BVI light curves of BL Cam obtained on December 10th, 2005 at SNO. in the residuals of the frequency spectra. The amplitude of the main periodicity f0 seems to be stable during decades but the majority of the secondary modes present strong amplitude changes from one epoch to another. Multicolour photometry analysis suggests that f0 corresponds to the fundamental radial mode whereas f1 =25.2523 cd−1 is suggested as a nonradial modes with =1. Moreover, the large changes occurring in the amplitude of f6 =32.6464 cd−1 do not support the sometimes claimed idea about this mode being the first overtone of radial pulsation and, thus, BL Cam being a radial double-mode pulsator. References Fauvaud S., Rodrı́guez E., Zhou A.-Y., et al., 2006, A&A, 451, 999 Lenz P., Breger M., 2005, Comm. Asteroseis., 146, 5 Rodrı́guez E., Rolland A., López-González M. J., Costa V., 1998, A&A, 338, 905 Comm. in Asteroseismology Vol. 150, 2007 δ Sct stars in eclipsing binaries: the case of Y Cam E. Rodrı́guez,1 J. M. Garcı́a,2 V. Costa,1 P. Van Cauteren,3 P. Lampens,4 E. C. Olson,5 P. J. Amado,1,6 M. J. López-González,1 A. Rolland,1 P. López de Coca,1 V. Turcu,7 S.-L. Kim,8 A.-Y. Zhou,9 M. A. Wood,10 E. Hintz,11 A. Pop,7 D. Moldovan,7 P. B. Etzel,12 D.-J. Lee,8 G. Handler,13 D. E. Mkrtichian 14,15 1 Instituto de Astrofı́sica de Andalucı́a, CSIC, E-18080 Granada, Spain, [email protected] 2 Departamento de Fı́sica, E.U.I.T. Industrial, UPM, E-28012 Madrid, Spain 3 Beersel Hills Observatory, 1650 Beersel, Belgium 4 Koninklijke Sterrenwacht van België, 1180 Brussel, Belgium 5 Astronomy Department, University of Illinois, Urbana, Illinois 61801, USA 6 Facultad de Ciencias, Universidad de Granada, Spain 7 Astronomical Institute of the Romanian Academy, Cluj-Napoca 3400, Romania 8 Korea Astronomy and Space Science Institute, Daejeon 305-348, Korea 9 National Astronomical Observatories, Chinese Academy of Sciences, Beijing 100012, China 10 Dept. of Physics & Space Sciences and SARA Obs., Florida Inst. of Technology, Melbourne, FL, USA 11 Department of Physics and Astronomy, Brigham Young University, Provo, UT 84602, USA 12 Department of Astronomy, San Diego State University, San Diego, CA 92182, USA 13 Institut für Astronomie, Universität Wien, 1180 Wien, Austria 14 Astrophys. Research Centre for the Structure and Evolution of the Cosmos, Sejong Univ., Seoul, Korea 15 Astronomical Observatory, Odessa National University, Odessa, 65014, Ukraine Eclipsing binary systems with components exhibiting pulsations are excellent laboratories where both pulsation and binarity theories can be combined to obtain very reliable results. In the case of δ Sct-type pulsators, they are very attractive for asteroseismic studies. In particular, the nature of the pulsational modes can be determined using different discrimination methods which use different parts of the orbital period. However, only a few of such systems are presently known, the majority of them having been discovered as pulsators in very recent years. Even much smaller is the number of such systems with detailed studies available in the bibliography. Here we present preliminary results obtained for Y Cam, an Algol-type eclipsing binary system in which the primary component is a δ Sct-type pulsator. The observations were collected during a three-continent photometric campaign carried out during the Northern winter 2002 – 2003. In total, about 100 nights and 500 hours of useful data were obtained with a time span larger than six months. This means the most extensive time series for this kind of system obtained so far. In particular, complete simultaneous uvby photometry was collected at Sierra Nevada Observatory (SNO) together with a few Crawford Hβ data around the orbital phase of first quadrature. They were used to obtain the binary solution of the system using the Wilson-Devinney code while the residuals from the computed binary light curves were then investigated for the pulsational content. The frequency analysis was performed using the method described by Rodrı́guez et al. (1998) and Lenz & Breger (2005). This way, the pulsational behaviour was shown to be complex (Table 1) with eight significant peaks detected in the periodograms, all of them in the range 14−20 cd−1 . The two main ones form a close frequency pair. The main excited modes are suggested to be nonradial on the basis of the observed phase shifts and multicolour photometry. As compared with previous work, some of the frequencies are reported in this work for the first time while strong amplitude variations are detected in others. 64 δ Sct stars in eclipsing binaries: the case of Y Cam Frequency (cd−1 ) f1 =15.0456 f2 =14.9859 f3 =18.3108 f4 =14.4460 f5 =17.7057 f6 =19.7297 f7 =14.6239 f8 =19.3803 Amplitude (mmag) ±0.24 10.23 6.70 6.61 4.98 4.22 2.72 3.72 2.72 S/N Table 1: Results obtained for the combined filter vby and SNO data set. 20.5 13.4 13.2 10.0 8.4 5.4 7.4 5.4 References Lenz P., Breger M., 2005, Comm. Asteroseis., 146, 5 Rodrı́guez E., Rolland A., López-González M. J., Costa V., 1998, A&A, 338, 905 Margit Paparó makes a comment. Comm. in Asteroseismology Vol. 150, 2007 Strömgren photometry of the δ Sct star V402 Cep V. Costa, P. López de Coca, A. Rolland, E. Rodrı́guez, I. Olivares, S. Martı́n-Ruiz, J. M. Garcı́a-Pelayo Instituto de Astrofı́sica de Andalucı́a, CSIC, P.O. Box 3004, E-18080 Granada, Spain Abstract A preliminary analysis of photometric observations carried out during the 2003 and 2005 campaigns of the δ Scuti-type variable star V402 Cep is presented. We show the results of the Strömgren uvby photometry. A few Hβ -Crawford measurements were also collected for calibration purposes in order to place this star inside the HR diagram. Introduction V402 Cephei (SAO 4125, HIP 2299, mv =10.44 mag) is a variable star newly discovered during the HIPPARCOS mission and classified as δ Scuti-type variable. The Variability Annex of the Hipparcos Catalogue (Perryman & ESA 1997) reports V402 Cep to have a period of 0.1229 d with Hp magnitudes ranging between 10.56 and 10.64 mag. The spectral type is listed as F2. In Kazarovets et al. (1999) and Rodrı́guez et al. (2000) V402 Cep is listed as a δ Scuti-type star. Beckstrand et al. (2000) observed it during seven nights and confirmed a primary period of about three hours. Observations The observations were carried out during two nights in November/December 2003 and six nights in October 2005, using the 90 cm telescope at Sierra Nevada Observatory, Spain. The telescope is equipped with a six channel uvbyβ photometer for simultaneous measurements in uvby or in the Hβ channels, respectively (Nielsen 1983). The data consist of 1341 measurements in the Strömgren uvby bands. Additionally, a few Hβ data were also obtained. The comparison stars were C1=SAO 4131 (mv = 9.67, A2) and C2=SAO 4110 (mv = 9.30, F5). Analysis The analysis of this star was carried out with the Fourier Transform method and we found four frequencies present in the data as shown in Table 1. Further observations are needed to obtain a more detailed picture of the pulsational behaviour of this star. The new indices obtained are: (b − y ) = 0.325 ± 0.002, m1 = 0.164 ± 0.002, c1 = 0.762 ± 0.003 and β = 2.732 ± 0.003. The stellar fundamental parameters of V402 Cep have been determined with the program TempLogG (Kupka & Bruntt 2001), giving M = 1.72 M , logTeff = 3.851, log g = 3.75 and [Fe/H] = 0.33. Acknowledgments. This research was supported by the Junta de Andalucı́a and the Dirección General de Investigación (MCYT) under project AYA 2003-04651. 66 Strömgren photometry of the δ Sct star V402 Cep Frequency (c/d) Amp (mag) Phase (rad) 8.1361 7.9633 16.2751 9.2641 0.065 0.026 0.013 0.011 1.618 0.337 4.840 4.095 Table 1: Results of the Fourier analysis of the v data. T0 = 2452945.0 References Beckstrand S. D., McLean A., Hintz E., 2000, BAAS, 32, 1478 Perryman M. A. C., ESA, 1997, The HIPPARCOS Catalogue. ESA SP-1200, Noordwijk Kazarovets E. V., Samus N. N., Durlevich O. V., et al., 1999, IBVS, 4659 Kupka F., Bruntt H. 2001, in Sterken C., ed., First COROT/MONS/MOST Ground Support Workshop. Vrije Universiteit Brussel, Brussel, p. 3 Nielsen R. F., 1983, in Hauge O., ed., Nordic Astronomy Meeting on the Nordic Optical Telescope. Oslo Report No. 59, Inst. Theor. Astrophys., Oslo, p. 141 Rodrı́guez E., López-González M. J., López de Coca P., 2000, A&AS, 144, 469 Comm. in Asteroseismology Vol. 150, 2007 New pulsation pattern of RZ Cas observed spectroscopically in 2006 Holger Lehmann,1 David Mkrtichian 2 1 Thüringer Landessternwarte, D-7778 Tautenburg, Germany 2 ARCSEC, Sejong University, Seoul 143-747, Korea Abstract We investigated the radial velocities of the mass-accreting Algol-type star RZ Cas measured from new observations obtained in 2006. After subtracting an improved orbital solution and all low-frequency variations we searched for the signature of short-term non-radial pulsations. We found three pulsation modes where one was never observed before. Also the amplitudes of the two other modes have changed since 2001. During the eclipse phases we observed a much stronger increase of the pulsation amplitudes than in 2001 and a less pronounced anomaly of the Rossiter-McLaughlin effect. RZ Cas is a member of the mass-accreting Algol-type stars with pulsating components (oEA stars, Mkrtichian et al. 2006). Multi-periodic, δ Scuti-type non-radial pulsations (NRPs) were observed for the primary, from photometry (Rodrı́guez et al. 2004) and from spectroscopy (Lehmann & Mkrtichian 2004, Paper I). The pulsations possess timely changing amplitude and frequency patterns as well as orbital amplitude modulation. RZ Cas shows a very pronounced Rossiter-McLaughlin effect (RME). The RME is a distortion in the orbital radial velocity (RV) curve that can be observed during the eclipse phases of eclipsing binaries with rapidly rotating components (during the eclipse the symmetry of the rotational broadening of the spectral lines is lifted in a time dependent manner). In RZ Cas the RME is anomalous, i.e. the positive and negative deviations from the orbital curve are of different strengths. To study the changes in the oscillation spectrum and the effects of the circum-primary accretion envelope on the RME and on the amplitude modulation of NRP modes further, we continued to monitor the star spectroscopically. We obtained 498 spectra in 7 nights in 2006 with the Coude-Echelle spectrograph at the 2-m telescope of the Thüringer Landessternwarte Tautenburg with a spectral resolution of 30 000 and typical S/N of 80. Based on the new RVs measured by a cross-correlation technique and on the data from 2001 (Paper I) we improved the orbital solution. In the residuals we observed low-frequency trends within single runs. After removal of the calculated orbital RVs and of the low-frequency trends (using spline fits in the second case) we investigated the star for NRPs in the high-frequency domain. Rodrı́guez et al. (2004) found one frequency of 64.1935 c/d in their photometric data from 1999. In the time between 1999 and 2001 this mono-periodicity changed multi-periodicity. Table 1 compares the frequencies obtained from our new data with those from 2001 (Paper I). RZ Cas has changed its pulsation pattern again. For the first time we observe three pulsation frequencies; f3 was never observed before (correctly speaking, also the values of f2 Table 1: High-frequency variations found in the radial velocities of RZ Cas. Errors were derived by the PERIOD04 code (Lenz & Breger 2005) and given in parentheses, in units of the last digit(s). f1 f2 f3 2001 f [c/d] A [m/s] 64.189(6) 99(26) 56.600(4) 151(27) – – f [c/d] 64.2703(3) 55.7610(6) 62.4062(4) 2006 A [m/s] 203(14) 94(14) 145(14) phase 0.78(1) 0.54(2) 0.85(2) 68 New pulsation pattern of RZ Cas observed spectroscopically in 2006 are significantly different and represent two different frequencies). For the determination of amplitude variations we built overlapping phase bins from all runs in 2006, each bin of width 0.2 in orbital phase; 20 such phase bins covered the orbital period in steps of 0.05. Then we applied sinusoidal fits including the three frequencies to the data of each bin. Fig. 1 shows the results. All three frequencies show small amplitude modulations in the out-of-eclipse phases and a strong (3-4 times) increase of amplitude during eclipse. This increase is much stronger than observed in 2001 (Paper I). Comparing the orbital solutions obtained from the 2001 data (Paper I) and from the new data alone we can confirm the increase of the period of about 2 sec since 2001 as obtained from photometry (Mkrtichian et al. 2007). The anomaly of the RME is less pronounced in the 2006 data compared to 2001 but still present. Figure 1: Amplitudes of the RV variation for frequencies f1 (solid), f2 (dotted), and f3 (dashed). Mean errors are indicated by the error bars, from left to right for f1 to f3 . Squares show the variation observed in 2001 (Paper I), filled squares correspond to f1 , open squares to f2 . Phase zero means the epoch of minimum light. Our conclusion so far is that all variations with the orbital period obtained from the 2001 and from the 2006 data reflect the respective density distributions of circum-stellar disk-like gas structures. In both cases the density and its gradient are highest near the epoch of minimum light causing the large amplitudes of RV variations at these phases and to the asymmetry of the RME. Besides more or less steady changes in the circum-stellar density distribution we assume also transient phases of abrupt, massive changes. The first give rise to the different low-frequency trends in RV observed for the same rotation phases with time. The second are assumed to originate from high mass-transfer episodes that change the pattern of NRP modes excited in RZ Cas and cause the observed unsteadiness of the rotation period. The assumption of a timely varying attenuation effect of circum-stellar disk-like structures also explains the different shape of the anomalous RME observed in 2001 and 2006. Results will be discussed in much more detail in a forthcoming paper where we also want to try to model the observed RME (screening effect by the secondary) for different NRP modes and different circum-stellar density distributions obtained from 3D hydrodynamical models. References Lehmann H., Mkrtichian D. E., 2004, A&A, 413, 293, Paper I Lenz P., Breger M., 2005, Comm. Asteroseis., 146, 53 Mkrtichian D. E., Kim S.-L., Kusakin A. V., et al., 2006, Astroph. Space Sci., 304, 169 Mkrtichian D. E., Kim S.-L., Rodrı́guez E., et al., 2007, ASP Conf. Ser., in press Rodrı́guez E., Garcia J. M., Mkrtichian D. E., et al., 2004, MNRAS, 347, 1317 Comm. in Asteroseismology Vol. 150, 2007 Physical properties of the oEA star IV Cas S.-L. Kim, C.-U. Lee, J. W. Lee, J.-H. Youn Korea Astronomy and Space Science Institute, Daejeon 305-348, Korea Abstract We present photometric and spectroscopic observing results of the oEA star IV Cas. Spectral types of the binary system are derived to be A3 (Teff = 8500 K) for the primary component and G9 (Teff = 5370 K) for the secondary. We detected two δ Scuti-type pulsation frequencies of f1 = 32.6894 c/d (cycles per day) and f2 = 36.6714 c/d, for the primary component. Introduction Mkrtichian et al. (2004) introduced the oEA (oscillating EA) stars as the (B)A-F spectral type mass-accreting main-sequence pulsating stars in semi-detached Algol-type eclipsing binary systems. The oEA stars are very interesting objects to show pulsations, eclipses and mass accretion. Furthermore, they are important from an asteroseismological point of view because we can get information of their pulsation modes through spatial filtration during the primary eclipse. We had discovered δ Scuti-type pulsations of the semi-detached Algol-type eclipsing binary IV Cas and had classified it as a member of the oEA stars (Kim et al. 2005). In order to investigate its physical properties in detail, we carried out photometric and spectroscopic observations. Results We have obtained a high-resolution spectrum on 30th November 2005, using a high-resolution echelle spectrograph attached to the 1.8m telescope at Bohyunsan Optical Astronomy Observatory in Korea. The echelle spectrograph has a resolution of 1.5 Å/mm at 5000 Å. Fitting the observed spectrum with a synthetic one by the SPECTRUM code (Gray & Corbally 1994) gave us atmospheric parameters such as Teff = 8500 K, log g = 4.0 and v sin i = 110 km/s for the primary component in the binary system. No emission features could be found in the spectral lines between 3500 Å and 9000 Å. Photometric observations were performed in 17 nights between November 2004 and September 2006, at the dual sites of Sobaeksan Optical Astronomy Observatory (0.6 m telescope) in Korea and Mt. Lemmon Optical Astronomy Observatory (1.0 m telescope) in Arizona, USA. Figure 1 shows B and V phase diagrams of IV Cas. For the light curve analysis, we applied the latest version of the Wilson-Devinney code (Wilson & Devinney 1971) and obtained the mass ratio q = 0.404, orbital inclination i = 87.1◦ and effective temperature of the secondary component Teff = 5370 K. An effective temperature for the primary component Teff = 8500 K was assumed from the spectroscopic results. We detected two δ Scuti-type pulsation frequencies of f1 = 32.6894 c/d and f2 = 36.6714 c/d from the multiple frequency analysis of the residuals which were calculated by subtracting the synthetic eclipsing light curve (solid lines in Fig. 1) from the data. 70 Physical properties of the oEA star IV Cas Figure 1: Phase diagram of IV Cas References Gray R. O., Corbally C. J., 1994, AJ, 107, 742 Kim S.-L., Lee C.-U., Koo J.-R., et al., 2005, IBVS, 5669 Mkrtichian D. E., Kusakin A. V., Rodrı́guez E., et al., 2004, A&A, 419, 1015 Wilson R. E., Devinney E. J., 1971, ApJ, 166, 605 Comm. in Asteroseismology Vol. 150, 2007 Pulsating components of eclipsing binaries from the ASAS-3 data Gabriela Michalska, Andrzej Pigulski Instytut Astronomiczny Uniwersytetu Wroclawskiego, Wroclaw, Poland Abstract We report detection of pulsating components in 14 eclipsing binaries as a result of the search among over 10 000 stars from the public ASAS-3 database. In addition, we found evidence for eclipses in the VV Cephei-type star FR Sct. Introduction It is well known that the combination of the light curve of an eclipsing binary with its doublelined spectroscopic orbit provides direct way to the determination of masses and radii of the components. These parameters are crucial in modelling stars and are extremely useful when a component is pulsating. Semi-detached and detached systems that could already have undergone mass-transfer episodes are especially interesting in this context. If the mass-gainer is pulsating, its internal structure and pulsation properties might be different from those of a single star. This is the case of mass-accreting pulsating components in Algols, called ‘oscillating EA’ (oEA) systems (Mkrtichian et al. 2004) which are now intensively studied. If the components are close enough, we may also investigate the influence of tidal effects on pulsations. In this paper we present the results of a search for pulsating components among over 10 000 stars from the public ASAS-3 database (Pojmański 2001) classified as eclipsing binaries. The results We found 14 eclipsing binaries which have pulsating components. Six stars with well-defined Algol-type light curves (HD 62571, HD 99612, HD 220687, MX Pav, IZ Tel, and VY Mic) show also changes with periods shorter than 0.11 d. They are therefore very good candidates for oEA systems in which the primary star is a δ Scuti-type pulsator while the late-type secondary fills its Roche lobe. This classification of the primary as δ Scuti-type pulsator is in accordance with the published spectral types ranging from A2 to F0. For two stars, HD 62571 and HD 220687, more than one periodicity was detected. In the ASAS-3 photometry of the next four systems with almost equal depths of eclipses, we found changes with periods ranging from 0.12 to 0.21 d. They could be also attributed to δ Scuti-type variability. For two stars, CPD-60◦ 871 and HD 94529, this is confirmed by their spectral types. However, the two other stars, CPD-41◦ 5106 and CPD-31◦ 6830, have no spectral type available and therefore they might be β Cephei pulsators as well. Another system in our list, ALS 1135, is a member of the OB association Bochum 7. The system consists of an O6.5[(f)] and a B1V component (Fernández Lajus & Niemela 2006). In addition to the eclipses, we found variations with a period of 0.4327 d. The period seems to be too long for a β Cephei star, unless the pulsations originate in the O-type primary. In such stars, modes with longer periods are predicted by theory. Three stars with sinusoidal variations with periods of 0.6 – 1.1 d, typical for SPB-type pulsations, were also found among eclipsing binaries. For two of them, HD 251168 and V4396 Sgr, this is confirmed by their late B spectral types. The third star, Y Cir, is slightly 72 Pulsating components of eclipsing binaries different, because it shows an Algol-type light curve and the spectral type of primary is A2. Still, because this spectral type is uncertain, the SPB classification is the most likely one. We have also found clear evidence for eclipses in FR Sct, a VV Cephei-type binary composed of an M-type supergiant and an O-type star (M3 Iaep + O9.5 V). The orbital period of 3.53393 d, deduced from the eclipses, must not be attributed to this pair. The most suitable explanation is that the hot component is itself a binary and we see eclipses in this system. It is therefore very likely that FR Sct is an hierarchical system consisting of three very massive stars. Acknowledgments. This work was supported by the MNiI grant 1 P03D 016 27. The authors are grateful to the EC for the establishment of the European Helio- and Asteroseismology Network HELAS, which made their participation at this workshop possible. References Fernández Lajús E., Niemela V. S., 2006, MNRAS, 367, 1709 Mkrtichian D. E., Kusakin A. V., Rodrı́guez E., et al., 2004, A&A, 419, 1015 Pojmański G., 2001, in Paczynski B., Chen W.-P., Lemme C., eds, ASP Conf. Ser. Vol. 246, Small Telecsope Astronomy on Global Scales. Astron. Soc. Pac., San Francisco, p. 53 Pawel Moskalik and Gabriela Michalska wandering around the posters. Comm. in Asteroseismology Vol. 150, 2007 A theoretical scenario for PMS δ Scuti stars A. Ruoppo,1,2 M. Marconi,2 M. Marques,3,4,5 M. J. P. F. G. Monteiro,4,5 J. Christensen-Dalsgaard,6 F. Palla,7 V. Ripepi 2 1 3 Dipartimento di Scienze Fisiche, Università Federico II, Napoli, Italy 2 INAF-Osservatorio Astronomico di Capodimonte, Napoli, Italy Universidade de Coimbra, Departamento de Matemática - FCTUC, Portugal 4 Departamento de Matemática Aplicada, Universidade do Porto, Portugal 5 Centro de Astrofı́sica da Universidade do Porto, Portugal 6 DASC and Institut for Fysik og Astronomi, Aarhus Universitet, Denmark 7 INAF-Osservatorio Astrofisico di Arcetri, Firenze, Italy Abstract Nonradial pulsation models have been computed by means of the Aarhus adiabatic code along an extensive set of CESAM PMS evolutionary tracks. A theoretical tool for the interpretation of observed periodicities is proposed. Introduction Pre-Main sequence (PMS) δ Scuti stars are intermediate mass stars that cross the pulsation instability strip of more evolved classical pulsators during their evolution towards the Main Sequence. The number of discovered pulsating PMS stars is growing, but only a few stars have been studied in detail. As a consequence, the overall properties of this class of variables are still poorly determined. In this context we present our first results based on an extensive grid of evolutionary PMS models computed using the CESAM (Morel 1997) code to which the Aarhus adiabatic code (http://astro.phys.au.dk/∼jcd/adipack.n/) is applied for the determination of the frequencies. This method can be in principle applied to other classes of pulsating stars and is expected to work best for variables pulsating in a large number of modes in the asymptotic frequency regime. A method to reproduce observed frequencies The steps we follow to compare the observed pulsation frequencies with the theoretical ones are: (1) to determine a range in mass and in the expected large frequency separation (Δν) based on the available estimates of luminosity and effective temperature; (2) to estimate Δν from the frequency data; (3) to reduce the mass range by using the observed Δν; (4) to compare the predicted frequencies with the observed ones in the echelle diagram for the selected models; (5) to provide the best fit model stellar parameters and a mode identification. Further details can be found in Ruoppo et al. (2007). The predictive capabilities of the method are tested by applying it to a test star (star1), that is a PMS stellar model computed using the STAROX code (Roxburgh 2005, http://www.astro.up.pt/corot/) with the pulsation radial and non radial frequencies computed using the POSC code (Monteiro 1996). Application of our procedure allows us to define the following ranges in mass and Δν for star1: 1.6 < M/M < 3.4 , 20 μHz< Δν < 80 μHz. We compared the simulated frequencies with the theoretical ones in the echelle diagram by varying Δν in the range determined above. The best agreement (see Fig. 1) is obtained for a PMS model with M = 2M , Teff = 8184 K. The obtained mass coincides with the true one whereas the effective temperature differs from 74 A theoretical scenario for PMS δ Scuti stars Figure 1: The best echelle diagram for Star1: the harmonic degree varies from 0 to 2 while the radial order ranges from 1 to 15. the true one by less than 250 K. Moreover, our best-fit model reproduces all the observed frequencies, with the correct mode identification. We note that we have not taken into account rotation that is expected to change the identification obtained for non-radial modes and shift the frequencies (more detail can be found in Ripepi et al. 2007 and Ruoppo et al. 2007). Acknowledgments. We thank the anonymous referee for valuable comments. References Monteiro M. J. P. F. G., 1996, PhD Thesis, Queen Mary College, Univ. of London, UK Morel P., 1997, A&AS, 124, 597 Ripepi V., Bernabei S., Marconi M., et al., 2007, A&A, 462, 1023 Ruoppo A., Marconi M., Marques M., et al., 2007, A&A, in press Comm. in Asteroseismology Vol. 150, 2007 44 Tau: Discrimination between MS and post-MS models P. Lenz,1 A. A. Pamyatnykh,1,2,3 M. Breger,1 V. Antoci 1 1 2 3 Institut für Astronomie, Türkenschanzstrasse 17, 1180 Vienna, Austria Copernicus Astronomical Center, Bartycka 18, 00-716 Warsaw, Poland Institute of Astronomy, Pyatnitskaya Str. 48, 109017 Moscow, Russia Observations and Mode Identification Antoci et al. (2006) analysed photometric data of 44 Tau from 2000 − 2003 and detected 29 oscillation frequencies of which 13 are independent. We performed a mode identification based on the amplitude ratios and phase differences from the photometric data set of 2000/01. As shown by Daszyńska-Daszkiewicz et al. (2003), the results are very sensitive to the treatment of convection in the envelope. We find that in the case of 44 Tau only models with ineffective convection (αconv ≈ 0) result in definitive mode identifications. The observed modes f1 (6.8980 c/d) and f5 (8.9606 c/d) can definitely be identified as = 0 modes. Their frequency ratio 0.7698 is close to the typical ratio of the radial fundamental and first overtone frequencies in the δ Scuti domain. Four modes are identified as = 1 and two other modes as = 2 modes. Two = 1 modes (9.1175 and 9.5613 c/d) and both = 2 modes look to be close to the avoided crossing stage and may be used as indicators of the efficiency of overshooting from the stellar convective core. Modelling 44 Tau From the HIPPARCOS parallax, Strömgren and Geneva photometry and from the Vienna grid of stellar atmospheres (Nendwich et al., 2004) we derive log L/L = 1.34 ± 0.07 and Teff = 6900 ± 100 K. With a log g value of 3.6 ± 0.1 it is not possible to determine the evolutionary status of 44 Tau unambiguously. Our main sequence models of 44 Tau that can fit the radial fundamental and first overtone generally are too cool and in some cases too faint. An acceptable fit of all identified modes can be obtained only for enhanced metal abundance and/or significant overshooting from the convective core. In the post-MS case it is possible to obtain a model within the observational error box in the HR Diagram with no need of overshooting and nonstandard chemical composition. For post-MS models we predict much more unstable modes than we observe. A possible explanation why only specific modes are observed is mode trapping in the stellar envelope. The predicted frequency spectra for the MS and post-MS case are given in Fig. 1. Conclusions For both MS and post-MS models it is possible to obtain good fits to the observed frequency spectrum. However, the MS models are significantly cooler than it can be estimated from photometry. Considering the good fit of both the observed frequencies and physical parameters, standard post-main sequence models with inefficient convection seem to be preferable. Acknowledgments. We would like to thank Rafa Garrido and Juan Carlos Suárez for valuable discussions during the conference. This work has been supported by the Austrian FWF. AAP acknowledges the financial support from HELAS and from the Polish MNiI grant No. 1 P03D 021 28. 76 44 Tau: Discrimination between MS and post-MS models Figure 1: Comparison of the predicted frequency spectrum with observations for a selected main sequence model (upper panel) and a post-MS model (lower panel). In the post-MS case trapped = 1 modes are indicated by different symbols. References Antoci V., Breger M., Rodler F., Bischof K., Garrido R., 2007, A&A, 463, 225 Daszyńska-Daszkiewicz J., Dziembowski W. A., Pamyatnykh A. A., 2003, A&A 407, 999 Nendwich J., Heiter U., Kupka F., Nesvacil N., Weiss W. W., 2004, Comm. Asteroseis., 144, 43 Comm. in Asteroseismology Vol. 150, 2007 An asteroseismic Main Sequence model for the δ Scuti star 44 Tau R. Garrido,1 J. C. Suárez,1,2 A. Grigahcène,3 M. A. Dupret,2 A. Moya 1 1 Instituto de Astrofı́sica de Andalucı́a (CSIC), Granada, Spain 2 Observatoire de Paris-Meudon, France 3 Observatoire d’Alger, CRAAG, Algeria Antoci et al. (2007) have found that 44 Tau oscillates with 13 independent frequencies with amplitudes higher than the observational limit of 0.6 mmag. The observations were made in the two Strömgren filters (v,y) which allow good discrimination of the spherical harmonic of the corresponding non-radial mode, as it was shown by Garrido et al. (1990). The star has Teff = 6900 ± 150K ; log g = 3.6 ± 0.05 (log L/L = 1.3 ± 0.2) and solar ([M/H] = 0.0 ± 0.1) composition. Different diagnostic diagrams for amplitude ratios and phase differences have been calculated using the “time-dependent convection (TDC)” described by Grigahcène et al. (2005) and Dupret et al. (2004) together with atmospheric parameters taken from Heiter et al. (2002) and Barban et al. (2003). All of these point to the tentative modal identification depicted in Table 1. The ratio f1 /f5 = 0.7698 ± 0.0005 indicates that these two frequencies correspond to the radial fundamental and first overtone. We can then use the Petersen diagrams to fix the evolutionary status of 44 Tau. Rotation is very low and has not been taken into account (see Suárez et al. 2006). Models with 1.85 M and solar composition do not fit the frequency ratio at the required period. We have tried different masses, compositions and overshooting parameters and the only reasonable combinations allow masses from 1.90 to 2.00 M and main sequence models (i.e. hydrogen not yet exhausted in the core). Work is in progress to find the best model (in a least squares sense) but the closest theoretical frequencies to those observed which agree with the mode identification indicated in Table 1 are for a model with 1.94 M , αov = 0.3, [M/H] = 0.10 and an age of 1130 Myr where the “avoiding crossing” phenomenon is present. The predicted range of instability depends on the α parameter: low values represent better the excited range of this star when time dependent convection theory is used. In conclusion, the observed frequencies of 44 Tau can be theoretically explained by a Main Sequence model of 1.94 M with a small metal overabundance and a moderate overshooting at an effective temperature 150 K lower than indicated by the photometric calibration. All the proposed frequencies fit the following constraints: colour identification, instability range, photometric visibility and period ratios for radial modes (Petersen diagrams). Besides, if our identification is correct, then values up to 2 are visible in this star, at the above mentioned photometric precision, and then three more new frequencies are predicted to be unstable in the observed range which could be detectable from new ground based observations. Acknowledgments. We would like to thank Alosha Pamyatnykh for valuable discussions during the conference. This work has been supported by the PNE project ESP2004-083855C03-C01. 78 An asteroseismic Main Sequence model for the δ Scuti star 44 Tau Table 1: Observed frequencies, amplitude ratios, phase differences and identifications of the 13 pulsation modes of 44 Tau. Freq f1 f2 f3 f4 f5 f6 f7 f8 f9 f10 f11 f12 f13 ν (c/d) 6.8980 7.0060 9.1175 11.5196 8.9606 9.5613 7.3034 6.7953 9.5801 6.3390 8.6394 11.2946 12.6967 v/y 1.459 ± .006 1.45 ± .01 1.46 ± .01 1.43 ± .01 1.44 ± .01 1.46 ± .01 1.48 ± .03 1.41 ± .06 1.49 ± .1 1.35 ± .1 1.34 ± .1 1.58 ± .5 1.48 ± .9 v-y (degrees) 3.2 ± 0.3 -1.8 ± 0.6 -1.9 ± 0.5 -2.0 ± 0.6 1.5 ± 0.7 -0.8 ± 0.5 -9.5 ± 1.6 -9.5 ± 2.2 -8 ± 3 -8 ± 3 -4 ± 5 2±8 14 ± 14 0 1 1 1 0 1 2 2 2 2 1 or 2 any any Identification F g4 g2 f1 1H g1 g4 g5 g2 g6 g3( = 2) 2H f( = 2) References Antoci V., Breger M., Rodler F., Bischof K., Garrido R., 2007, A&A, 463, 225 Barban C., Goupil M.-J., Van’t Veer-Menneret C., et al., 2003, A&A, 405, 1095 Dupret M.-A., Grigahcène A., Garrido R., Gabriel M., Scuflaire R., 2004, A&A, 414, L17 Garrido R., Garcı́a-Lobo E., Rodrı́guez E., 1990, A&A, 234, 262 Grigahcène A., Dupret M.-A., Gabriel M., Garrido R., Scuflaire R., 2005, A&A, 434 1055 Heiter U., Kupka F., van’t Veer-Menneret C., et al., 2002, A&A, 392, 619 Suárez J. C., Garrido R., Goupil M.-J., 2006, A&A, 447, 649 Comm. in Asteroseismology Vol. 150, 2007 The Nainital-Cape Survey: contributions to asteroseismology of CP stars S. Joshi,1 V. Girish,2 P. Martinez,3 D. W. Kurtz,4 R. Sagar,5 S. Seetha,2 D. L. Mary,6 B. N. Ashoka 2 1 Inter-University Centre for Astronomy and Astrophysics (IUCAA), Ganeshkhind, Pune 411007, India 2 ISRO Satellite Centre, Air Port Road, Bangalore 560017, India 3 South African Astronomical Observatory (SAAO), PO Box 9, Observatory 7935, South Africa 4 Centre for Astrophysics, University of Central Lancashire, Preston PR1 2HE, UK 5 Aryabhatta Research Institute of Observational Sciences (ARIES), Manora Peak, Nainital 263129, India 6 Astronomisches Rechen-Institut am Zentrum für Astronomie, 69120 Heidelberg, Germany Abstract We present a progress report on the Nainital-Cape Survey. Pulsations of the δ Scuti type have been discovered in the chemically peculiar A-type stars HD 13038, HD 13079, HD 98851, HD 102480, HD 113878 and HD 118660. HD 12098 has been discovered to be a roAp star. We have also detected evidence for roAp-like 6.1-minute oscillations in the Am star HD 207561. The Nainital-Cape Survey The “Nainital-Cape Survey” was initiated in 1997 to search for pulsations in chemically peculiar stars in the Northern Hemisphere. This is a collaboration involving the Aryabhatta Research Institute of Observational Sciences (ARIES), Nainital; the Indian Space Research Organization, and the South African Astronomical Observatory. The strategy adopted for the survey was to select candidates having Strömgren indices similar to those of the known variable Ap and Am stars (Martinez et al. 2001). Photometric observations were carried out from ARIES using a three-channel fast photometer attached to the 1.0-m Sampurnanand telescope. The time-series photometric observations consist of continuous 10-s integrations obtained through a Johnson B filter and a photometric aperture of 30 . The data reduction process comprises removing bad data points, correction for coincident counting losses, subtraction of the interpolated sky background and correction for the mean atmospheric extinction. The reduced time-series data are then Fourier-analysed to reveal their component frequencies. Table 1 lists eight newly discovered variables. The evolved Am stars HD 98851 and HD 102480 exhibit pulsations with alternating high and low maxima, with a period ratio of ∼ 2:1. HD 12098 was discovered to be a roAp star pulsating with a period of 7.6 min. We have also found evidence of possible roAp oscillations with a period of 6.1 min in the star HD 207561. More details on these objects and the null results of the survey can be found in the papers by Martinez et al. (2001) and Joshi et al. (2006), as well as in the other references cited here. Acknowledgments. SJ acknowledges CSIR (No:TG/2235/06-HRD) and DST (No. SR/PF/839/2006-2007), Government of India, for providing a travel grant to attend the Vienna Workshop on the Future of Asteroseismology. P. Martinez acknowledges support from the South African DST and NRF for this joint project. 80 The Nainital-Cape Survey Table 1: Pulsating variables newly discovered in the course of the Nainital-Cape survey. Star HD 12098 13038 13079 98851 P1 (min) 7.6 28.0 73.2 81.0 P2 (min) 34.0 162.0 102480 156.0 84.0 113878 118660 207561 138.6 60.0 6.1? 151.2 - Comments References roAp star δ Scuti star δ Scuti star Alternating highand low-maxima Alternating highand low-maxima δ Scuti star Multi-periodic Possible roAp star Girish et al. 2001 Martinez et al. 2001 Martinez et al. 2001 Joshi et al. 2003 Joshi et al. 2003 Joshi et al. 2006 Joshi et al. 2006 Joshi et al. 2006 References Girish V., Seetha S., Martinez P., et al., 2001, A&A, 380, 142 Joshi S., Mary D. L., Martinez P., et al., 2006, A&A, 455, 303 Joshi S., Girish V., Sagar R., et al., 2003, MNRAS, 344, 431 Martinez P., Kurtz D. W., Ashoka B. N., et al., 2001, A&A, 371, 1048 Comm. in Asteroseismology Vol. 150, 2007 Vertical structure of pulsations in roAp stars M. Sachkov,1 T. Ryabchikova,1,2 O. Kochukhov,3 D. Lyashko 4 1 3 Institute of Astronomy, Russian Academy of Science, 48 Pyatnitskaya str., 119017 Moscow, Russia 2 Institute of Astronomy, University of Vienna, 1180 Vienna, Austria Department of Astronomy and Space Physics, Uppsala University, Box 515, SE-751 20 Uppsala, Sweden 4 Tavrian National University, Yaltinskaya 4, 330000 Simferopol, Ukraine Abstract We present a detailed analysis of the vertical cross-section of the pulsation modes of roAp stars. We use unique properties of roAp stars, in particular their chemical stratification, to resolve the vertical structure of p-modes and to study the propagation of pulsation waves. The aim of this analysis is to derive a complete picture of the depth-dependence of amplitudes and phases of magnetoacoustic waves from the variability of hundreds of spectral lines of different elements/ions. Spectroscopic observations The main observational data set analysed in our study consists of 958 observations of eight roAp stars (HD 9289, HD 12932, HD 19918, HD 101065, HD 122970, HD 128898, HD 134214, HD 137949), obtained with the UVES instrument at the ESO VLT between October 8, 2003 and March 12, 2004 in the context of the observing program 072.D-0138. The ESO Archive facility was used to search and retrieve science exposures and the respective calibration frames. Observations of each target cover 2 hours and consist of an uninterrupted high-resolution spectroscopic time-series with a total number of exposures ranging from 69 to 265. The length of individual exposures was 40s or 80s , except for the brightest roAp star HD 128898 (α Cir), for which a 1.5s exposure time was used. Details of these observations are given by Kurtz et al. (2006). In addition, we used the observations of HD 24712 obtained on November 11, 2004 in the DDT program 274.D-5011 (92 time-resolved spectra collected with UVES) and 70 observations of HD 201601 (γ Equ) obtained on 19 August, 2003 with the NES spectrograph attached to the 6-m telescope of the Russian Special Astrophysical Observatory. Phase-amplitude diagrams The radial velocities were measured with a centre-of-gravity technique. We used only unblended or minimally blended lines. It was shown (Sachkov et al. 2006) that a model of nonadiabatic nonradial pulsations (Saio 2005) calculated for the roAp star HD 24712 roughly explains amplitude and phase changes from the photospheric level up to log τ5000 = −4: amplitude and phase increase towards the outer layers. Model calculations do not extend above this level, but observations show that the phases continue to increase gradually from one element/ion to another (see also Fig. 1 in Kochukhov, these proceedings). This was interpreted as a propagation of the pulsation wave through the stellar atmosphere: the later in time a pulsation wave reaches its maximum, the higher in the atmosphere a chemical element is concentrated. Consequently, the pulsation phase can be used to study the vertical structure of pulsation modes. 82 Vertical structure of pulsations in roAp stars We propose to use the phase-amplitude diagrams as a first step in the interpretation of roAp pulsational observations. Such an approach has an advantage of being suitable to compare the pulsational behaviour of different elements, while the phase/amplitude dependence on the line intensity may be applied to one element only because of the chemical stratification. This analysis requires accurate measurements of both amplitudes and phases of many lines including weak ones. Therefore, our sample was limited to slowly rotating roAp stars. In all stars we have detected pulsational variability in the lines of the rare-earth elements (REE), which show maximum radial velocity (RV) amplitude. Except 33 Lib, no pulsations were detected in the lines of the elements lighter than Sr. The lowest significant RV amplitudes were derived for the Yii lines. Finally, for the first time we found pulsations in doublyionized thorium lines in four coolest roAp stars of our sample: HD 101065, HD 122970, HD 24712 and HD 134214. Similar to REEs, thorium shows a characteristic abundance anomaly: a 1 – 2 dex difference in the element abundance derived from the lines of the first and second ions. We attribute this anomaly to a strong vertical stratification similar to REEs – a layer with 4 – 5 dex overabundance above log τ5000 = −4. At present thorium is the heaviest element with this kind of stratification which shows measurable pulsation amplitudes. Although the overall pulsational behaviour of roAp stars is different, we found certain common features. The phase shifts of the RV curves are arranged in the following sequence: • The lowest RV amplitudes are detected in the layers of the Euii (and Fe in 33 Lib) line formation, then they go through the layers where the Hα core, Nd and Pr lines are formed, reach maximum and after that, show a decrease of amplitude in most stars; • the phases of the RV curves of the first ions are always followed by the second ones; • the largest phase shifts are detected in Tbiii and Thiii lines; • in the atmospheres of roAp stars with pulsation frequencies much below the cut-off frequency, the pulsations have a standing wave character in the deeper layers and then behave like a running wave in the outer layers. In three stars: HD 24712, HD 134214, α Cir, which have pulsation frequency close to (or even higher than) the cut-off frequency, the pulsation wave is running from the deeper layers. • the Yii lines show the lowest detectable RV amplitudes. However, their phases differ by ≈0.5 periods from other weakly pulsating lines. This may be an indication of the existence of pulsation node in deep photospheric layers, in agreement with theoretical predictions. Acknowledgments. This work was supported by the RFBR grant 04-02-16788, by the Presidium RAS program ’Non-stationary phenomena in astronomy’. MS also gratefully acknowledges the support of RF president grant MK-954.2005.2. References Kurtz D. W., Elkin V. G., Mathys G., 2006, MNRAS, 370, 1274 Sachkov M., Ryabchikova T., Bagnulo S., et al., 2006, Mem. Soc. Astron. Ital., 77, 397 Saio H., 2005, MNRAS, 360, 1022 Comm. in Asteroseismology Vol. 150, 2007 Non-LTE line formation in the atmospheres of Ap stars: importance for pulsational analysis of roAp stars T. Ryabchikova,1,2 L. Mashonkina,1 A. Ryabtsev,3 R. Kildiyarova,3 M. Khristoforova 4 1 Institute of Astronomy, Pyatnitskaya 48, 119017, Moscow, Russia Institute of Astronomy, University of Vienna, 1180 Vienna, Austria 3 Institute of Spectroscopy, Troitsk, Moscow region, Russia 4 Institut für Astronomie und Astrophysik der Universität München, München, Germany 2 Abundance analyses of cool Ap stars have revealed a huge ionization imbalance in Pr ii – Pr iii and Nd ii – Nd iii which may reach 2 dex in the atmospheres of rapidly oscillating (roAp) stars (Ryabchikova et al. 2001). In an LTE analysis of one of these stars, γ Equ, Ryabchikova et al. (2002) interpreted the observed imbalance as a stratified Pr and Nd distribution with an accumulation of the elements above log τ5000 = −8. In upper atmospheric layers departures from LTE are expected. Therefore non-local thermodynamical equilibrium (NLTE) line formation should be considered to obtain theoretical line profiles and equivalent widths for a range of effective temperatures and Pr-Nd overabundances typical for cool Ap stars. Also, for a correct analysis of bisector pulsational measurements across the core of the Hα line, NLTE formation of hydrogen lines has to be taken into account. NLTE formation of Nd ii/Nd iii lines was studied by Mashonkina et al. (2005). Here we present calculations of the statistical equilibrium of Pr ii – Pr iii in the atmospheres of A-type stars, and NLTE formation of the hydrogen lines. The code DETAIL (K. Butler, private communication) based on the Accelerated Lambda Iteration method was used in Pr and Nd calculations and the NONLTE3 code (Sakhibullin 1983) was used for the hydrogen lines. The final model atoms include: • 19 levels of H i, • 203 Pr ii combined levels + 54 Pr iii combined levels + the Pr iv ground state, • 247 Nd ii combined levels + 68 Nd iii combined levels + the Nd iv ground state. In this study, we calculated energy levels and transition probabilities for Pr ii – iii and Nd ii – iii. For other atoms/ions, the data were extracted from the NIST (Martin et al. 1978) and VALD (Kupka et al. 1999) databases. We used photoionization cross-sections for hydrogen. For the REE elements, electron collision cross-sections were calculated for allowed transitions following van Regemorter (1962). For hydrogen, the recent electronimpact excitation data of Przybilla & Butler (2004) were used for transitions between energy levels with n ≤ 7 and the approximation formula of Johnson (1972) for the remainder. Electron-impact ionization rates were calculated applying the Seaton formula as described by Mihalas (1978). In the atmospheres with Teff between 7250 K and 7700 K H i is still the dominant ionization stage and at each depth point the ground state keeps its thermodynamical level population. However, excited levels are subject to non-thermal excitation effects such that the second level is underpopulated and the third one is overpopulated relative to the corresponding LTE number densities in the layer between log τ5000 = −1 and −3. In the upper layers, up to log τ5000 = −4.5, the second level shows an opposite effect and its departure coefficient, b2 > 1, decreases outwards, while b3 reaches its maximum value around log τ5000 = −3. This behaviour explains the weakening of the core-to-wing transition in the NLTE Hα profile compared to the LTE one. Our calculations for chemically homogeneous Ap atmospheres with +3 dex Pr overabundance show that the NLTE corrections for Pr ii lines grow rapidly with the effective temperature, but they stay nearly constant for Pr iii lines. NLTE effects in chemically homogeneous 84 Non-LTE line formation in the atmospheres of Ap stars: importance for pulsational analysis of roAp stars atmospheres may explain no more than 0.6 dex in the 1 – 2 dex ionization imbalance (REE anomaly), observed in cool roAp stars. Because a statistical equilibrium of Pr ii and Nd ii depends strongly on radiative b-f transitions, the test NLTE calculations have been made for the stratified abundance distribution with multiplying the photoionization cross-sections for hydrogen by scaling factors of 100 and 0.01. An increase of the photoionization cross-sections for hydrogen does not, in fact, affect NLTE line formation, while a decrease of the cross-sections leads to a reduction of the NLTE effects. A step distribution of Pr and Nd with a steep 4 dex increase of the abundance of both elements towards the upper layers starting at log τ5000 ≈ −3.5 in the atmosphere of roAp star HD 24712 allows to explain the observed REE abundance anomalies. In the first approximation an influence of the star’s ∼ 3 kG magnetic field was accounted for by using a pseudo-microturbulence of 1 km s−1 . We checked a change in line depth formation caused by Zeeman splitting. The line profile of Pr iii 5300 calculated with the magnetic spectral synthesis code SYNTHMAG (Piskunov 1999) was approximated by a sum of triplet Zeeman components. Magnetic desaturation results in a shift of the line depth formation by 0.6 dex (in log τ5000 scale) towards the deeper atmospheric layers. Taking into account both the photoionization cross-section uncertainty and magnetic effects we conclude that the error in the position of the Pr and Nd abundance jumps may be as large as ±0.5 – 0.6 dex. NLTE depth formation of the Hα core, Pr and Nd lines was used to explain the observed pulsational radial velocity (RV) amplitudes and phases in the atmosphere of HD 24712 (see Fig. 1 by Kochukhov 2007). Tracing the region between Hα core formation and the upper atmosphere, pulsational phase values of different elements gradually increase. A step in pulsational phase between the Hα core and Pr lines may be caused by limitations of our modelling, e.g. the model fit to the Hα core is still unsatisfactory and vertical Pr and Nd distributions can only be schematically determined. However, we can reconstruct and explain pulsational phenomena in atmospheres of roAp stars only by detailed studies of spectral line formation. Acknowledgments. This work was supported by RFBR grant 04-02-16788, and by the Presidium RAS program ’Non-stationary phenomena in astronomy’. TR thanks the Austrian Science Fund (FWF-P17580N2) for partial financing. References Johnson L. C., 1972, ApJ, 174, 227 Kochukhov O., 2007, these proceedings Kupka F., Piskunov N., Ryabchikova T. A., Stempels H. C., Weiss, W. W., 1999, A&AS, 138, 119 Martin W. C., Zalubas R., Hagan L., 1978, Atomic energy levels - The rare-Earth elements. National Bureau of Standards, U.S. Department of Commerce Mashonkina L., Ryabchikova T., Ryabtsev A., 2005, A&A, 441, 309 Mihalas D., 1978, Stellar Atmospheres, 2nd Edition, Freeman, San Francisco Piskunov N. E., 1999, in Nagendra K., Stenflo J., eds, Astrophysics and space science library, Vol. 243, 2nd International Workshop on Solar Polarization. Kluwer, Dordrecht, p. 515 Przybilla N., Butler K., 2004, ApJ, 610, L61 Ryabchikova T. A., Savanov I. S., Malanushenko V. P., Kudryavtsev D. O., 2001, Astron. Rep., 45, 382 (Erratum: Astron. Rep., 46, 696) Ryabchikova T., Piskunov N., Kochukhov O., et al., 2002, A&A, 384, 545 Sakhibullin N. A., 1983, Kazanskaia Gorodskaia Astron. Obs., 48, 9 van Regemorter H., 1962, ApJ, 136, 90 Comm. in Asteroseismology Vol. 150, 2007 First Magnetic Doppler Images of a roAp star T. Lüftinger,1 O. Kochukhov,2 T. Ryabchikova,1,3 W. W. Weiss,1 I. Ilyin 4 2 1 Institute of Astronomy, University of Vienna, 1180 Vienna, Austria Department of Astronomy and Space Physics, Uppsala University Box 515, SE-751 20 Uppsala, Sweden 3 Institute of Astronomy, Russian Academy of Sciences, Pyatnitskaya 48, 119017 Moscow, Russia 4 Astrophysikalisches Institut Potsdam, An der Sternwarte 16, D-14482 Potsdam, Germany Abstract We present the first analysis of the magnetic field geometry and elemental abundance distributions on the surface of a rapidly oscillating Ap (roAp) star, using an elaborate magnetic Doppler Imaging (MDI) code (Piskunov et al. 2002, Kochukhov et al. 2002), INVERS10, which allows to reconstruct simultaneously and consistently the magnetic field geometry and abundance distributions on a stellar surface without any a priori assumptions. We analysed Stokes I and V time series obtained with the SOFIN polarimeter and recovered the magnetic field and surface abundance structures of Fe and Nd (among others). These two elements are found to be anticorrelated. Introduction and MDI analysis Still very little is known about the origin and structure of magnetic fields and their connection and interaction with surface abundance patches, pulsation, and stratification. Ap stars exhibit magnetic fields that appear to be highly ordered, very stable, and often very strong. Many Ap stars also show dramatic line profile variations synchronized to stellar rotation, which is attributed to oblique magnetic and pulsation axes and to the presence of a non-uniform distribution of chemical elements on their surface. An important subgroup of the Ap stars, the rapidly oscillating Ap (roAp) stars, in addition, exhibit high-overtone, low-degree, non-radial p-mode pulsations with periods of 6 – 21 minutes. HD 24712 (HR 1217, DO Eri) is the best studied roAp star that was discovered to be a pulsator by Kurtz (1982). Matthews et al. (1988) found radial velocity variations with an amplitude of 0.4±0.05 km s−1 at the main photometric period of 6.14 min. We found atmospheric parameters of Teff =7350 K and log g = 4.2, and derived v sin i = 5.6 km s−1 . Spectropolarimetric observations of HD 24712 were carried out in October and November 2003, using the high resolution échelle spectrograph SOFIN, attached to Nordic Optical Telescope (NOT), La Palma, Spain, with a nominal resolving power of ≈ 80 000. Rotational phases of HD 24712 were calculated according to the ephemeris and rotation period obtained by Ryabchikova et al. (2005): HJD(Bz max ) = 2453235.18(40) + 12.45877(16) d. The determination of the geometry of the magnetic field on the surface of HD 24712 was performed choosing 7 different Fe i and 5 different Nd iii lines suitable for magnetic Doppler imaging. The tilt and the azimuth angle of the stellar rotational axis, i and Θ, were used as determined by Bagnulo et al. (1995): i = 137◦ and Θ = 4◦ . A clear dipolar geometry (Fig. 1) yielded the best fit to the observed Stokes I and V line profiles in our magnetic Doppler imaging analysis. The resulting magnetic field strength varies between +2.2 kG and +4.4 kG. The surface abundances of Fe and Nd mapped simultaneously with the magnetic field geometry are presented in Fig. 2. It can be clearly seen that the abundances of both elements are globally structured. Nd is extremely overabundant, varying between −8.0 and −7.0 dex (−10.59 dex solar). Both elements seem to be perfectly anticorrelated: Fe is accumulated where Nd is depleted, and minimum Fe abundance can be found where Nd is 86 First Magnetic Doppler Images of a roAp star at its maximum. We find that the Fe abundance enhancement region is associated with the area of minimum magnetic field strength around φ 0.5, whereas the Nd map shows its area of maximum abundance around the magnetic field maximum, where the positive magnetic pole is orientated towards the observer. The additional 14 chemical elements we mapped, including Mg, Ca, Sc, Ti, Cr, Co, Ni, Y, La, Ce, Pr, Gd, Tb, and Dy, exhibit comparable behaviour. Due to limited space, we are not able to present details for all elements in this paper and would like to refer to a forthcoming publication (Lüftinger et al. 2007). Figure 1: First mapping of the distribution of magnetic field strength (a) and field orientation (b) on the surface of a roAp star. Top: distribution of the field strength, bottom: orientation of the magnetic vectors. The black arrows correspond to field vectors pointing outwards the stellar surface, while grey vectors are pointing inside. Figure 2: The abundance distributions of Fe and Nd iii on the surface of HD 24712. These maps were derived using the Stokes I and V spectra. Acknowledgments. PP17890). This work was supported by the Austrian Science Fund (FWF- References Bagnulo S., Landi Degl’Innocenti E., Landolfi M., Leroy J. L., 1995, A&A, 295, 459 Kochukhov O., Piskunov N., 2002, A&A, 388, 868 Kurtz D. W., 1982, MNRAS, 200, 807 Lüftinger T., Kochukhov O., Ryabchikova T., Weiss W. W., Ilyin I., 2007, in Romanyuk I. I., Kudryavtsev D. O., eds, Magnetic Stars. Special Astrophysical Observatory, Russian Academy of Sciences, in press Matthews J. M., Wehlau W. H., Walker G. A. H., Yang S., 1988, ApJ, 324, 1099 Piskunov N., Kochukhov O., 2002, A&A, 381, 736 Comm. in Asteroseismology Vol. 150, 2007 Discussion on δ Scuti and roAp stars led by D. W. Kurtz Centre for Astrophysics, University of Central Lancashire, Preston PR1 2HE, UK Kaye: We’ve seen data for very fast rotators and some data for slow rotators. There’s the assumption made that you can map 1:1 the position in the line profile with the position across the stellar disk. There are times when that is an OK assumption and there are times when it is not. I leave to anybody to comment on that. Kurtz: I’m trying not to keep this on the topics that Oleg and I are interested in, but when you [to Kochukhov] said ”assumption-free” in your model for the pulsation what worries me is that you can use Nd or the rare earths that are concentrated towards the poles. So let’s imagine a radial pulsation where the amplitude is the same on the whole surface. When you go to the pole, the abundance is higher, the opacity is higher, you’re higher in the atmosphere and we know that there’s a depth effect, so you might just map the abundance instead of the real pulsation amplitude. Kochukhov: I had no time to mention this issue in my talk. In fact, the pulsation Doppler Imaging technique fully takes into account a non-homogeneous horizontal abundance structure. We have reconstructed horizontal chemical maps for many elements in HR 3831. None of the rare-earth ions (including Nd that was used in pulsation mapping) shows a strong abundance concentration at the magnetic poles. It is a common assumption, frequently used in studies of Ap stars, that rare-earth ions concentrate at the poles, but studies of real stars reveal different patterns for different ions. For instance, Eu is concentrated in small spots (which are offset from the magnetic poles), but there is no such concentration for Nd. Kaye: If you look at your data, you only have a limited number of pixels across your line profile, and each single pixel has signal to noise. So at a very slowly rotating star, where the line profiles become very narrow, even at very high resolution you’re not going to have that many pixels across the line profile. So when you draw your conclusions from that, it may be worthwhile to make some comment and take some care. Kochukhov: In my presentation, I did not discuss Doppler Imaging of slowly rotating stars. The only star for which indirect surface mapping of pulsations was applied so far is a fast rotator (v sin i ≈ 30 km s−1 ). Ryabchikova: We also presented the results of abundance mapping of HR 1217, with v sin i of 5.6 km/s. It was still possible for this star. Bedding: I’d like to remind you of the work by Ivan Baldry et al. on Hα . The rare earth elements are of course interesting, but you made the statement that 33 Lib was the only star with a node in the atmosphere. Ivan found a node in Hα for α Cir, and hydrogen is uniformly distributed over the surface. So I would like to remind both the observers and the theorists about Hα and its bisectors. Kochukhov: The problem is that these observations were done at very low resolution. In this case the blending of the wings of Hα with various rare-earth lines cannot be resolved. We now have very high-resolution time-resolved spectra of several roAp stars (including α Cir) from UVES and we can see different pulsation patterns in the rare-earth lines and in Hα . So, the results by Baldry et al. were really interesting, but the question is, was their interpretation correct and applicable to Hα or was the whole picture a result of unresolved blending of variable rare-earth lines with Hα ? 88 Discussion on δ Scuti and roAp stars Cunha: Moving back to theory, one of the limitations of the study of the influence of the magnetic field and rotation on the oscillations was that in practice the magnetic fields of these stars are larger than 1 kG. Therefore the effect of rotation isn’t obvious. When you look at the perturbations to the eigenfrequencies, you see that they follow a cyclic pattern, and that, at certain values of high frequencies or high magnetic field, they actually go through zero again, i.e. the eigenfrequencies don’t seem to be perturbed. Thus, the question is: if you go to higher magnetic field still, and find a frequency where the magnetic perturbation is close to zero, can the rotational effect become important again? Dziembowski: I promised Don Kurtz perhaps a year ago that I will calculate the effect, but I forgot. But I know the answer! The answer is that the magnetic frequency perturbation is in certain ranges very small, so that the rotational effects are again important. But then, one should see the asymmetry, but we don’t, so that’s a problem. Metcalfe: We know from the Sun that there is a latitude dependence of rotation. Is there any way to take this into account? Kochukhov: There is quite a large range of observations of spotted Ap stars, and the spottiness allows us to trace the movements of those chemical features over many rotation cycles. The answer is no, there is not a single observation that suggests that there is differential rotation. There are some models of the interaction of magnetic fields and differential rotation and they do not survive. Either the differential rotation kills the magnetic field or the magnetic field kills the differential rotation. Matthews: With MOST, we have a lot of observations of rotationally variable stars, including solar-type stars. We just submitted a paper showing the rotation profile of κ1 Ceti that has actually the same functional dependence as the Sun. We also have data for several Ap stars among our guide stars and we see absolutely no evidence for differential rotation in those stars. So I think it’s self-consistent with the spectroscopic data. Reed: Kind of relating the differential rotation of the δ Scuti stars, Mike Breger was saying earlier that all the slow rotators have stronger radial modes. Maybe it would be interesting for the theorists to investigate what the effects of differential rotation would be on the radial modes. Dziembowski: If you add solar-like differential rotation, you may couple radial modes not only to quadrupole modes, but also to = 4, = 6, and things become so complicated that for the time being, I would prefer to think only about uniform rotation. Michel: Considering the correlation between the amplitudes and v sin i for the δ Scuti stars, we studied a number of stars in a few clusters a few years ago. Therefore we knew we are dealing with stars on the main sequence. We found a correlation between amplitude and v sin i . We separated the two quantities v and sin i and found a correlation of the amplitude with sin i . We could understand this in the sense that the amplitude changes due to geometric projection effects, rather than something that’s directly related with the rotation rate. Breger: This correlation becomes quite difficult on the main sequence because you also have to consider that metallic-line A stars pulsate much less than normal stars and many show very slow rotation. The effort that you have done is valid, but it always becomes very difficult if there is more than one variable parameter. So the simple things become more complicated... Frandsen: As we also see for the Sun, even if you have a nice set of frequencies, you are in very bad shape for seismic modelling if you don’t have any additional constraints. Even for solar-type stars there are too many free parameters so that different models match the same frequencies. Maybe this will change when very precise observations become available, but I’m not even sure of that. Now for δ Scuti stars the situation is much worse because there is nothing in the distribution of the frequencies that helps to find out where you are in the frequency spectrum. Now, if you fix for instance the mass and chemical composition that might help you with the mode identification, and then there are a few free parameters less in your model fit, this gives a fantastic improvement in your chances to getting things right. D. W. Kurtz 89 You can work on eclipsing binaries, where you can determine the masses, or, as Eric already mentioned, in open clusters. The only problem with clusters is that the δ Scuti stars are faint, so you need big telescopes to get precise spectroscopic observations, which is a hassle. Paparo: Jadwiga showed a nice presentation of FG Vir, where we have many many modes, but finally she gave identifications only for the dominant modes. How can we use the many other modes if we don’t have identifications for them? Why do we need so many modes if we cannot use them? For many other δ Scuti stars we have information on the dominant modes. Have you used your method for these stars? How many stars have you investigated and did you find a case where the method failed? Daszynska: I start with the last question. We did β Cas, AB Cas, 20 CVn and 1 Mon. In all cases the method worked, especially when you add the radial velocity information because it is uncorrelated with the photometric observables. In all cases we got a mode identification and in all cases we found that convection should be rather inefficient. For FG Vir we got mode identifications for twelve modes because only those were detected in spectroscopy (we had two photometric passbands and radial velocity information). For modes with very high frequencies, above 30 c/d, we found instability only for very high-degree modes (with larger than 60). So, the low-amplitude peaks in FG Vir’s oscillation spectrum may correspond to high-degree modes of unknown azimuthal order, hence are not useful for asteroseismic probing. Breger: May I add to what Margit said: if you have, say, 100 frequencies, but a mode identification for only 12 of them, what about the other 88? It’s of course a question of the S/N ratio. If you get more colour photometry or spectroscopy, you can increase the number of identified modes. I was alluding to that earlier when I compared our ground-based work with space-based observations. At a certain point it doesn’t matter how many frequencies you have discovered, it is a matter of what you can do with the frequencies. Dupret: I would like to stress that for all stars towards the red edge of the instability strip (say Teff < 7500 K) it is important to include time-dependent convection in the models. It changes significantly the predictions of the f values, especially their phases. With this in a non-adiabatic code we can get a much better agreement with the observations. It’s not only important to use time-dependent convection for the mode identification, but also for the determination of the other parameters. For instance, the predictions are then less sensitive to the mixing-length parameter α, because of the control of the temperature variations by the energy equation throughout the time-dependent convective flux (high superadiabatic gradients leading to large phase lags in the H ionization zone are no longer allowed). Daszynska: We applied time-dependent convection to FG Vir. Dupret: The theoretical predictions depend also on what atmosphere models you use, not only the smoothness of the derivatives but also the physical prescriptions, for example the treatment of convection. Different physical prescriptions give very different monochromatic flux and limb darkening. Gamma Doradus stars and solar-like oscillators Comm. in Asteroseismology Vol. 150, 2007 Asteroseismology of γ Doradus Variables: Past, Present, and Future A. B. Kaye George Mason University, Department of Physics and Astronomy, Virginia 22030, USA Abstract In this paper, we present the current state of research of the γ Doradus phenomenon, review past work, and look towards possible future research opportunities. Although published observations have not yet yielded enough information for explicit asteroseismological solutions, recent space-based missions, coupled with intense, coordinated ground-based support and continued advances in the theoretical understanding of these variable stars will likely allow us to probe stellar interiors in the next several years. The Past More than 40 years ago, Cousins & Warren (1963) published a paper announcing the variability of γ Doradus. Future papers would identify other “variables without a cause,” all with spectral types close to F0 and luminosity classes of V, IV-V, or IV. Because of their unique place in the colour-magnitude diagram [overlapping the red (cool) edge of the δ Scuti instability strip and extending to redder colours], the specific physical mechanism causing the observed variations remained a contentious subject [see Abt, Bollinger & Burke (1983); Krisciunas et al. (1993); Zerbi, Mantegazza & Poretti (1994); Mantegazza, Poretti & Zerbi (1994); Balona, Krisciunas & Cousins (1994); Hatzes (1998)]. Early efforts at producing a catalogue of these variables for use by the community proved to be difficult, since their discovery was usually incidental to other efforts; stars with “mistaken identities” were still catalogued, but were relegated to a “Stars Formerly Under Consideration” (SFUC) list [see, e.g., Kaye, Henry & Rodrı́guez (2000; misclassified δ Scuti star) and Paparó et al. (2000; binary system tidal effects)]. Despite these minor setbacks, the γ Dor variables were defined as a class by Kaye et al. (1999a) who, based on informal discussions at a conference held in 1995 at Cape Town, South Africa (Stobie & Whitelock 1995), and upon several papers in the literature (e.g., Krisciunas et al. 1993; Balona et al. 1996; Zerbi et al. 1997a, 1997b; Poretti et al. 1997; Kaye 1998a; Kaye et al. 1999b), defined the class to consist of “variable stars with an implied range in spectral type A7–F5 and in luminosity class IV, IV-V, or V; their variations are consistent with the model of high-order (n), low-degree ( ), nonradial, gravity-mode oscillations.” The Present Since Cousins & Warren’s paper in 1963, more than 100 papers have been published on various observational aspects of γ Dor variables1 . As of the date of this meeting, the number of “bona fide” γ Dor stars stands at 54 (Henry, Fekel & Henry 2005). In addition to the continuous serendipitous discoveries, there have been a large number of dedicated searches for these variables. 1 The figure of 100 papers includes actual γ Dor variable discovery papers, analysis of data revealing the presence (or absence) of γ Dor stars, database searches for γ Dor stars, and an estimate of the large number of papers that discuss data analysis techniques relevant to these stars. This list of references, considered to be tentatively complete through June 2006, may be requested from the author. 92 Asteroseismology of γ Doradus Variables: Past, Present, and Future Database mining has resulted in the discovery of some γ Dor stars [including, e.g., the Hipparcos catalogue (Handler 1999); the Geneva Photometric Database (Eyer & Aerts 2000); and the R00 Catalogue (Rodrı́guez & Breger 2001)]; a number of space missions have retrieved data on γ Dor variables [including the Canadian MOST satellite; see Matthews (2007)], several space missions are likely to find even more [e.g., COROT (Mathias et al. 2006) and WIRE (see Bruntt, 2007)]; and ground-based networks have provided insights that no single observing site could reveal alone [e.g., the Whole Earth Telescope and the Delta Scuti Network; see Breger et al. (1997)]. Early studies suggested that the γ Dor phenomenon may be restricted to younger stars (Krisciunas et al. 1995b), and since then, more than 15 studies of clusters from NGC 6231 (Arentoft et al. 2001; log t ∼ 6.8) to the Pleiades (Martı́n & Rodrı́guez 2000; log t ∼ 8.1) to NGC 2420 (Kim et al. 2001; log t ∼ 9.0) support the claim that the γ Dor phenomenon is limited to stars younger than log t = 8.4 (see the discussion in Kim et al. 2001). A collection of some of the most notable γ Dor variables includes the following: Variable star class namesake: γ Doradus2 (Cousins & Warren 1963) Brightest γ Dor star in the Northern Hemisphere: 9 Aurigae (Krisciunas & Guinan 1990) γ Dor stars with identified pulsation modes: γ Doradus (Balona et al. 1996), 9 Aurigae (Aerts & Krisciunas 1996), HD 207223 (Aerts & Kaye 2001), HD 12901 (Dupret et al. 2005a; see also Moya et al. 2005), HD 48501 (Dupret et al. 2005a; see also Suárez et al. 2005) Chemically peculiar (λ Boötis-type): HR 8799 (Gray & Kaye 1999) Chemically peculiar (Am-type): HD 8801 (Henry & Fekel 2005), HD 100215 (Grenier et al. 1999), HD 221866 (Kaye, Gray & Griffin 2004) Part of a confirmed binary system: HD 7169 (Fekel et al. 2003), HD 19684 (Henry & Fekel 2002), HD 23874 (Fekel et al. 2003), HD 62454 (Kaye et al. 1998b), HD 86358 (Henry & Fekel 2003), HD 100215 (Griffin 2006), HD 105085 (Henry & Fekel 2003), HD 113867 (Henry & Fekel 2003), HD 160295 (Henry & Fekel 2003), HD 167858 (De Cat et al. 2006), HD 209295 (Handler et al. 2002), HD 221866 (Kaye, Gray & Griffin 2004) Also show p-mode pulsations: HD 8801 (Henry & Fekel 2005), HD 2092953 (Handler et al. 2002) It is interesting to note that although HD 8801 is reported to be an Am star (Henry & Fekel 2005), it is not among the list of confirmed binary γ Dor stars. If this is verified, HD 8801 will be a very unique object, showing both γ Dor and δ Sct variations as well as being one of a very few single Am stars (see Abt 1961, Abt 1965, and the more recent discussions in Noels, Montalbán & Maceroni 2004 and references therein). For completeness, we note that the MOST mission has tentatively reported the discovery of two similar stars (Matthews, 2007). 2 In addition to being the variable star class namesake, γ Doradus is the brightest star in the class (V = 4.24). At least some of the g-mode variations in HD 209295 are driven (or even amplified) by the tidal interactions between the two stars in this binary system (Handler et al. 2002). 3 A. B. Kaye 93 Theoretical Aspects While observers had a large head-start on theorists, theorists have also contributed a tremendous amount of work in this field. Between 1998 and the date of this conference, roughly 27 papers have been published on various theoretical aspects of γ Doradus stars. A detailed review of this work is provided by Dupret (2007), but a very short summary is provided here: • The first discussion of the γ Dor g -mode driving mechanism was published by Guzik et al. (2000). • The first purely theoretical instability strip for γ Dor stars was published by Warner, Kaye & Guzik (2003). • A revised theoretical instability strip using time-dependent convection was published by Dupret et al. (2004). • The discussion of the importance of convection-pulsation coupling in γ Dor stars was published by Dupret et al. (2004, 2005b) • The seventeenth international conference on stellar pulsation was held in Rome in June 2005; the proceedings of that conference were published in 2006 as volume 77 of the Memorie della Societá Astronomica Italiana. A significant portion of that volume contains cutting-edge research (including theoretical work) of γ Dor and δ Sct stars. The Future There has been a great deal of work done on γ Dor stars, and the results of progress reveal more information about this variable star class each year. There are, however, a number of issues that we still do not understand; four of the larger issues are discussed below4 . Edges of the instability strip As has been discussed in many papers, the number of known bona fide γ Dor stars is small (cf. the number of known δ Sct stars). This fact in and of itself makes it difficult to “map” the edges of the γ Dor instability strip by simply plotting each member on a colour-magnitude diagram [again, cf. the case for δ Sct stars; see Breger (1979)]. Several attempts have been made [see, e.g., Handler & Shobbrook (2002) and Henry & Fekel (2005)], but there are simply not enough objects to set “firm” instability strip boundaries based on observations (again, cf. Fig. 2 in Breger 1979 and Fig. 8 in Rodrı́guez & Breger 2001). Temporal dependence/stability of pulsation modes Some γ Dor stars show clear evidence of modes that are unstable over the course of several observing seasons. In this case, the term “unstable” is used to indicate modes that do not appear reasonably regularly from one observing season to the next. While some may suspect that this is due to the intrinsically difficult nature of analysing γ Dor data, this particular issue has been verified with double-blind tests using different software and different analytical and numerical techniques on the same sets of data. Interested readers are encouraged to examine the published literature on 9 Aurigae (see, e.g., Krisciunas et al. 1991; Krisciunas et al. 1993; Zerbi, Mantegazza & Poretti 1994; Mantegazza, Poretti & Zerbi 1994; Balona, Krisciunas & Cousins 1994; Krisciunas et al. 1995a; Aerts & Krisciunas 1996; Balona et al. 1996; Zerbi et al. 1997a); in addition, more than 10 years of BV differential photometry is now available on this object, yet the temporal dependence of the various modes is not understood. 4 The “mystery” of HD 8801 and the recently discovered similar objects are discussed in the previous section. 94 Asteroseismology of γ Doradus Variables: Past, Present, and Future Additional scatter at times of maximum brightness In several γ Dor variables, there is clear evidence of “extra” scatter at the time of maximum brightness that some liken to the Blazhko effect seen in RR Lyrae stars; the most often-cited (and thus, likely most extreme) example of this is HR 8799 (Zerbi et al. 1999) in which the additional scatter may be large compared to the observational scatter in other portions of the phased light curve (see, e.g., Fig. 1, below and Figs. 2, 8, 10, 14, 16, and 20 in Henry, Fekel & Henry 2005). Although this particular issue has not received a great deal of attention to date, it may be related to the temporal stability of the pulsational modes (see above) and thus be used to more fully understand this class of variable stars. Figure 1: Johnson V light curve phased using the primary period of HR 8799 showing the “extra” scatter at the time of maximum brightness (from Zerbi et al. 1999; see text for details). Presence and role of magnetic fields An early study by Kaye & Strassmeier (1998) on the Ca ii H&K lines in a collection of γ Dor stars reported that there was no significant chromospheric activity in any of the observed stars. Since the debate regarding the physical mechanism causing the variability of these stars was coming to a close and large starspots were being ruled out, this subject seemed moot. However, the driving mechanism of the gravity modes in these stars is linked directly to the thin convective shell in the outer portion of the star (see Guzik et al. 2000 and Dupret et al. 2004). The fine structure of this convective shell could potentially be affected by differential rotation (that would then result in a non-negligible dynamo-produced magnetic field). Since γ Dor stars are hot compared to “typical” spotted stars (e.g., RS CVn and BY Dra stars), the cores of the Ca ii H&K lines are washed out. A more useful indicator of chromospheric activity (and therefore of magnetic fields) is the He i D3 triplet at λ5876Å [for details, see Wolff, Heasley & Varsik (1985), Wolff, Boesgaard & Simon (1986); Rachford & Canterna (2000); Rachford (2000)]. A collection of high-SNR, high-resolution spectra in the λ5876Å region is in hand for a number of northern-hemisphere γ Dor stars, including a time series of spectra for 9 Aurigae. A. B. Kaye 95 The Path Ahead The future of γ Doradus research is bright. In addition to planned space missions dedicated to asteroseismology, there are new asteroseismological collaborations being formed each year. As a community, we continue to grow and thrive. George Mason University has recently completed the construction of a new on-campus observatory and will install a new 0.8-meter telescope within the next 18–24 months. Plans for this telescope revolve around asteroseismology, and the potential for new collaborations with nearby institutions are promising. Farther-reaching collaborations with other individual institutions and with larger organizations like HELAS to form more complete networks will continue to bring the community together and to enhance the understanding of γ Doradus and related objects. Acknowledgments. I would like to express my sincere thanks to the scientific organizing committee for inviting me to give this presentation and for their continued support. 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M., Rodrı́guez E., Garrido R., et al., 1997b, MNRAS, 292, 43 Zerbi F. M., Rodrı́guez E., Garrido R., et al., 1999, MNRAS, 303, 275 A. B. Kaye 97 DISCUSSION Matthews: MOST has found a number of γ Dor stars and candidates among its guide stars and Michael Gruberbauer in Vienna is working on these as part of his Master’s thesis. We’ve also found at least two hybrid stars with both γ Dor and δ Scuti pulsations. Concerning HD 8801 you asked whether it was incomplete or just odd. The first of our two hybrids was classified as an Am star and it shows an oscillation spectrum very much like the Henry & Fekel star: oscillation modes in three groups, although we see more frequencies. We got spectra for the other one and it’s also an Am star. We don’t know enough to rule out any long or short-period spectroscopic binarity, but it’s intriguing that there a now three potentially single hybrid pulsators and all three of them are Am stars. So there may be a pattern emerging but I certainly agree with your opinion that all of them need more follow-up work for mode identification but also to rule out binarity. Harry Shipman, Mike Montgomery, Tony Kaye and Ian Roxburgh at the conference dinner, with John Bohannon (= ”Mr. Kolenberg”) in the background. Comm. in Asteroseismology Vol. 150, 2007 Theoretical aspects of g-mode pulsations in γ Doradus stars M.-A. Dupret,1 A. Miglio,2 A. Grigahcène,3 J. Montalbán 2 1 Observatoire de Paris, LESIA, CNRS UMR 8109, 92195 Meudon, France 2 Institut d’Astrophysique et de Géophysique, Liège, Belgique CRAAG - Algiers Observatory BP 63 Bouzareah 16340, Algiers, Algeria 3 Abstract γ Dor stars are main sequence variable A-F stars whose long periods (between 0.35 and 3 days) correspond to high-order gravity mode pulsation. First, we present some aspects of their internal physics and evolutionary status. Second, we consider the potential of the g modes as a probe of these internal physics. In particular, we consider the effect of sharp features present near the convective core top on the g-mode period pattern. Third, we analyse the driving mechanism of the γ Dor g modes, we stress the role of Time-Dependent Convection (TDC) and for the first time we study the role played by turbulent viscosity variations in this frame. Finally, we consider the important problem of mode identification. We show that the theoretical multi-colour photometric amplitude ratios and the phase differences between the light and velocity curves predicted by TDC models much better agree with observations than Frozen Convection (FC) models. Hence, a more secure photometric mode identification is possible with TDC models. Internal physics and evolutionary status of γ Dor stars As detailed by Kaye (2007), γ Dor stars are intermediate-mass main-sequence stars pulsating in high-order gravity modes. For Z = 0.02, their masses range typically from 1.5 to 1.7 M . They are located in a narrow region at the red side of the δ Sct instability strip. In this particular region of the HR diagram, the thin convective zones associated with the partial ionization of He and H begin to merge and form a single larger convective envelope (CE). As we are going to show, this is important for the understanding of their driving mechanism. The exact extension of this CE is subject to theoretical uncertainties and depends on the treatment of convection adopted. We refer to the paper of Montalbán et al. (2007) for more details about this aspect. Concerning the central regions, in the γ Dor mass domain, the main energy source changes from PP-chain nuclear reactions to CNO cycle ones, and because of the high sensitivity to the temperature of the latter, a convective core (CC) appears. The evolution of this CC depends on the mass of the star, as can be seen in Fig. 1, left panel. For higher masses it shrinks, while for lower masses it grows. In simple models, a growing CC is expected to create a discontinuity of chemical composition at its upper boundary. Hence, in a thin region above it, the radiative gradient can be again larger than the adiabatic gradient, which could lead to partial mixing. This phenomenon called semi-convection (Gabriel & Noels 1977; Crowe & Matalas 1982) is still a matter of debate. In the two cases of a shrinking and growing CC, the determination of its exact extension is subject to large uncertainties (as for the CE). There is for example the well known overshooting parameter widely used in stellar evolution codes and which just reflects our lack of knowledge at this level. M.-A. Dupret et al. 99 Figure 1: Left: Mass fraction of the convective core (Mcc /M) during the main sequence for models in a mass range 1.25-1.8 M . Each line describes the evolution of a model of a given mass. Right: Period spacing ΔPn as a function of the radial order n of = 1 g modes in 1.6 M models with decreasing central hydrogen abundance. A constant period spacing, on which are superposed periodic components, describes the spectrum of g modes. Dotted lines represent the constant period spacing predicted by Eq. 1. g-mode periods as a probe of the deep layers of γ Dor stars The gravity modes of γ Dor stars have the highest inertia in the very deep layers near the top of the CC. Hence, they give a unique opportunity to probe these poorly known deep regions. As shown by Tassoul (1980), in the asymptotic regime and if the effect of rotation is neglected, the periods of high-order gravity modes are approximately given by: Pn = Π0 2π 2 (n + 1/2) p ( + 1) (1) R where Π0 −1 = rrab N/r dr is the integral of the Brunt-Väisälä frequency N from the base to the top of the g-mode cavity (typically the radiative region between the CC and CE, for high-order g modes), we call it the buoyancy radius. Similarly to the dynamical time in the case of p modes, the buoyancy radius is the first quantity that can be deduced from the g-mode periods. It is closely related to the size of the CC and its determination allows to constrain it. A method called the Frequency Ratio Method (FRM) based on this asymptotic relation was recently proposed by Moya et al. (2005). For any couple of modes with same , we have σn1 /σn2 = (n2 + 1/2)/(n1 + 1/2). Different combinations of possible n can be determined by this way, and finally the constraints given by the buoyancy radius can be used to restrict the number of possible models for the star. The FRM has been applied to different γ Dor stars: HD 12901 (Moya et al. 2005), HD 218427 (Rodrı́guez et al. 2006a), HD 239276 (Rodrı́guez et al. 2006b) and 9 Aurigae (Moya et al. 2006). In this latter case, the FRM was part of a full consistent scheme including photometric mode identification and stability analysis based on TDC models (see next sections). This study allowed to constrain simultaneously the deep and superficial layers of 9 Aur. However, the FRM not always gives conclusive results, it has been applied only to stars with very few modes (3) and does not take into account the significant effect of rotation on the periods (see next section). 100 Theoretical aspects of g-mode pulsations in γ Doradus stars As shown for white dwarfs (e.g. Brassard et al. 1992), sharp variations in N affect the period spacing of g modes (ΔPn = Pn+1 − Pn ). We recall that the Brunt-Väisälä frequency can be written as: ρg 2 δ ϕ (2) (∇ad − ∇ + ∇μ ), N2 = P δ where ∇μ = d ln μ/d ln P, δ = −∂ ln ρ/∂ ln T |P , ϕ = ∂ ln ρ/∂ ln μ|P,T . We see that sharp variations of N can come from the behaviour of the superadiabatic gradient (∇ − ∇ad ) and from the mean molecular weight gradient ∇μ . In the case of mainsequence models with a convective core, sharp variations of N are built near the top of the CC by the combined action of convective mixing, nuclear burning and by the displacement of the CC border. The signatures of such sharp variations in the g-mode period pattern are presented in the right panel of Fig. 1 in the case of 1.6 M main-sequence models. ΔPn can be described as a superposition of the uniform period spacing predicted by Eq. 1, expected for a model without sharp variations in N, and a periodic component resulting from the sharp variation of N near the stellar core. In analogy with the case of white dwarfs, it can be shown (see Miglio 2006) that the periodicity and amplitude of such a periodic component can be related, respectively, to the location and sharpness of the variation in N. As an example we show in Fig. 1 that, as a star evolves on the main sequence and the edge of the convective core is displaced, the periodicity of the components in ΔPn changes. These periodic components represent very sensitive probes of the location and sharpness of the chemical composition gradient in the core of γ Dor stars, nonetheless, whether these signatures could be detected and correctly interpreted given the effects of rotation on g-mode periods (see next section) needs further investigations. In present ground based observations, only a few modes are observed and it is clearly not possible to detect such signatures. Theoretical models predict however all the modes to be excited in a determined range of periods (see next sections). With future space observations for example with COROT, many more modes should be detected at lower amplitude, and we could observe maybe signatures of non-equidistant spacing. Rotation-oscillation interactions Rotation can affect significantly stellar oscillations in two ways. First, when the centrifugal acceleration is not negligible compared to gravity, the spherical symmetry is broken. Second, when the pulsation periods are of the same order as the rotation period, the Coriolis acceleration plays a major role in the movement pulsation equation. The latter case occurs typically in γ Dor stars because of their long periods. Hence, for a correct modelling of these stars we would have to include the terms associated with rotation in the pulsation equations. Perturbative and non-perturbative approaches can be followed in modelling the rotationoscillation interactions. The non-perturbative ones are much more appropriate in the case of γ Dor stars. Non-perturbative theories have been derived by Lee & Saio (1987) (LS), Dintrans & Rieutord (2000) (DR), Lignières et al. (2006) and Reese et al. (2006) (RL). DR applied their theory to a typical γ Dor model, showing that the second order perturbative theory reaches its limits for σrot /σpul 0.1. Whatever the treatment adopted, it is evident that rotation affects strongly the pulsation frequency pattern of γ Dor stars. The rotational splittings are larger than the frequency spacing of consecutive modes (|σl ,n,m+1 − σl ,n,m | > |σl ,n+1,m − σl ,n,m |) and they are not equidistant at all (σl ,n,m+1 − σl ,n,m = σl ,n,m − σl ,n,m−1 ), which makes it impossible to detect them without mode identification based on other observables (see last section). Moreover, if we consider the evolution of the theoretical frequencies as a function of the rotation frequency, a lot of avoided crossings occur between consecutive modes, which complicates a lot the pulsation frequency pattern. For these reasons, we must not be too optimistic when trying to interpret the observed frequencies with simple models. 101 M.-A. Dupret et al. 1.5 2.0 M0 1.4 35 _=2 30 1.3 1.8 M0 Log(L/L0) 1.2 _=1.5 1.1 25 20 1.6 M0 1 15 10 _=1 0.9 5 0.8 1.4 M0 0 -5 0.7 -10 0.6 7 3.9 Re(bF/F) TDC FC 3.88 3.86 3.84 3.82 3.8 3.78 3.76 3.74 Log(Teff) 6.5 6 5.5 5 4.5 4 3.5 log T Figure 2: Left: γ Dor theoretical IS for = 1 modes, for three families of models with different values of α: 1, 1.5 and 2 obtained with TDC treatment (Dupret et al. 2005a; thick lines), compared to the FC results of Warner et al. (2003) (thin dashed lines, α = 1.87). The small circles correspond to observations. Right: {δF /F } (relative variation of the radial component of the total flux) as a function of log T , obtained with TDC and FC treatments, for the mode = 1, g22 (f = 1.192 c/d). Model with M = 1.55 M , Teff = 7020 K, log(L/L ) = 0.872, α = 2. Driving mechanism of the g modes To understand the driving mechanism of the γ Dor gravity modes, we have to consider more closely the transition region where the pulsation periods are of the same order as the thermal relaxation time. The important point is that, for γ Dor stars, this transition region is near the bottom of the Convective Envelope (CE). This lead Guzik et al. (2000) (G00) to explain the driving of the γ Dor g modes as follows. The radiative luminosity drops suddenly at the bottom of the convection zone. Therefore, at the hot phase of pulsation, the increasing energy coming from below the convection zone cannot be transported by radiation inside it. If we admit that the convective flux does not adapt immediately to the changes due to oscillations, the energy is thus periodically blocked and transformed in mechanical work like in a heat engine, leading to the oscillations. G00 used a Frozen Convection (FC) treatment in their non-adiabatic modelling; but this approximation is not justified in most of the convection envelope. We have implemented in our linear non-radial non-adiabatic pulsation code the more realistic Time-Dependent Convection (TDC) treatment of Gabriel (1996) and Grigahcène et al. (2005). This treatment takes the time-variations of the convective flux (δFc ), the turbulent pressure (δpt ) and the dissipation rate of turbulent kinetic energy (δ2 ) into account. The results presented in Dupret et al. (2004, 2005a) show that these TDC terms do not affect much the driving of the g modes; this supports the driving mechanism proposed by G00. We show in the left panel of Fig. 2 the theoretical instability strips for the γ Dor g modes obtained by Dupret et al. (2004, 2005a) with TDC treatment and by Warner et al. (2003) with FC treatment. A good agreement with the observed instability strip can be obtained for α 2 (near the solar calibrated value). The theoretical instability strip is displaced towards lower effective temperatures when we decrease α, simply because the size of the convective envelope (key point for the driving) is directly related to α. The TDC formalism of Gabriel allows also the determination of the variations of the nondiagonal components of the Reynolds stress tensor (turbulent viscosity) (Gabriel 1987). We have recently implemented for the first time the corresponding terms and equations in a nonadiabatic pulsation code. Preliminary results indicate that they can play a significant role in 102 Theoretical aspects of g-mode pulsations in γ Doradus stars the driving and damping of high order g modes. However, the equations become singular at the convective envelope boundaries when these terms are included, which leads to serious numerical problems. Further work is required to solve them. The stabilization of the high-order g modes at the red side of the γ Dor instability strip is explained by a radiative damping mechanism occurring in the g-mode cavity. We refer to Dupret et al. (2005a) for more details about this damping mechanism. We note also that TDC models predict the existence of stars having simultaneously unstable high-order gravity modes of γ Dor type and unstable low-order p-g modes of δ Sct type. The detection of stars with such hybrid behaviour would present a very high interest for asteroseismology: their high order g modes would enable us to probe the very deep layers of the star and their low-order p-g modes would enable us to probe the intermediate and superficial layers. Much observational effort has been performed to detect such hybrid stars and two have been discovered: HD 209295 (Handler et al. 2002) and HD 8801 (Henry & Fekel 2005). We refer to Grigahcène et al. (2006) for more details about this aspect. Mode identification A crucial problem in asteroseismology is mode identification. This problem is particularly difficult for γ Dor stars, because of the combined effect of rotation and convection on the frequencies, the amplitudes, the phases and the surface geometry of the modes. As shown by Mathias et al. (2004), many γ Dor stars show line-profile variations. Hence, spectroscopic mode identification can often be performed for these stars (Balona et al. 1996; Aerts & Krisciunas 1996). Photometric mode identification methods, which are based on the analysis of the amplitude ratios and phase differences between different photometric passbands, can be also applied in γ Dor stars. These latter observables are particularly interesting from a theoretical point of view, because they are very sensitive to the non-adiabatic treatment of convection-pulsation interaction. Hence, comparison with observations enables us to constrain this treatment. We restrict the discussion to this last case. An important result shown by Dupret et al. (2005b) is that TDC and FC non-adiabatic treatments give completely different predictions for the phase difference ψT between the flux variation and the displacement. The interpretation of these very different results can be deduced from the right panel of Fig. 2, where we give (δF /F ), as obtained with TDC and FC treatment. We first note the drop of (δF /F ) near the base of the CE (log T 5, vertical line) present in both TDC and FC results. This corresponds to the flux blocking mechanism discussed above. In the FC case, the κ-mechanism occurs inside the convective envelope, in the partial ionization zones of Heii (log T 4.8) and H (log T 4.1). These κ-mechanisms imply additional decreases of (δF /F ) down to negative values, which explains the phase lags around 180◦ predicted by the FC models with high α. In contrast, these κ-mechanisms inside the CE are not allowed by TDC models, because they would lead to too high superadiabatic gradients. Therefore, δF /F remains flat and positive after the flux blocking drop and its phase remains near 0◦ . In Dupret et al. (2005b), the application to specific γ Dor stars is considered. These authors show that TDC results much better agree with the observed photometric amplitude ratios between different passbands, allowing a better identification of the degree of the modes. Finally, we stress that the photometric amplitude ratios and phase differences and the lineprofile variations are expected to be strongly affected by rotation. Following the approach of Lee & Saio (1987), Townsend (1997, 2003) determined the effect of rotation on these observables which are widely used for mode identification. The main surface effect of rotation is to concentrate the oscillations along equatorial waveguides. This effect is expected to be significant in γ Dor stars and it would be important to take it into account in spectroscopic and photometric mode identification methods. M.-A. Dupret et al. 103 Conclusions The analysis of the gravity-mode oscillations in γ Dor stars gives a unique opportunity to probe the deep layers near the CC edge in young intermediate mass stars. However, the effect of rotation complicates strongly the interpretation of their frequency pattern, and much work must still be done at this level. TDC models confirm that the driving of these g modes is due to a periodic flux blocking at the base of the convective envelope. The balance between this flux blocking driving and the radiative damping in the g-mode cavity explains the location of their instability strip. TDC models are required for a secure photometric mode identification in these stars. 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Dupret et al. 105 Dennis Stello, Don Kurtz, Alosha Pamyatnykh and Wojtek Dziembowski concentrated on a talk. Conny Aerts and Michel Breger. Comm. in Asteroseismology Vol. 150, 2007 Observations of solar-like oscillations Timothy R. Bedding,1 Hans Kjeldsen 2 1 2 School of Physics A28, University of Sydney, NSW 2006, Australia Department of Physics and Astronomy, University of Aarhus, DK-8000 Aarhus C, Denmark Abstract There has been tremendous progress in observing oscillations in solar-type stars. In a few short years we have moved from ambiguous detections to firm measurements. We briefly review the recent results, most of which have come from high-precision Doppler measurements. We also review briefly the results on giant and supergiant stars and the prospects for the future. Main-sequence and subgiant stars There has been tremendous progress in observing oscillations in solar-type stars, lying on or just above the Main Sequence. In a few short years we have moved from ambiguous detections to firm measurements. Most of the recent results have come from high-precision Doppler measurements using spectrographs such as CORALIE, HARPS, UCLES and UVES (see Fig. 1 for an example). The best data have been obtained from two-site campaigns, although single-site observations are also being carried out. Meanwhile, photometry from space gives a much better observing window than is usually achieved from the ground but the signal-to-noise is poorer. The WIRE and MOST missions have reported oscillations in several stars, although not without controversy, as discussed below. Observations of solar-like oscillations are accumulating rapidly, and measurement have now been reported for several main-sequence and subgiant stars. The following list includes the most recent observations and is ordered according to decreasing stellar density (i.e., decreasing large frequency separation): • τ Cet (G8 V): this star was observed with HARPS by T. C. Teixeira et al. (in prep.). The data were compromised by noise at 3 and 6 mHz caused by a periodic error in the guiding system. Nevertheless, the authors were able to measure the large separation (170 μHz) and extract a number of individual oscillation frequencies. • 70 Oph A (K0 V): this is the main component of a spectroscopic visual binary (the other component is K5 V). It was observed over 6 nights with HARPS by Carrier & Eggenberger (2006), who found Δν = 162 μHz but were not able to give unambiguous mode identifications from these single-site data. • α Cen A and B (G2 V and K1 V): see separate section below. • μ Ara (G3 V): this star has multiple planets. Oscillations were measured over 8 nights using HARPS by Bouchy et al. (2005) (see Fig. 1) and the results were modelled by Bazot et al. (2005). They found Δν = 90 μHz and identified over 40 frequencies, with possible evidence for rotational splitting. • HD 49933 (F5 V): this is a potential target for the COROT space mission and was observed over 10 nights with HARPS by Mosser et al. (2005). They reported a surprisingly high level of velocity variability on timescales of a few days. This was also present as line-profile variations and is therefore presumably due to stellar activity. The observations showed excess power from p-mode oscillations and the authors determined the large separation (Δν = 89 μHz) but were not able to extract individual frequencies. Timothy R. Bedding and Hans Kjeldsen 107 Figure 1: Radial velocity time series of the star μ Ara made over 8 nights with the HARPS spectrograph. Figure from Bouchy et al. (2005). • β Vir (F9 V): oscillations in this star were detected in a weather-affected two-site campaign with ELODIE and FEROS by Martić et al. (2004). Subsequently, Carrier et al. (2005) used CORALIE with good weather but a single site, and reported 31 individual frequencies. Those results were modelled by Eggenberger & Carrier (2006), who also reported tentative evidence for rotational splittings. The large separation is 72 μHz. • Procyon A (F5 IV): see separate section below. • β Hyi (G2 IV): oscillations were detected in β Hyi in 2001 using UCLES (Bedding et al. 2001) and CORALIE (Carrier et al. 2001). This star was the target for a two-site campaign in 2005, with HARPS and UCLES, that resulted in the clear detection of mixed modes (Bedding et al. 2007). The large separation is 57.5 μHz. • δ Eri (K0 IV): Carrier et al. (2003) observed this star over 12 nights in 2001 with CORALIE and found a large separation of 44 μHz. • η Boo (G0 IV): see separate section below. • ν Ind (G0 IV): this a metal-poor subgiant ([Fe/H] = −1.4) which was observed from two sites using UCLES and CORALIE. The large separation of 25 μHz, combined with the position of the star in the H-R diagram, indicated that the star has a low mass (0.85 ± 0.04 M ) and is at least 9 Gyr old (Bedding et al. 2006). Analysis of the power spectrum produced 13 individual modes, with evidence for avoided crossings and with a mode lifetime of 16+34 −7 days (Carrier et al. 2007). 108 Observations of solar-like oscillations α Cen A and B On the main-sequence, the most spectacular results have been obtained for the α Cen system. The clear detection of p-mode oscillations in α Cen A by Bouchy & Carrier (2002) using the CORALIE spectrograph represented a key moment in this field. This was followed by a dualsite campaign on this star with UVES and UCLES (Butler et al. 2004) that yielded more than 40 modes, with angular degrees of = 0 to 3 (Bedding et al. 2004). The mode lifetime is about 2 – 4 days and there is now evidence of rotational splitting from photometry with the WIRE satellite analysed by Fletcher et al. (2006) (see Fig. 2) and also from ground-based spectroscopy with HARPS (Bazot et al. 2006). Figure 2: Four oscillation modes in α Cen A from the WIRE power spectrum, with fits that indicate the linewidth and rotational splitting. Figure from Fletcher et al. (2006). Meanwhile, oscillations in the B component were detected from single-site observations with CORALIE by Carrier & Bourban (2003). Dual-site observations with UVES and UCLES (see Fig. 3) allowed measurement of nearly 40 modes and of the mode lifetime (Kjeldsen et al. 2005). Figure 3: Power spectrum of α Cen B from velocity observations. Note the double-humped structure with a central dip. Figure from Kjeldsen et al. (2005). Timothy R. Bedding and Hans Kjeldsen 109 We have previously pointed out (Bedding & Kjeldsen 2006) that the power spectrum of Procyon appears to show a dip at 1.0 mHz that is apparently consistent with the theoretical models of Houdek et al. (1999). A similar dip for low-mass stars was also discussed by G. Houdek (private comm.; see also Chaplin et al. 2007), and the observations of α Cen B in Fig. 3 do indeed show such a dip, although not at the frequency indicated by the models. It seems that the shape of the oscillation envelope is an interesting observable that can be extracted from the power spectrum and compared with theoretical models. η Boo This star, being the brightest G-type subgiant in the sky, remains a very interesting target. The claimed detection of oscillations a decade ago by Kjeldsen et al. (1995), based on fluctuations in Balmer-line equivalent-widths, has now been confirmed by further equivalent-width and velocity measurements by the same group (Kjeldsen et al. 2003) and also by independent velocity measurements with the CORALIE spectrograph (Carrier et al. 2005). With the benefit of hindsight, we can now say that η Boo was the first star for which the large separation and individual frequencies were measured. However, there is still disagreement on some of the individual frequencies, which reflects the subjective way in which genuine oscillation modes must be chosen from noise peaks and corrected for daily aliases. Fortunately, the large separation is Δν = 40 μHz, which is half way between integral multiples of the 11.57-μHz daily splitting (40/11.57 = 3.5). Even so, daily aliases are problematic, especially because some of the modes in η Boo appear to be shifted by avoided crossings. The first spaced-based observations of η Boo, made with the MOST satellite, have generated considerable controversy. Guenther et al. (2005) showed an amplitude spectrum (their Fig. 1) that rises towards low frequencies in a fashion that is typical of noise from instrumental and stellar sources. However, they assessed the significance of individual peaks by their strength relative to a fixed horizontal threshold, which naturally led them to assign high significance to peaks at low frequency. They did find a few peaks around 600 μHz that agreed with the ground-based data, but they also identified eight of the many peaks at much lower frequency (130–500 μHz), in the region of rising power, as being due to low-overtone p-modes. Those peaks do line up quite well with the regular 40 μHz spacing, but extreme caution is needed before these peaks are accepted as genuine. This is especially true given that the orbital frequency of the spacecraft (164.3 μHz) is, by bad luck, close to four times the large separation of η Boo (164.3/40 = 4.1). Models of η Boo based on the combination of MOST and ground-based frequencies have been made by Straka et al. (2006). Procyon Procyon has long been a favourite target for oscillation searches. There have been at least eight separate velocity studies, mostly single-site, that have reported a hump of excess power around 0.5–1.5 mHz. See Martić et al. (2004), Eggenberger et al. (2004), Bouchy et al. (2004), Claudi et al. (2005) and Leccia et al. (submitted to A&A) for the most recent examples. However, there is not yet agreement on the oscillation frequencies, although a consensus is emerging that the large separation is about 55 μHz. This star generated controversy when MOST data reported by Matthews et al. (2004) failed to reveal oscillations that were claimed from ground-based data. However, Bedding et al. (2005) argued that the MOST non-detection was consistent with the ground-based data. Using space-based photometry with the WIRE satellite, Bruntt et al. (2005) extracted parameters for the stellar granulation and found evidence for an excess due to p-mode oscillations. A multi-site campaign on Procyon is being organized for January 2007, which will be the most extensive velocity campaign so far organized on a solar-type oscillator. 110 Observations of solar-like oscillations G and K giants There have been detections of oscillations in red giant stars with periods of 2 – 4 hours. Ground-based velocity observations were presented by Barban et al. (2004), who used the CORALIE and ELODIE spectrographs to find excess power and a possible large separation for both Oph (G9 III) and η Ser (K0 III). The data for Oph have now been published by De Ridder et al. (2006). Hekker et al. (2006) have analysed the line-profile variations and found evidence for non-radial oscillations. Meanwhile, earlier observations of oscillations in ξ Hya (G7 III) by Frandsen et al. (2002) have been further analysed by Stello et al. (2004), who found evidence that the mode lifetime is only about 2 days. If confirmed, this would significantly limit the the prospects for asteroseismology on red giants. Figure 4: Power spectra of red supergiants from visual observations (thin lines) with Lorentzian fits (thick lines). Figure from Kiss et al. (2006). Timothy R. Bedding and Hans Kjeldsen 111 Red giants and supergiants If we define solar-like oscillations to be those excited and damped by convection then we expect to see such oscillations in all stars on the cool side of the instability strip. Evidence for solar-like oscillations in semiregular variables, based on visual observations by groups such as the AAVSO, has already been reported. This was based on the amplitude variability of these stars (Christensen-Dalsgaard et al. 2001) and on the Lorentzian profiles of the power spectra (Bedding 2003, Bedding et al. 2005). Recently, Kiss et al. (2006) used visual observations from the AAVSO to show that red supergiants, which have masses of 10 – 30M , also have Lorentzian profiles in their power spectra (see Fig. 4). The future In the future, we expect further ground-based observations using Doppler techniques. The new spectrograph SOPHIE at l’Observatoire de Haute-Provence in France should be operating very soon (http://www.obs-hp.fr/). From space, the WIRE and MOST satellites continue to return data and we look forward with excitement to the expected launches of COROT (December 2006) and Kepler (2008). Looking further ahead, the SIAMOIS spectrograph is planned for Dome C in Antarctica (Seismic Interferometer Aiming to Measure Oscillations in the Interior of Stars; see http://siamois.obspm.fr/). Finally, there are ambitious plans to build SONG (Stellar Oscillations Network Group), which will be a global network of small telescopes equipped with high-resolution spectrographs and dedicated to asteroseismology and planet searches (see http://astro.phys.au.dk/SONG). Acknowledgments. This work was supported financially by the Australian Research Council, the Science Foundation for Physics at the University of Sydney, the Danish Natural Science Research Council, and the Danish National Research Foundation through its establishment of the Theoretical Astrophysics Center. References Barban C., de Ridder J., Mazumdar A., et al., 2004, in Dansey D., ed, SOHO 14/GONG 2004 Workshop, Helio- and Asteroseismology: Towards a Golden Future. ESA SP-559, Noordwijk, p. 113 Bazot M., Bouchy F., Kjeldsen H., et al., 2007, A&A, submitted Bazot M., Vauclair S., Bouchy F., Santos N. C., 2005, A&A, 440, 615 Bedding T. R., 2003, Ap&SS, 284, 61 Bedding T. 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B., et al., 2004, Nat, 430, 51, Erratum: 430, 921 Mosser B., Bouchy F., Catala C., et al., 2005, A&A, 431, L13 Stello D., Kjeldsen H., Bedding T. R., et al., 2004, Solar Physics, 220, 207 Straka C. W., Demarque P., Guenther D. B., Li L., Robinson F. J., 2006, ApJ, 636, 1078 DISCUSSION Kovacs: How can amateur observers catch the few hundredths of a magnitude change expected for stochastically excited oscillations at the periods of giants? Bedding: The nice thing is that the amplitudes get bigger when you move up the HR diagram to higher luminosities. The amplitudes of these stars are several tenths of a magnitude. When you have dozens and dozens observers over many decades then you can. Kovacs: I think that’s still a long way to go by amateurs to get an accuracy of a few tenths of a magnitude. Kurtz [to Kovacs]: The amateurs can reach accuracies of 0.1 magnitudes and they reach a few tenths of a magnitude on a regular basis. They have been doing that for over a century and they are trustworthy. Reed: How many mode lifetimes do you have to observe to get a Lorentzian profile in the Fourier Transform? Bedding: About five to ten. Timothy R. Bedding and Hans Kjeldsen 113 Two astronomers who are often mistaken for each other. We provide a unique identification: Hans Bedding is the person on the left and Tim Kjeldsen on the right. 114 Observations of solar-like oscillations Jørgen Christensen-Dalsgaard and Conny Aerts seem to like this talk. Comm. in Asteroseismology Vol. 150, 2007 Stellar Oscillations in Giant Stars A. P. Hatzes,1 M. P. Döllinger,2 M. Endl 3 1 2 Thüringer Landessternwarte Tautenburg, Sternwarte 5, D-07778 Tautenburg, Germany European Southern Observatory, Karl-Schwarzschild-Straße 2, D-85748 Garching, Germany 3 McDonald Observatory, The University of Texas at Austin, Austin, TX 78712, USA Abstract Walker et al. (1989) were the first to establish, using precise stellar radial velocity measurements, that K giant stars were a new class of variables. The variability of some of these stars can be quite complex showing several periods ranging from several hours to several hundreds of days. The long-period variations result from sub-stellar companions or rotational modulation, but the short-period variability certainly arises from stellar oscillations. We present recent of precise stellar radial velocity measurements (σ ≈ 6 m s−1 ) of two oscillating K giant stars: β Oph and γ Dra. These stars show oscillation periods of hours (β Oph) and days (γ Dra). These periods are consistent with solar-like stellar oscillations, given the stellar properties of the star. Radial modes are a prime candidate for the type of oscillations in these stars. Introduction Over 15 years ago precise stellar radial velocity (RV) measurements established that K giant stars were a new class of variables (Walker et al. 1989). Subsequent investigations showed that these stars showed periodic variations on two time scales: hundreds of days (Hatzes & Cochran 1993) and several days (Smith et al. 1987, Hatzes & Cochran 1994a). Hatzes & Cochran (1993) hypothesized that the long period variations could arise from either sub-stellar companions or rotational modulation. Later work revealed that planetary companions can indeed be the cause of some of the long period RV variations in these stars (Frink et al. 2000; Setiawan et al. 2003, 2005; Hatzes et al. 2005). More recently, Hatzes et al. (2006) showed that the long period variations in β Gem originally found by Hatzes & Cochran (1993) were indeed caused by a planetary companion. Short-period RV variations (P = 1.8 days) were first found in α Boo by Smith et al. (1989). Hatzes & Cochran (1994a) later found pulsation periods of 2.46 and 4.03 days (and possibly an 8.5 day period) in this star thus providing the first evidence for the presence of multiple modes. Some K giant stars can pulsate with much shorter periods. Hatzes & Cochran (1994b) found evidence for pulsations with a period of 3.9 hours in β Oph. Frandsen et al. (2002) detected possibly up to 9 modes in the period range 2 – 5.5 hours with a mean separation of 7.2 μHz. These were well matched by overtone radial modes. Recently, RV measurements of the giant Oph revealed excess power in the frequency spectrum corresponding to periods ≈ 4.6 hours (de Ridder et al. 2006). Oscillations in giant stars have also been established through photometric studies. Edmonds & Gilliland (1996) used the Hubble Space Telescope to find variations in several K giants in 47 Tuc on time scales of a few days with semi-amplitudes of 10 – 30 mmag in U. Buzasi et al. (2000) found 10 oscillation modes in α UMa (K0 III) using the star camera of the Wide Field Infrared Explorer (WIRE) satellite. The modes had amplitudes of 100 – 400 μmag and the lowest frequency mode was at 1.82 μHz (6.36 days). Retter et al. (2003), also using the WIRE guide camera, found around four photometric modes in α Boo with periods ranging from 2 – 4 days. However, they noted that these could be consistent with one mode with a short lifetime. 116 Stellar Oscillations in Giant Stars Photometric variations on time scales of hours have also been found in K giant stars. Kallinger et al. (2005) found evidence for three approximately equidistant frequencies in the K2.5 giant star GSC 09137-03505 based on photometry made with the Fine Guidance Camera of HST. The frequency range for these were 21 – 71 μHz (0.163 – 0.55 days) with amplitudes of 291 – 341 ppm. However, these frequencies were significantly above the acoustic cutoff frequency casting some doubts as to their origin. Early evidence points to the oscillations in K giants stars being caused by fundamental or overtone radial modes. The periods found in α Boo and β Oph were consistent with fundamental or overtone radial modes (Hatzes & Cochran 1994a, 1994b). The 10 modes found in α UMa by Buzasi et al. (2000) were also identified as radial modes (Guenther et al. 2000). The 0.57-day RV period in α Ari is also consistent with an overtone radial mode (Kim et al. 2006). However, ground-based observations over a short time span may be giving us an incomplete picture of oscillations in giant stars. New Results We conducted observations spanning 9 nights on a sample of fifteen K giant stars using the 2Dcoude spectrograph of the 2.7 m telescope of McDonald Observatory. Precise stellar radial velocity measurements were obtained using an iodine absorption cell placed in the light path of the telescope. The use of iodine cells has become a common technique for the measurement of precise stellar radial velocities (see Endl et al. 2000). The strategy of the observations was to look at a modest sample of K giant stars that spanned a wide range of spectral parameters rather than concentrating on a few objects. The sample size forced us to have a time sampling that may miss some modes. However, we were primarily interested in understanding how the characteristics of the stellar oscillations varied among K giant stars. Future observations would concentrate on extensive observations of a few interesting targets. Objects were chosen from the sample of Döllinger et al. (2007) which showed significant RV variations on short time scales. Our preliminary analysis showed that the oscillations in K giant stars could be divided into two classes: stars that show periods of several hours, and stars showing periods of several days. We present here two representative examples from this study. β Oph Eighty-nine observations were made of β Oph spanning nine days. Figure 1 shows the LombScargle periodogram of the RV measurements as well as the data window. There is significant power near frequencies of about 3.5 c d−1 (= 40 μHz). The highest peak at a frequency of 3.43 c d−1 (= 39.7 μHz) is statistically significant having a false alarm probability (chance that it is due to noise), FAP = 6.5×10−5 . This was assessed by randomly shuffling the RV measurements, keeping the times fixed and computing a periodogram over the frequency range shown in the figure. The number of random noise periodograms after a large number of shuffles (2×105 ) having power larger than the observed power yielded the FAP. Additional frequencies were searched using a pre-whitening procedure. The program Gaussfit (Jefferys et al. 1988) was used to fit a sine function to the RV data. The frequency found by the periodogram analysis was used as an initial guess, but Gaussfit was allowed to vary the period, amplitude, and phase of the data to obtain a least-squares solution. A periodogram analysis was then performed on the residual RV data. A second significant peak was found at a frequency of 34.72 μHz. The false alarm probability over the same frequency interval was again assessed using periodograms of randomly shuffled data sets. After 2 × 105 shuffles there was no instance where the random data periodogram had power greater than the residual data periodogram. This implies FAP < 5×10−6 . An additional application of this procedure by subtracting the contribution of the 34.72 μHz frequency yielded a highest 117 A. P. Hatzes, M. P. Döllinger and M. Endl Data Lomb-Scargle Power 10 5 0 Window 10 5 0 0 2 4 6 Frequency (c/d) 8 10 Figure 1: The Lomb-Scargle periodogram of the RV measurements of β Oph. The highest peak has a false alarm probability of 6.5×10−5 . Frequency (μHz) 38.79 34.72 Period (hrs) 6.98 8.00 Amplitude m s−1 7.43 7.39 Table 1: Detected pulsation modes in β Oph peak at 40.97 μHz, but this had low significance (FAP = 0.03 assessed with random data periodograms). Table 1 lists the two most significant detected frequencies. γ Dra Eighteen RV measurements were made of γ Dra over nine nights. The top panel of Fig. 2 shows the time series of these measurements. It is clear that γ Dra shows stellar oscillations with much longer periods and larger amplitudes than β Oph. There are clear deviations of the RV measurements from the dominant period of 3.97 days. A prewhitening procedure was also performed on the γ Dra data by finding the leastsquares sine-fit to the data using Gaussfit, subtracting this component, and performing a sine-fit on the residuals. This is shown in the lower panels of Fig. 2. After finding 3 sine components the final residual in the RV values was σ = 5.8 m s−1 which is comparable to the mean error of the measurements (mean σ = 5.7). The pulsation modes found in γ Dra are listed in Table 2. For one set of residuals (third panel from top in Fig. 2) two periods could fit the data: 2.5 days, or an alias of 1.6 days (shown as a dashed line in the figure). The 2.5-day period provided a slightly better fit although the sampling of our data is such that we do not know if the 2.5 or the 1.6-day period is actually present in the data. The false alarm probabilities of the detected peaks in γ Dra were determined using the “random shuffle” technique described above and 2×105 shuffles. This resulted in FAP = 0.0004, 0.034, and 0.0072 for the 4.02, 9.09, and 2.5-day periods, respectively. We should mention several caveats. After subtraction of the dominant 4-day period there are clear longterm variations in the RV residuals, but with a period that is comparable to the time span 118 Radial Velocity (m/s) Stellar Oscillations in Giant Stars 100 50 0 -50 -100 40 20 0 -20 -40 20 10 0 -10 -20 40 20 0 -20 -40 P = 3.97 d P = 9.09 d 53530 53532 53534 JD - 2400000 53536 53538 Figure 2: RV measurements of γ Dra taken on 9 consecutive nights. Each panel shows successive steps of the pre-whitening procedure. In the second panel from the bottom the best fit period of 2.5 days is shown as a solid line. The dashed line shows an alias period of 1.62 days. Frequency (μHz) 2.89 1.27 4.63 Period (days) 4.02 9.09 2.50 Table 2: Detected pulsation modes in γ Dra Amplitude m s−1 39.7 14.4 10.2 of the data. This period is uncertain. This is also probably reflected in the rather large FAP since Lomb-Scargle periodograms tend to give rather high FAPs for partial sine waves, even though a real signal is in the data. Although the FAP for the 2.5-day period is rather low our data sampling is sparse so this may be uncertain as well. Table 3 lists the basic stellar parameters for β Oph and γ Dra. Temperatures are from McWilliam (1990) and the masses and radii were determined using the method outlined in da Silva et al. (2006). Also listed is the period of the fundamental radial mode for each star, derived from the empirical relationships of Cox, King & Stellingwerf (1972). Parameter Radius [R ] Mass [M ] Teff [K] F (days) Amplitude (m s−1 ) ν0 (μHz) γ Dra 47 2.9 4550 8.4 41 0.71 β Oph 14 2.6 3903 1.2 5.6 4.2 Table 3: Stellar Parameters for γ Dra and β Oph. F is the radial fundamental mode period and ν0 is the asymptotic p-mode frequency spacing A. P. Hatzes, M. P. Döllinger and M. Endl 119 Discussion Kjeldsen & Bedding (1995) proposed a scaling relationship for the the velocity amplitudes, V , for stellar oscillations that was proportional to the ratio of stellar luminosity to mass (V ∝ L/M). β Oph and γ Dra have comparable masses. γ Dra has a higher effective temperature and has approximately 10 times the surface area. Its luminosity should thus be 10 – 20 times greater than that of β Oph. The amplitudes for the oscillations seen in γ Dra are a factor of ten higher than for β Oph which is more or less consistent with the Kjeldsen & Bedding relation. Table 3 also lists the predicted RV amplitudes for β Oph and γ Dra using the Kjeldsen & Bedding scaling law. Both the time scales and amplitudes are consistent with solar-like p-mode oscillations given the radius and mass for each star. For p-mode solar-like oscillations the frequency spacing scaled to solar parameters is ν0 = 1/2 −3/2 μHz, where the mass and radius (M and R) are in solar units (Brown & 135M∗ R∗ Gilliland 1994). For high order modes (n >> 1) p-modes are evenly spaced with a frequency spacing of ν0 /2. Table 3 also lists the values ν0 . If we are to believe the additional periods found in β Oph and γ Dra, then we can use these for a rough estimate of the frequency spacing. This “spacing” is 1.7 μHz for γ Dra and 4.3 μHz for β Oph, both within a factor of 2–3 from the expected spacing. However we should be cautious in interpreting the separation of the modes to ν0 /2. More modes need to be detected to get a better measurement of the frequency spacing. The periods we have detected are comparable to those of the fundamental radial modes for these stars suggesting that these may be radial as opposed to nonradial modes. The classical definition of the pulsation constant is Q = P(M/M )0.5 (R/R )−1.5 where M, and R are the stellar mass and radius, respectively. This results in pulsation constants of Q = 0.048, 0.0212, and 0.0132 for the 3 modes of γ Dra (in increasing frequency) and Q = 0.013 and 0.0114 for the two highest amplitude (and thus most significant) modes in β Oph. Using the theoretical models of Guenther et al. (2000) the 3 modes in γ Dra can be identified with the fundamental, first, and third overtone modes, respectively (n = 0, 1, and 4). The two modes in β Oph are consistent with the 4 and 5th overtone mode (n = 4 and 5). This is consistent with radial modes inferred for other K giant stars. In spite of over a decade of (admittedly intermittent) studies of variability of giant stars we still know little about oscillations in giant stars. We do know that giant stars vary with periods ranging from hours to several days, but the exact mode identification remains elusive. There are hints of mode switching but the lifetimes of the modes are unknown. Possibly the one thing we can be sure of about these stars is that we probably have yet to derive the full oscillation spectrum for even a single giant star. The reason is clear, with pulsation periods ranging up to several days it is difficult to derive such a spectrum without extensive time coverage using multi-site campaigns. This will change with the launch of the CoRoT satellite. This French-led mission (with participation from Austria, Belgium, Brazil, Germany, Spain, and ESA) has the dual goal of asteroseismology and the detection of transiting planets. Ultra-precise light curves will be obtained for thousands of stars and among them many G – K giants. Observations will be made continuously for up to 150 days. CoRoT will, for the first time, be able to derive the full oscillation spectrum for many giant stars as well as to determine the mode lifetimes. Acknowledgments. This work is based on observations made with the 2.7m Harlan J.Smith Telescope at McDonald Observatory. The authors would like to thank the anonymous referee for suggested improvements to the manuscript. The observations at McDonald Observatory were made possible through grant HA 3279/4-1 of the Deutsche Forschungsgemeinschaft (DFG). 120 Stellar Oscillations in Giant Stars References da Silva L., Girardi L., Pasquini L., et al., 2006, A&A, 458, 609 Brown T. M., Gilliland R. L., 1994, ARA&A, 32, 37 Buzasi D., Catanzarite J., Laher R., et al., 2000, ApJ, 532, L133 Cox J. P., King D. S., Stellingwerf R. F., 1972, ApJ, 171, 39 de Ridder J., Barban C., Carrier F., et al., 2006, A&A, 448, 689 Döllinger, M. P., Hatzes A. P., Pasquini L., et al., 2007, A&A, in press Edmonds P. D., Gilliland R. L., 1996, ApJ, 464, L157 Endl M., Kürster M., Els S., 2000, A&A, 362, 585 Frandsen S., Carrier F., Aerts C., et al., 2002, A&A, 394, L5 Frink S., Mitchell D. 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J., 1987, ApJ, 317, L79 Walker G. A. H., Yang S., Campbell B., Irwin A. W., 1989, ApJ, 343, L21 DISCUSSION Matthews: Considering the giants that we already observed with MOST, supported by some ground-based spectroscopic observations, and that we will be observing NGC 752 with ∼ 20 giants in different evolutionary stages, we share your feeling that every giant will show variability and possibly every giant will show p-mode oscillations. A. P. Hatzes, M. P. Döllinger and M. Endl 121 Ennio Poretti, Günter Houdek, Atsuko Nitta and Judi Provencal signing Michel Breger’s birthday card; Mike Montgomery still wonders where to sign. As usual, Kepler makes his point very clear. Comm. in Asteroseismology Vol. 150, 2007 Theoretical asteroseismology of solar-like oscillations G. Houdek Institute of Astronomy, University of Cambridge, Cambridge CB30HA, UK Abstract Having a rich acoustic oscillation spectrum makes solar-like stars particularly interesting for studying fluid-dynamical aspects of the stellar interior. I present some of the recent progress in formulating the physical processes that drive the acoustic oscillations to the observed amplitudes via their coupling with the turbulent velocity field in the outer convectively unstable stellar layers. I shall also discuss some asteroseismic diagnostic techniques that allow us to measure some of the gross stellar properties derived from a seismic signature contained in the variation of the large frequency separation of measured low-degree acoustic modes. Introduction Solar-type stars possess extended surface convection zones. The observed oscillation modes generally behave as acoustic modes and their frequencies are sensitive predominantly to the sound speed in the stellar interior. It appears that all possible oscillation modes are intrinsically stable. They are excited stochastically by the strong emission of acoustic noise by the turbulent velocity field in the upper convectively unstable layers of the star. The excitation occurs in a broad frequency range, giving rise to a rich pulsation spectrum. The amplitudes of the oscillations are small, typically 5 ppm L /M (Kjeldsen & Bedding 1995), allowing us to describe the pulsations with linear theory. Only modes of low degree can be observed. The diagnostic properties of this type of mode have been studied extensively in the solar case. From asymptotic theory we find for the cyclic oscillation frequencies νn, with radial order n and spherical degree (Gough 1986, see also Tassoul 1980) νn, (n + /2 + α) ν0 + εn, , (1) h R i −1 is the inverse of twice the sound travel time between the centre where ν0 = 2 0R dr /c and surface (R is surface radius), and α is a constant. The value of ν0 can be estimated from taking the average (over n and ) of the so-called large frequency separation νn, ≡ νn, − νn−1, . The correction term εn, lifts the degeneracy between modes with the same value of n + /2 and leads to the so-called small frequency separation δνn, ≡ νn, − νn−1,+2 . This frequency structure is illustrated in Fig. 1 for a solar spectrum. The small frequency separation is predominantly determined by the acoustic sound speed in the stellar core and hence is sensitive to the chemical composition there and consequently is an indicator for the stellar age (e.g., Gough 2001). Oscillation amplitudes In the Sun and other solar-like oscillators mode stability is governed not only by the perturbations in the radiative fluxes (i.e., via the κ-mechanism) but also by the perturbations in the turbulent fluxes (heat and momentum). The study of mode stability therefore demands a theory for convection that includes the interaction of the turbulent velocity field with the G. Houdek 123 Figure 1: Small section of a solar acoustic power spectrum. The radial order n and spherical degree are indicated in pairs of (n,) for each mode. The large and small frequency separations, Δνn, and δνn, are in general functions of n and and can be used to infer the mass and age of a star (adapted from Christensen-Dalsgaard 2001). pulsation. It appears that in solar-like stars all possible modes of oscillation are stable; thus, if a given oscillation is somehow excited, it will be damped over a finite time, typically of the order of days to months, the inverse of which is the damping rate η. The power spectrum (Fig. 1) can be described in terms of an ensemble of intrinsically damped, stochastically driven, simple-harmonic oscillators, provided that the background equilibrium state of the star were independent of time. In that case the mode profile is essentially Lorentzian, and the intrinsic damping rates of the modes could then be determined observationally from measurements of the pulsation linewidths. The other fundamental quantity that any full description of mode excitation must model is the energy supply rate, P, which is sometimes called the acoustic noise generation rate. The observed velocity signal v (t) = dξ/dt (where ξ(t) is the surface displacement of the damped, stochastically driven, harmonic oscillator) can then be related to the modelled energy supply rate P by taking the Fourier transformation of the harmonic oscillator followed by an integration over frequency to obtain the total mean energy E in a particular pulsation mode with inertia I (e.g., Chaplin et al. 2005, Houdek 2006). The squared surface rms velocity is then given by V 2 := E P 1 = = ηH, I 2η I 2 (2) where the height H (in cm2 s−2 Hz−1 ) is the maximum of the discrete power, i.e. the integral of power spectral density over a frequency bin. As such, it is not the total integrated power, V 2 , that is observed directly, but rather the power spectral density (Chaplin et al. 2005). The excitation process can be regarded as multipole acoustic radiation (Lighthill 1952). Acoustic radiation by turbulent multipole sources in the context of stellar aerodynamics has been considered by various authors (for a recent review see Houdek 2006). Here we follow the procedure by Chaplin et al. 2005, who derived the following expression for estimating the energy supply rate arising from the fluctuating Reynolds stresses PR (another contribution comes from the fluctuating gas pressure Pg , i.e. the total energy supply rate P = PR + Pg ; here we neglect Pg ): 124 Theoretical asteroseismology of solar-like oscillations Figure 2: Reynolds stress as a function of the depth variable z = R − r for various solar models. Results are shown for the non-local mixing-length model (solid curve) and from hydrodynamical simulations by Trampedach et al. (1999, dashed curve) and Ludwig (2005, dot-dashed curve). PR = π 9I Z R 0 „ l3 ΦΨrp t ∂ξr ∂r «2 S(r ; ν) dr , (3) where l is the mixing length, p t is the (r , r )-component of the Reynolds stress, and ξr is the normalized radial component of the displacement vector. The spectral function S accounts for contributions to P from the small-scale turbulence. The parameter Ψ = [2Φ/3(Φ − 1)]1/2 is unity for isotropic turbulence (Chaplin et al. 2005) and is obtained from a consistent kinematic transformation of the turbulent velocity correlation uu (angular brackets denote an ensemble average) in the Boussinesq-quasi-normal approximation, where Φ = u · u/u32 describes the anisotropy of the turbulent velocity field u = (u1 , u2 , u3 ). The relative (r , r )-component of the Reynolds stress p t /p = ρu32 /p (ρ is density and p is the total pressure) is compared with hydrodynamical simulations in Fig. 2. The Reynolds stress of the non-local mixing-length model shows a narrow peak near the depth z 120 km and falls off more rapidly with z than the results from both hydrodynamical simulations. This contributes to make the energy supply rate for the mixing-length model smaller than that from the hydrodynamical simulations, and consequently the modelled heights H need to be scaled with a scaling factor > 1 in order to reproduce the observed values of the mode peak heights (Chaplin et al. 2005). With a model for P and estimates for η from nonadiabatic pulsation calculations the oscillation amplitude V is obtained from Eq. (2). Fairly accurate measurements of solar-like oscillation amplitudes in other stars are available today from ground based observations (see Bedding & Kjeldsen, these proceedings). Results for models of α Cen A and for the sub-giant ξ Hydrae are illustrated in Fig. 3. Bedding et al. (2004) reported mode lifetimes for α Cen A between 1–2 days which are in reasonable agreement with the theoretical estimates of about 1.7 days for the most prominent modes (the mode lifetime τ = η−1 ; see lower left panel of Fig. 3). For ξ Hydrae, however, the theoretical mode lifetimes of the most prominent modes are τ 17 days which are in stark contrast to the measured values of about 2–3 days by Stello et al. (2006), yet the estimated velocity amplitudes are in almost perfect agreement with the observations by Frandsen et al. (2002). G. Houdek 125 √ Figure 3: Predicted apparent velocity amplitudes (defined to be 2 times the rms value V , top) and damping rates (bottom) of radial acoustic modes for models of α Cen A (left) and ξ Hydrae (right). The predicted maximum velocity amplitudes for various solar-like stars are compared in Fig. 4 with recently performed observations. For the cooler stars the theoretical results are in reasonable agreement with the observations. For the rather hotter star Procyon, however, the theoretical velocity amplitudes are severely overestimated. The dotted line is the scaling law by Kjeldsen & Bedding (1995), and the dashed line is the scaling relation reported by Samadi et al. (2005) using the convective velocity profiles from numerical simulations (Stein & Nordlund 2001), and the theoretical damping rates from Houdek et al. (1999). For hotter stars they find better agreement with observations. It is, however, interesting to note that the numerical simulations by Stein et al. (2004) show for hotter stars partial cancellation between the two excitation sources, PR and Pg , arising from the fluctuating Reynolds stresses and gas pressure (buoyancy force) respectively. On average, this results in a total energy supply rate that is smaller by a factor of about two than the energy supply rate from the turbulent pressure fluctuations alone. One is therefore tempted to argue that the overestimated values of the modelled energy supply rate P in Procyon could be partially attributed to having neglected the gas pressure fluctuations in Eq. (2) and in particular its cancellation with the turbulent pressure fluctuations. By adopting the simulated results by Stein et al. (2004) of the √ energy supply rate P for Procyon the velocity amplitude is reduced by a factor of about 2 (indicated by the dot-dashed vertical line in Fig. 4). This suggests, according to Eq. (2), that the remaining factor of about 1.8, which is necessary to make the estimated velocity amplitude agree with the observed value (dotted vertical line), can be predominantly attributed to the underestimation of the linear damping rates η (see Houdek 2006). The signature of helium ionization Abrupt variation in the stratification of a star (relative to the scale of the inverse radial wavenumber of a seismic mode of oscillation), such as that resulting from the (smooth, albeit acoustically relatively abrupt) depression in the first adiabatic exponent γ = (∂ln p/∂ln ρ)s caused by the ionization of helium, where p, ρ and s are pressure, density and specific entropy, 126 Theoretical asteroseismology of solar-like oscillations Figure 4: Predicted velocity amplitudes (in solar units) as function of light-to-mass ratio for stochastically excited oscillations in other stars. Observations from several authors are plotted by the plus and triangle symbols. Theoretical estimates are plotted as diamond √ symbols. The dot-dashed vertical line indicates the reduction of the Procyon amplitude by a factor of 2 if the energy supply rate P of Stein et al. (2004) is assumed; the vertical dotted line indicates the remaining factor of about 1.8 by which the theoretical amplitude estimate according to Eq. (2) is still in error with the observations. or from the sharp transition from radiative to convective heat transport at the base of the convection zone, induces small-amplitude oscillatory components (with respect to frequency) in the spacing of the cyclic eigenfrequencies νn, of seismic oscillation and consequently also in Δνn, and δνn, . We call such abrupt variations an acoustic glitch. One might hope that the variation of the sound speed c induced by helium ionization might enable one to determine from the low-degree eigenfrequencies a measure that is directly related to, perhaps even almost proportional to, the helium abundance, with little contamination from other properties of the structure of the star. A convenient and easily evaluated measure of the oscillatory component produced by acoustic glitches is the second multiplet-frequency difference with respect to order n amongst modes of like degree : Δ2 νn, ≡ νn−1, − 2νn, + νn+1, (4) (Gough 1990). Any localized region of rapid variation of either the sound speed c or the density scale height, or a spatial derivative of them, induces an oscillatory component in Δ2 ν with a ‘cyclic frequency’ approximately equal to twice the acoustic depth Z τ = R c −1 dr (5) rglitch of the glitch, and with an amplitude which depends on the amplitude of the glitch and which decays with ν once the inverse radial wavenumber of the mode becomes comparable with or less than the radial extent of the glitch. Various approximate formulae for the oscillatory components that are associated with the helium ionization have been suggested and used, by e.g., Basu et al. (1994, 2004), Monteiro & Thompson (1998, 2005) and Gough (2002), not all of which are derived directly from explicit acoustic glitches. Gough used an analytic function for modelling the dip in the 127 G. Houdek first adiabatic exponent. In contrast, Monteiro & Thompson assumed a triangular form. Basu et al. have adopted a seismic signature for helium ionization that is similar to that arising from a single discontinuity; the artificial discontinuities in the sound speed and its derivatives that this and the triangular representations possess cause the amplitude of the oscillatory signal to decay with frequency too gradually, although that deficiency may not be immediately noticeable within the limited frequency range in which adequate asteroseismic data are or will imminently be available. More recently Houdek & Gough (2007) proposed a seismic diagnostic in which the variation of γ in the helium ionization zone is represented with a pair of Gaussian functions. This correctly results in a decay of the amplitude of the seismic signature with oscillation frequency that is faster than that which the triangular and the single-discontinuity approximations imply, and also takes some account of the two ionization states of helium. Moreover, Houdek & Gough (2007) incorporated the acoustic cutoff frequency into the variation of the eigenfunction phase with acoustic depth, thereby improving the discrepancy between the seismically inferred depths of the acoustic glitches and that of a corresponding stellar model. In particular these authors suggest the following seismic diagnostic for the oscillatory component associated with helium ionization δosc ν ˆ ˜` −8π 2 μ2 κ2I Δ2II ν 2 −ΓII ν0 ν + 12 (m + 1)ν0 μβκ−1 cos 2ψI I e −8π + κ−1 II e 2 2 2 2 κII ΔII ν ´ cos 2ψII , (6) in which the dominant glitch term δγ/γ in the helium ionization zone is represented by a pair of (negative) Gaussian functions of acoustic depth τ , with widths ΔI and ΔII , whose integrals are ΓI and ΓII , and which are centred about the acoustic depths τI and τII of the first and second ionization zones of helium beneath the seismic surface r = R of the star. The phases ψI = ψ(τ̃I ) and ψII = ψ(τ̃II ), where ωτ̃ = ωτ + II (ω = 2πν), are evaluated by representing the envelope by a plane-parallel polytrope of index m = 3.5 and adding a phase constant II to ωτ to account for the deviation of the actual envelope from the polytrope: ψ(τ ) = ωτ κ − (m + 1) cos−1 „ m+1 ωτ « + π . 4 (7) In Eq. (7), κI = κ(τ̃I ) etc, with κ(τ ) = [1−(m+1)2 /4π 2 ν 2 τ 2 ]1/2 . The ratios β = ΓI ΔII /ΓII ΔI , μ = ΔI /ΔII and τI /τII hardly vary amongst stellar models whose masses and radii vary by factors of at least five. To complete the description of Δ2 ν an oscillatory contribution with amplitude Ac (and phase constant c ) from the near discontinuity in the density scale height at the base τc of the convection zone is added. It is then straightforward to evaluate the second difference Δ2 ν, to which must be added a smooth term which is represented by a third-degree polynomial in ν −1 : Δ2,sm = 3 X ai ν −i . (8) i =0 The eleven parameters ΓII , Ac , ΔII , τII , τc , II , c and ai are adjusted to fit by least squares the theoretical curve to the second frequency differences of the actual eigenfrequencies of the modes. The top panel of Fig. 5 shows second differences Δ2 ν (symbols), defined by Eq. (4), of lowdegree solar frequencies with =0,1,2 and 3, obtained from BiSON (Basu et al. 2007). The solid curve is the seismic diagnostic (6)–(8), whose eleven parameters have been adjusted to fit the data by least squares. The values so obtained for the acoustic depth of the centre of the He II ionization zone is τII 819 s and the value for the magnitude of the relative depression 128 Theoretical asteroseismology of solar-like oscillations Figure 5: Top: the symbols (with error bars) are second differences Δ2 ν (Eq. (4)) of low-degree solar frequencies from BiSON (Basu et al. 2007). The solid curve is the diagnostic by Houdek & Gough (2007) which has been fitted to the data by least squares. The dashed curve represents the smooth contribution of the seismic diagnostic. Bottom: individual (oscillatory) contributions of the seismic diagnostic. The solid curve is the He II contribution, the dotted curve the He I contribution and the dot-dashed curve is the contribution from the base of the convection zone. of γ is −δγ/γ|τII 0.047. 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Astron., 26, 171 Stein R., Nordlund Å., 2001, ApJ, 546, 585 Stein R., Georgobani D., Trampedach R., Ludwig H.-G., Nordlund Å., 2004, Solar Physics, 220, 229 Stello D., Kjeldsen H., Bedding T. R., et al., 2004, Solar Physics, 220, 207 Tassoul M., 1980, ApJS, 43, 469 Trampedach R., Stein R. F., Christensen-Dalsgaard J., Nordlund Å., 1999, in Giménez A., Guinan E. F., Montesinos B., eds, ASP Conf. Ser. Vol. 173, Theory and Tests of Convection in Stellar Structure. Astron. Soc. Pac., San Francisco, p. 233 130 Theoretical asteroseismology of solar-like oscillations DISCUSSION Kupka: You mentioned that there may be some physics missing in the prediction of the mode amplitudes. I guess that in any of your models there is nothing that expresses the asymmetries between up- and downflows? Houdek: It is possible that the effect of acoustic wave scattering on mode damping plays an important role and consequently also on the mode amplitudes. The asymmetries between up- and downflows of the turbulent velocity field could also be important but I don’t know to which extent. It would require a convection formulation that goes beyond the Boussinesq approximation. Kupka: A short comment about Procyon: I believe that you are aware that there is disagreement between the simulations by the Yale group and by H.-G. Ludwig, for example, so we should be more careful with the simulations as compared to the solar case. Houdek: Yes. Roxburgh: A word of caution is needed, in the sense that the precision on the solar frequencies is much better than we are ever likely to get for other stars, at least in the near future. Therefore some of the things you are talking about are not realistic when applied to data from satellites as well as from the ground. The other point I would like to make is that you said nothing about the interior structure, but even with data that are worse than for instance the ones from BiSON, with precisions of the order of 0.1 - 0.2 μHz you can still make inversions to get the interior structure. Günter Houdek and Douglas Gough - still discussing solar-like oscillations? Comm. in Asteroseismology Vol. 150, 2007 λ Boo stars among the γ Dor-type pulsators: the cases of HD 218427 and HD 239276 E. Rodrı́guez,1 J. C. Suárez,1,2 A. Moya,1,2 M. A. Dupret,2 A. Grigahcène,3 V. Costa,1 M. J. López-González,1 A.-Y. Zhou,4 P. J. Amado,1 E. Poretti,5 J.-Y. Wei,4 Y. Fan 4 1 Instituto de Astrofı́sica de Andalucı́a, CSIC, P.O. Box 3004, E-18080 Granada, Spain, E-mail:[email protected] 2 LESIA, Observatoire de Paris-Meudon, UMR 8109, 92190 Meudon, France 3 CRAAG, Algiers Observatory, BP 63 Bouzareah 16340, Algiers, Algeria 4 National Astronomical Observatories, Chinese Academy of Sciences, Beijing 100012, China 5 INAF-Osservatorio Astronomico di Brera, Via E. Bianchi 46, 23807 Merate, Italy The γ Dor-type variables constitute a relatively recently recognized class of pulsating variables in the zone where the red edge of the δ Sct region intersects with the main sequence. λ Boo stars are metal-poor Population I stars that show significant underabundances of metals, except for the elements C, N, O and S. These stars are also characterized by showing broad, but often shallow, hydrogen-line wings and weak Mgii λ 4481 lines. A number of λ Boo stars are known to be δ Sct pulsators, but this question is still open concerning the γ Dor-type pulsators. To date, HR 8799 is the unique case known of a γ Dor-type variable being a λ Boo star too. However, some of these variables seem to be metal-deficient. This has important implications in asteroseismology of γ Dor stars concerning the distinction between the two possibilities or, vice versa, if a star is already known to be of the λ Boo-type, this can be used to constrain asteroseismic models. In this work, we study the cases of HD 218427 and HD 239276. Both variables were discovered as multiperiodic γ Dor-type pulsators (Rodrı́guez et al. 2006a,b), by means of simultaneous uvbyβ photometry, while they were used a check stars for observations devoted to other already well-known pulsators in the Lower Instability Strip, AC And and XX Cyg. HD 218427 and HD 239276 present very similar photometric characteristics to the multiperiodic γ Dor HR 8799, including a slight deficiency in metal content. This could be a sign of a λ Boo nature as was already found for HR 8799 by Gray & Kaye (1999). Indeed, the three stars are located inside the λ Boo region of both (m1 , b − y ) and ([m1 ], β) diagrams (Gray 1988, Gray & Corbally 1993). The Time-Dependent Convection (TDC) treatment for multicolour photometry (Dupret et al. 2005, Grigahcéne et al. 2005) and the Frequency Ratio Method (FRM) are used to discriminate the angular orders of the three main modes excited in these two stars. However, no definitive conclusions are obtained concerning the true nature of the observed metal deficiency, such as: (a) they really are metal-deficient stars or (b) they are λ Boo stars. In the case of HD 239276, by means of the TDC study, the two main modes are identified as = 1 and the third mode is suggested to be = 1 or 2. However, our results do not allow us to discriminate between a λ Boo or a truly metal-poor nature for this star. On the other hand, the FRM suggests low metallicity for this star, but a λ Boo nature cannot be ruled out. References Dupret M.-A., Rodrı́guez E., Garrido R., et al., 2005, MNRAS 360, 1143 Gray R. O., 1988, AJ, 95, 220 Gray R. O., Corbally C. J., 1993, AJ, 106, 632 Gray R. O., Kaye A. B., 1999, AJ, 118, 2993 Grigahcéne A., Dupret M.-A., Gabriel M., Garrido R., Scuflaire R., 2005, A&A, 434, 1055 Moya A., Suárez J. C., Amado P. J., Martı́n-Ruiz S., Garrido R., 2005, A&A, 432, 189 Rodrı́guez E., Amado P. J., Suárez J. C., et al., 2006a, A&A, 450, 715 Rodrı́guez E., Costa V., Zhou A.-Y., et al., 2006b, A&A, 456, 261 132 λ Boo stars among the γ Dor-type pulsators: the cases of HD 218427 and HD 239276 1.8 f1 f2 f3 f3 Ax/Ay 1.6 1.4 1.2 th th th th l=1 l=1 l=1 l=2 f1 f2 f3 obs obs obs 1 0.8 350 400 450 500 550 600 Wavelength (nm) Figure 1: Strömgren photometric amplitude ratios obtained for HD 239276 with the TDC treatment for a model with M=1.3 M , Z =0.01, log Te =3.8569, α=2. Juan Carlos Suarez, Pedro Amado, Rafa Garrido and Eric Michel. Comm. in Asteroseismology Vol. 150, 2007 Coordinated observational campaigns for non-radially pulsating objects K. R. Pollard,1 D. J. Wright,1 P. L. Cottrell,1 R. M. Woollands,1 D. J. Ramm,1 T. Böhm2 1 Department of Physics and Astronomy, University of Canterbury, Christchurch 8020, New Zealand 2 Laboratoire Astrophysique de Toulouse, Observatoire Midi-Pyrenees, Toulouse, France Abstract In recent years we have initiated and contributed to a number of campaigns to study nonradially pulsating objects. Our observing facility is the Mt John University Observatory 1.0 m telescope equipped with a high-efficiency and extremely stable echelle spectrograph, ideal for spectroscopic mode identification. Our current interests include δ Scuti star campaigns and a programme to study the non-radial pulsations in γ Dor stars. We are investigating several different methods of line profile analysis and spectroscopic mode identification of these targets. An overview of the programme, with specific examples, is presented. Spectroscopy at the Mt John University Observatory The instrumentation for asteroseismology at the University of Canterbury’s Mt John University Observatory (MJUO) is the 1.0 m telescope with the fibre-fed High Efficiency and Resolution Canterbury University Large Echelle Spectrograph, HERCULES (R ≈ 40 000 or 80 000; Hearnshaw et al. 2002;). The major elements of HERCULES are fixed to an optical bench located inside a cylindrical vacuum tank (4.3 × 1.2 m) in which the pressure is maintained at 1 to 5 torr. The tank is situated in a thermally isolated and insulated room. RMS stability of 15 m s−1 over time spans of 4 to 5 years is being achieved. This is ideal for high-resolution, time-series asteroseismological studies of reasonably bright stars (V < 9). The longitude of MJUO, coupled with our ability to acquire long sequences of observing time using this facility, allow us to coordinate and contribute to both single-site and multi-site asteroseismology campaigns. Target stars, analysis techniques and results We have completed the observational aspect of one multi-site campaign on QW Pup and HD 139095 (Wright et al. 2006) and are undertaking single-site observations from MJUO of a larger list of targets (Table 1). We have measured projected rotational velocities, identified binary or multiple systems and are investigating line-profile variations (LPV). A number of our targets have turned out to be in multiple stellar systems and orbital periods are still being determined. Line profiles are tested for variation by visual inspection of stacked plots and by plotting the residuals after subtraction of the average line profile. To increase our sensitivity to small-scale line profile variations, a high S/N representative line profile is obtained through cross correlating selected lines in each spectrum. Techniques used to analyse the line profile variations include the moment method (Briquet & Aerts 2003) and the phase change across the profile method (Telting & Schrijvers 1997). Our intention is to carry out spectroscopic mode identification by comparing the observed line profile variations with those predicted from models of the various non-radially pulsation modes. 134 Coordinated observational campaigns for non-radially pulsating objects Table 1: Targets observed using the MJUO 1.0 m and HERCULES. Star HD 10167 HD 14940 HD 17310 HD 27377 HD 40745 HD 41448 HD 75747 HD 166114 HD 172416 HD 187028 HD 189631 HD 214291 HD 216910 Comments F0V, V =6.676, SB2 F0IV,V =6.673, γ Dor F0, V =7.79 F0V, V =7.4 F2IV, V =6.207, γ Dor A9V, V =7.6 A7V, V =6.07, RS Cha, SB2 F2V, V =5.858, Triple system? F5V, V =6.632, SB1 F0V, V =7.5, γ Dor F0V, V =7.54, LPV F7V, V =6.581, SB2 F2IV, V =6.699, γ Dor, LPV # obs 2 2 2 1 2 2 351 19 10 1 7 78 11 V sini (km s−1 ) 6±2, 6±2 44±2 7±3 8±2 40±2 106±5 69±2, 72±2 8±2, 7±2 54±3 95±7 51±5 69±3, 69±3 100±6 References Briquet M., Aerts C., 2003, in Sterken C., ed., ASP Conf. Ser. Vol. 292, Interplay of Periodic, Cyclic and Stochastic Variability in Selected Areas of the H-R Diagram. Astron. Soc. Pac., San Francisco, p. 365 Hearnshaw J. B., Barnes S. I., Kershaw G. M., et al., 2002, Experimental Astronomy, 13, 59 Telting J. H., Schrijvers C., 1997, A&A, 317, 723 Wright D. J., Pollard K. R., Cottrell P. L., 2006, Mem. Soc. Astron. Ital., 77, 490 Comm. in Asteroseismology Vol. 150, 2007 Analysis tools for non-radially pulsating objects D. J. Wright, K. R. Pollard, P. L. Cottrell Department of Physics and Astronomy, University of Canterbury, Christchurch, New Zealand Abstract At the University of Canterbury we have been developing a set of tools for the analysis of spectra of varying types of non-radially pulsating objects. This set currently includes: calculation of the moments, calculations of the phase across the profile as well as basic binary profile fitting for determination of orbital characteristics and projected rotational velocity (v sin i ) measurement. Recently the ability to calculate cross-correlation profiles using either specified or synthesized line lists has been added, all implemented in MATLAB. A number of observations of γ Doradus candidates is currently being used to test these tools. For information on our observing facilities see Pollard et al. (2007). Introduction The set of tools that is being developed for the analysis of spectra of different types of non-radially pulsating objects include computing the moments of line profiles (Balona 1986), calculations of the phase across the profile (Telting & Schrijvers 1997), binary profile fitting for the determination of orbital characteristics and projected rotational velocity (v sin i ) measurements. We will employ profile inversions on fast rotators in the near future. Objects of this type require very high signal-to-noise (S/N) spectra for precise measurements of the line profiles. This need is lessened by the use of a cross-correlation technique to obtain a representative line profile. A number of observations of γ Doradus candidates and δ Scuti stars is currently being used to test these tools. Cross-correlation and projected rotational velocity Using cross-correlation of an object’s spectrum with a template of Delta Functions shifted to the rest wavelength position of the line and scaled to their relative depths, we achieve a high S/N representation of the line profile. This is valid for lines similarly distorted by the pulsation. The projected rotational velocity of the object is measured using the Fourier analysis technique outlined by Gray (1992, see his Fig. 17.12 (a)). The position of the first minimum on the abscissa of a Fourier-transformed line profile is compared with a theoretically calculated position obtained by the Fourier transform of the convolution of the spectrograph’s instrumental profile with the rotational broadening function. This theoretical position has been tested and is not very sensitive to the instrumental width. Line profile variations and periodicity of the moments Line profiles are tested for variation by examining the residuals after subtraction of the average line profile. If enough observations are obtained the moments of the line profiles are tested for variability. We can examine the periodicities present in the various moments to obtain some basic pulsation mode information. For example, the periodogram of the first moment shows all periodicities present in the star (with cross terms), whilst the second moment does 136 Analysis tools for non-radially pulsating objects not show the axisymmetric modes (m = 0) that are potentially present. The line moments technique is useful for δ Scuti stars where the main line profile variations are significant. However, for γ Doradus stars, where the line profile variations are not so apparent, other techniques have greater sensitivity and are therefore more useful for this class of non-radial pulsator. An example of this is the technique of line profile inversion (Berdyugina 1998). Acknowledgments. We thank the Royal Society of New Zealand (Canterbury Branch) for support toward travel to this conference and the Physics and Astronomy Department at the University of Canterbury. References Balona L. A., 1986, MNRAS, 220, 647 Berdyugina S. V., 1998, A&A, 338, 97 Gray D. F., 1992, The Observation and Analysis of Stellar Photospheres, Cambridge University Press Pollard K. R., Wright D. J., Cottrell P. L., et al., 2007, these proceedings Telting J., Schrijvers C., 1997, A&A, 317, 723 Theresa Lüftinger and Duncan Wright listening to an obviously interesting talk. Partially occulted in the background: Thierry Morel. Comm. in Asteroseismology Vol. 150, 2007 The convective envelope in γ Doradus stars: theoretical uncertainties J. Montalbán, A. Miglio and S. Théado Institut d’Astrophysique et de Géophysique de l’Université de Liège, B-4000 Liège, Belgium Abstract The depth of the convective envelope plays a fundamental role in the driving mechanism proposed by Guzik et al. (2000) to explain the high-order g modes of γ Dor pulsators. In this paper we study the sensitivity of the convective envelope depth to the description of convective transport, to relevant physical processes, such as microscopic diffusion, and to other uncertainties in theoretical stellar models. Depth of the convective envelope The “convection blocking” of radiation can drive high-order g-modes only for stellar models with a temperature, at the bottom of the convection envelope (CE), between 2 × 105 K and 4.8 × 105 K (Guzik et al. 2000). Unfortunately, convection modelling is one of the most serious shortcomings in theoretical stellar evolution. The “standard model” of convection, the mixing length theory (MLT), is a simple model that contains essentially one adjustable parameter, α, which relates the mixing length to the local pressure scale height. Convection efficiency increases with α as well as, for a given stellar mass and chemical composition, the depth of the CE. Usually α is tuned to produce the solar radius at the solar age, but 2D and 3D numerical simulations of convection suggest that its value should decrease with increasing stellar mass so that, for the γ Dor HR domain, it should be lower than the solar value. Furthermore, as the stellar mass increases, the effect of α on the stellar radius decreases, so that 1.5 M stellar models computed with α between 1.8 and 1.4 have the same Teff (i.e., corresponding to the middle of the observational γ Dor instability strip, for a metal mass fraction Z=0.02) while the depth of their CE is quite different (see Fig.1, left panel). An alternative to the MLT is the Full Spectrum of Turbulence treatment of convection (FST, Canuto et al. 1996). MLT is more efficient than FST in low efficiency convection regions, while FST is much more efficient than MLT for highly efficient convection. As a consequence, the depth of the CE for FST models changes from shallow to deep in a very narrow domain of Teff (see Fig. 1, left panel). The range of Teff of models whose Tcz is between 2 × 105 K and 4.8 × 105 K is reduced with respect to the MLT case and, therefore, the width of the γ Dor instability strip predicted by FST treatment is also smaller. The depth of the CE for models in the observational γ Dor instability strip is also affected by: (1) the microscopic diffusion, that increases by He settling the H abundance and, therefore, the opacity in the outer layers (see Fig. 1, right panel), and that, by effect of radiative acceleration and consequent Fe accumulation, can produce an additional convective region at 2 × 105 K. (2) the chemical composition: low metallicity models in the instability strip have shallower convective envelopes than solar metallicity ones. Acknowledgments. The authors acknowledge financial support from the Prodex-ESA Contract Prodex 8 COROT (C90199). 138 The convective envelope in γ Doradus stars: theoretical uncertainties Figure 1: Temperature of the convective envelope boundaries along the main sequence evolution of a 1.5 M star. Left panel: for three different treatments of convection: MLT with α=1.6 and 1.8, and FST. Right panel: models without microscopic diffusion (dots) and with gravitational settling of He (grey squares). References Guzik J. A., Kaye A. B., Bradley P. A., Cox A. N., Neuforge C., 2000, ApJ, 542, L57 Canuto V. M., Goldman I., Mazzitelli I., 1996, ApJ, 473, 550 Comm. in Asteroseismology Vol. 150, 2007 A search for solar-type oscillations in K giants in M4 S. Frandsen,1 H. Bruntt,1,2 F. Grundahl,1 G. Kopacki,3 R. L. Gilliland,4 E. Michel,5 T. R. Bedding,2 H. Kjeldsen,1,6 T. Arentoft,1,6 D. Stello,2 J. Mathiasen,1 P. D. Edmonds,7 A. Jacob 2 1 Dept. of Physics and Astronomy, University of Aarhus, Denmark 2 School of Physics, University of Sydney, Australia 3 Institute of Astronomy, University of Wroclaw, Poland 4 Space Telescope Science Institute, Baltimore, USA 5 Observatoire de Paris, Meudon, France 6 Danish AsteroSeismology Centre, University of Aarhus, Denmark 7 Center for Astrophysics, Cambridge, MA, USA Abstract A large CCD photometry campaign has been organized, where more than 6000 frames were collected, to search for solar-like oscillations among K-giants in M4. The results are presented here with the main result being: amplitudes are below predictions. The setting Stars up to 60 L are known to show a p-mode spectrum (Frandsen et al. 2002) with short lifetimes (Stello et al. 2006). Is this also true for even higher luminosities? If so, could one then make seismic studies along the giant branch in open/globular clusters? This is the question to be addressed here. The observed stars are shown in Fig. 1. The stars with the best time series are indicated with large, filled symbols. p modes with amplitudes A in the interval 600–1200 ppm are predicted in a frequency range 10–50 μHz by Kjeldsen and Bedding (1995), where A ∝ L/M. Conclusion The detailed conclusion will be presented elsewhere, but the short version is, as illustrated in Fig. 2, that p modes (and granulation) are not present at the expected amplitudes given by Kjeldsen and Bedding (1995). References Frandsen S., Carrier F., Aerts C., et al., 2002, A&A, 394, L5 Kjeldsen H., Bedding T. R., 1995, A&A, 293, 87 Ludwig H.-G., 2006, A&A, 445, 661 Stello D., Kjeldsen H., Bedding T. R., Buzasi D., 2006, A&A, 448, 709 140 A search for solar-type oscillations in K giants in M4 Figure 1: Small part of the Colour-Magnitude diagram illustrating the large number of targets (K giants) present in M4. The scatter on the HB is due to the variability of the RR Lyrae stars: the V magnitude is not the mean/average value. Figure 2: The upper panel is an amplitude spectrum for a simulation of granulation (based on Ludwig 2006), white noise and a p mode spectrum with A=300 ppm and a lifetime of 8 days. The lower panel is the spectrum for the brightest K giant in the sample. The spectrum and the simulation look alike. Both have p mode power below the predictions (600–1200 ppm). Comm. in Asteroseismology Vol. 150, 2007 Rotation and small separations of α Cen A M. 2 Bazot,1,2 F. Bouchy,3,4 H. Kjeldsen,1 S. Charpinet,2 M. Laymand,2 S. Vauclair 2 1 Institut for Fysik og Astronomi, Aarhus Universitet, DK-8000 Aarhus C., Denmark Laboratoire d’Astrophysique de Toulouse-Tarbes, Observatoire Midi-Pyrénées, 31400 Toulouse, France 3 Observatoire de Haute Provence, 04870 St Michel l’Observatoire, France 4 Institut d’Astrophysique de Paris, 98bis Bd Arago, 75014 Paris, France Abstract We observed α Cen A during five nights using HARPS. We identified 34 p modes. We observed multiple frequencies for some value of radial order n and degree . We analyse the scatter of these frequencies relative to the asymptotic relation and argue that they result from rotational splitting. We derive new values for the small separations taking in account this effect. Observations We report here on a five-night run on α Cen A using the high-precision spectrograph HARPS. Our exposure time range typically between 2 s and 10 s. The typical signal-to-noise ratio in the data is in the range 300 – 450. In the time series, the dispersion for each individual night is in the range 1.5 – 3.3 ms−1 . In the amplitude spectrum, we found a 3.7 cms−1 mean noise level in the range 4 – 5.5 mHz. The estimated photon noise is 0.51 cms−1 . The difference is mainly due to guiding noise. Results We used both on-sight identification and the CLEAN algorithm to extract frequencies from the power spectrum. We then selected the p modes using the asymptotic relation as a reference. We eventually obtained a set of 34 oscillation frequencies with degrees = 0, 1, 2, 3 and radial orders n in the range 16 – 26. The amplitudes of the modes range from 13 cms−1 to 48 cms−1 . In the case of = 2 modes, we identified 5 multiplets for radial orders 19 to 23. Assuming that our modes are unresolved, we adopted an uncertainty of 1.3 μHz on our frequencies, which is half the frequency resolution. Our results are in good agreement with the previous runs on α Cen A, the thirteen-night CORALIE campaign (Bouchy & Carrier 2002) and the multi-site campaign using UVES and UCLES (Bedding et al. 2004). For each degree, the frequencies were fitted using a second-order polynomial. We then computed the scatter around these polynomials. Such a scatter is the consequence of several effects, both observational (S/N, sampling) and stellar (finite mode lifetimes, rotational splitting). The resulting scatters are for HARPS: σ0 = 0.41 μHz, σ1 = 0.57 μHz, σ2 = 1.50 μHz (subscripts indicate the mode degree). For high inclinations of the rotation axis, this effect could be interpreted as a signature of rotational splitting. We note that multiplets were also identified with UVES/UCLES, not with CORALIE. Considering the effect of rotational splitting, frequencies have to be averaged over the azimuthal order m to compute accurate small spacings, defined by δνnl = νn,l − νn−1,l +2 . These quantities are extremely useful to constrain theoretical models. We display small spacings obtained from each run in Fig. 1. 142 Rotation and small separations of α Cen A Figure 1: Small spacings of α Cen A from the HARPS (filled squares), CORALIE (open squares) and UVES/UCLES (open circles) runs. The trends in the HARPS and UVES/UCLES spacings are in good agreement. References Bouchy F., Carrier F., 2002, A&A, 390, 205 Bedding T. R., Kjeldsen H., Butler R. P., et al., 2004, ApJ, 614, 380 Michael Bazot and Mélanie Godart. Comm. in Asteroseismology Vol. 150, 2007 Solar-like Oscillations with Kepler J. Molenda-Żakowicz,1 T. Arentoft,2,3 H. Kjeldsen,2,3 M. Vaňko 4 1 Institute of Astronomy, Wroclaw University, Kopernika 11, 51-622, Wroclaw, Poland 2 Danish AsteroSeismology Centre (DASC), University of Aarhus, Denmark 3 Institute of Physics and Astronomy, University of Aarhus, Denmark 4 Astronomical Institute, Slovak Academy of Sciences, Tatranska Lomnica, Slovakia Abstract We describe our program of ground-based spectroscopic and photometric observations of stars selected to be scientific targets in the Kepler Asteroseismic Program. Introduction Kepler is a NASA Discovery space mission scheduled for launch in November 2008. It will perform continuous observations of all V = 9 − 15 mag stars that fall into its field of view. The observations will be continued for the entire life–time of the mission, i.e., 4–6 years, with an expected precision at the level of several ppm. The main purpose of the mission is the detection of terrestrial planets with the method of transits. The other scientific aim of the Kepler mission is a study of pulsating stars which will support the interpretation of planetary transit events and the study of stars that harbour planetary systems. The mission is described in more detail by Christensen-Dalsgaard et al. (2007). Along with the main aims, Kepler will realize the Kepler Asteroseismic Program. This program will be coordinated from the University of Aarhus, under the lead of Professor Jørgen Christensen-Dalsgaard. One of the ongoing activities related to this program are spectroscopic and multi–colour observations of the most promising asteroseismic targets listed by MolendaŻakowicz et al. (2006). Since the majority of these stars have solar–like spectral type, we expect them to show solar–like oscillations. Observations Our observations are made at four observatories, namely, Harvard-Smithsonian Astrophysical Observatory, SAO (USA), Serra la Nave Observatory (Italy), Stara Lesna Observatory (Slovakia) and Bialków Observatory (Poland). At the SAO, the Kepler targets are observed spectroscopically by Prof. David Latham who uses the 6.5-m MMT telescope, the 1.5-m Tillinghast Reflector and the 1.5-m Wyeth Reflector. At Serra la Nave Observatory, the targets are observed by Dr. Molenda-Żakowicz who uses a 1-m telescope of Catania Astrophysical Observatory, the FRESCO echelle spectrograph and a set of UBVuvby β filters. At the Observatory of the Slovak Academy of Sciences in Stara Lesna, and the Bialków Astrophysical Observatory of Wroclaw University, Drs. M. Vaňko and J. Molenda-Żakowicz perform time-series observations of NGC 6811 and NGC 6866, two open clusters that fall into Kepler’s field of view and that are selected to be Kepler asteroseismic targets. 144 Solar-like Oscillations with Kepler Results We determined Vr , [Fe/H], v sin i , log Teff , log g , E (B − V ) and UBVuvby β standard magnitudes and for all targets that were selected for observations in the first run of our observing program (Molenda-Żakowicz et al. 2007). In the next observing season we will continue the observations and determinations of astrophysical parameters of the remaining stars. We will also study the variability of stars that fall into the fields of NGC 6811 and NGC 6866. Our final aim is an asteroseismic study of all the Kepler asteroseismic targets and a detailed analysis of solar–like pulsations in other stars. Acknowledgments. J. Molenda-Żakowicz acknowledges the EC for the establishment of the European Helio- and Asteroseismology Network HELAS, which made her participation at this workshop possible. This work was partly supported by MNiSW grant No N 203 014 ¯ 31/2650. References Christensen-Dalsgaard J., Arentoft T., Brown T. M., et al., 2006, Comm. Asteroseis., 150, these proceedings Molenda-Żakowicz J., Arentoft T., Kjeldsen H., Bonanno A., 2006, in Fletcher K., ed., SOHO 18/GONG 2006/HelAs I: Beyond the spherical Sun. ESA SP-624, Noordwijk, p. 110.1 Molenda-Żakowicz J., Frasca A., Latham D., Bazot M., 2007, in preparation Joanna Molenda-Żakowicz, Jadwiga Daszyńska-Daszkiewicz and Anna Dziembowski. Comm. in Asteroseismology Vol. 150, 2007 High-frequency interference peaks in solar-like stars C. Karoff 1,2 1 Department of Physics and Astronomy, University of Aarhus, Denmark 2 Danish AsteroSeismology Centre, University of Aarhus, Denmark Introduction The oscillation modes we observe in solar-like stars are the eigenmodes of the stars. This means that these modes are the sound waves that make constructive interference with themselves inside the stars and, in order for a wave to make constructive interference, it needs to be reflected somewhere. The p modes in solar-like stars are reflected by the stellar atmosphere, but this reflection only takes place up to a given frequency – known as the acoustic cut-off frequency. But from observations of the Sun (Garcı́a et al. 1998) and α Cen B (Kjeldsen et al. 2005) we know that these stars do show oscillations with frequencies above the acoustic cut-off frequency. These oscillations are known as High-frequency Interference Peaks (HIPs). Analysis Two different models exist for explaining the nature of these oscillations known as HIPs. Balmforth & Gough (1990) have suggested that the HIPs are due to reflection of ordinary p modes at the transition layer between the chromosphere and the corona. Kumar & Lu (1991) on the other hand have argued that constructive interference between a direct and a reflected wave from a source just below the photosphere could cause the HIPs. The two different models predict different behaviour of the frequency separations of the HIPs (equivalent to the large separation for the p modes) as a function of frequency. It is the plan for future work to use the model predictions of the large separation to evaluate the success of the model in predicting the observations. In order to evaluate the two different models of HIPs I have carried out the same data analysis to the Sun, β Hydri and α Cen A & B. The data on the Sun are from the GOLF instrument on SOHO, while the data on β Hydri and α Cen A & B are from UCLES at AAT, HARPS at La Silla or UVES at VLT (see: Garcı́a et al. 2005, Bedding et al. 2007, Butler et al. 2004, Kjeldsen et al. 2005). In order to see the HIPs I have calculated the echelle diagram of half the large separations for the 4 stars and smoothed them with a Gaussian PSF with a FWHM of Δν/16 in the horizontal and 8 echelle orders in the vertical direction. This is a technique that is well known from image manipulation – that one increases the contrast in an image by defocusing it a little bit. The large separations can then be obtained as the peak in each echelle order in the echelle diagram. The obtained large separations are shown in Fig. 1. Acknowledgments. I would like to thank J. Christensen-Dalsgaard and H. Kjeldsen for many useful comments on this study. I also acknowledge support from the Instrument Centre for Danish Astrophysics. References Balmforth N. J., Gough D. O., 1990, ApJ, 362, 256 Bedding T. R., Kjeldsen H., Arentoft T., et al., 2007, ApJ, submitted 146 High-frequency interference peaks in solar-like stars Figure 1: The large separation as a function of frequency. Butler R. P., Bedding T. R., Kjeldsen H., et al., 2004, ApJ, 600, L75 Garcı́a R. A., Pallé P. L., Turck-Chièze S., et al., 1998, ApJ, 504, L51 Garcı́a R. A., Turck-Chièze S., Boumier P., et al., 2005, A&A 442, 385 Kjeldsen H., Bedding T. R., Butler R. P., et al., 2005, ApJ, 635, 1281 Kumar P., Lu E., 1991, ApJ, 375, L35 Comm. in Asteroseismology Vol. 150, 2007 Detection of p-mode oscillations in β Hydri from photometric observations with WIRE C. Karoff,1,2 H. Bruntt,3 H. Kjeldsen,1,2 T. Bedding,3 D. L. Buzasi 4 1 Department of Physics and Astronomy, University of Aarhus, Denmark 2 Danish AsteroSeismology Centre, University of Aarhus, Denmark 3 School of Physics, University of Sydney, Australia 4 US Air Force Academy, Department of Physics, Colorado, USA Abstract β Hydri was observed with the star tracker on the WIRE satellite for 34 days in August and September 2005. After correcting the data for stray light and satellite jitter, a clear excess is seen around 1 mHz in the power spectrum. The photometric observations with WIRE were performed simultaneously with a groundbased campaign on β Hydri, where ultra-precise radial velocity data were obtained with HARPS at the ESO 3.6-m telescope and with UCLES at the 3.9-m AAT. Using the frequencies from the velocity data, we have obtained estimates of mode lifetime, rotation period and inclination by fitting a model to the power spectrum of the photometric data. Observations and data reduction The raw light curve of β Hydri from WIRE has a sampling rate (and integration time) of 0.5 s, an orbital duty cycle of 28%, and a rms noise of 28 mmag. As the main part of the noise in the raw light curve originates from stray light and satellite jitter, the light curve needs to be decorrelated to see oscillations with amplitudes of the order of ppm. By decorrelation, we mean that we remove any correlation between the measured flux and a set of decorrelation parameters. The decorrelation parameters we used were orbit phase, orbit number and the position of the star on the CCD chip. After correcting the light curve, we used Butler et al.’s (2004) technique for adjusting the measured error related to a given data point. Fig. 1 shows the final power spectrum. A large excess of power is seen at the orbital frequency (178.5 μHz) and its harmonics. We therefore excluded frequencies separated by less than 1.3 μHz from the orbital frequency or its harmonics in the simulation of the power spectrum. Figure 1: Normalized power spectrum of β Hydri. The spectrum has been normalized to the mode with the highest amplitude identified in the data (marked by an arrow at 916 μHz). The regularly separated peaks in the spectrum with amplitudes higher than 1 are the harmonics of the orbital frequency. 148 Detection of p-mode oscillations in β Hydri with WIRE Simulation of the power spectrum We employed the technique by Fletcher et al. (2006) for fitting the power spectrum. The model we fitted is a sum of standard Lorentzians centred on the frequencies of modes identified in a preliminary analysis of the ground-based velocity data (excluding =3 modes; Bedding et al. 2007), their first and second sidebands, their rotational splitting, and an offset with a 1/f background. The uncertainties were estimated assuming that the variance of the likelihood function was equal to 1/n, where n is the number of frequencies fitted. The fit to the data is shown in Fig. 2. Vertical dashed lines mark the modes that have been identified in the ground-based velocity data and used in the simulation of the power spectrum. Each panel is shifted by 178.5 μHz, equal to the satellite’s orbital frequency, and so sidebands from each mode are aligned vertically in adjacent panels. We note that some of the modes (peaks) have quite different amplitudes in the photometry and velocity data, although the observations were made simultaneously. A difference in amplitudes is expected (because of the finite mode lifetime) as the photometry campaign lasted four times longer than the spectroscopy campaign. This also explains why some modes are only present in the velocity data. Figure 2: Normalized power spectrum of β Hydri (dotted line) and the simulation (solid line). Each panel is shifted by 178.5 μHz to make the sidebands align vertically. The vertical dashed lines mark the modes used in the simulation. The orbital frequency and its harmonics have been excluded from the plot. The normalization is the same as in Fig. 1. Our results can be summarized as follows: we find a mode lifetime of 4.2+2.0 −1.4 days, a lower ◦ limit on the rotation period of 65 days and an inclination of 68◦ +17 . The rotation period −52◦ and inclination are compatible within the uncertainties with a v sin i of 2 ± 1 km s−1 and a radius of 1.6 ± 0.5 R (Dravins et al. 1993). The analysis of the β Hydri data is still not complete and the results presented here should only be considered as preliminary. The complete analysis will be presented in a later paper. Acknowledgments. CK acknowledges support from the Instrument Centre for Danish Astrophysics. HB is supported by the Australian Research Council. References Bedding, T. R., Kjeldsen H., Arentoft T., et al., 2007, ApJ, submitted Butler, R. P., Bedding T. R., Kjeldsen H., et al., 2004, ApJ, 600, L75 Dravins, D., Lindegren L., Nordlund A., Vandenberg D. A., 1993, ApJ, 403, 385 Fletcher S. T., Chaplin W. J., Elsworth Y., Schou J., Buzasi D., 2006, MNRAS, 371, 935 Comm. in Asteroseismology Vol. 150, 2007 Solar-like oscillations in open cluster stars Stello,1 D. H. Bruntt,1 T. Arentoft,2,3 R. L. Gilliland,4 J. Nuspl,5 S.-L. Kim,6 Y. B. Kang,6 J.-R. Koo,6 J.-A. Lee,6 C.-U. Lee,6 C. Sterken,7 A. P. Jacob,1 S. Frandsen,2,3 Z. E. Dind,1 H. R. Jensen,2 R. Szabó,5 Z. Csubry,5 L. L. Kiss,1 M. Y. Bouzid,7 T. H. Dall,8 T. R. Bedding,1 H. Kjeldsen 2,3 2 1 School of Physics, University of Sydney, NSW 2006, Australia Institut for Fysik og Astronomi (IFA), Aarhus Universitet, 8000 Aarhus, Denmark 3 Danish AsteroSeismology Centre, Aarhus Universitet, 8000 Aarhus, Denmark 4 Space Telescope Science Institute, 3700 San Martin Dr., Baltimore, USA 5 Konkoly Observatory, 1525 Budapest, PO Box 67, Hungary 6 Korea Astronomy and Space Science Institute, Daejeon 305-348, Korea 7 Vrije Universiteit Brussel, Pleinlaan 2, B-1050 Brussels, Belgium 8 European Southern Observatory, Casilla 19001, Santiago 19, Chile Introduction Asteroseismology of stellar clusters is potentially a powerful tool. The assumption of a common age, distance, and chemical composition provides constraints on each cluster member, which significantly improves the asteroseismic output. Hence, detecting oscillations in cluster stars in a range of evolutionary stages holds promise of providing more stringent tests of stellar evolution theory. Driven by this great potential, we carried out multi-site observations aimed at detecting solar-like oscillations in the red giant stars in the open cluster M67 (NGC 2682). To obtain these data we observed for 43 days with nine 0.6-m to 2.1-m class telescopes in January and February 2004 (Stello et al. 2006). The photometric time series comprises roughly 18000 data points. The properties of the red giant stars we present here are given in Table 1 and their location in the colour-magnitude diagram is shown in Fig. 1 (left panel). Figure 1: Left Panel: The colour-magnitude diagram of the open cluster M67. The red giant target stars and their ID are indicated. Right Panel: Average power distributions for three groups of stars sorted according to luminosity: most luminous (clump stars), intermediate, and least luminous (lower RGB). Arrows show expected locations of solar-like oscillations (see Table 1). Only stars with a white-noise level lower than 50 μmag have been used. 150 Solar-like oscillations in open cluster stars Table 1: Properties of red giant target stars. Luminosities and temperatures are from photometry (Montgomery et al. 1993). Estimates of oscillation amplitudes, characteristic frequencies and large separations are from known scaling relations in the literature (Kjeldsen & Bedding 1995, Brown et al. 1991), Cross references are to Sanders (1977) and Gilliland et al. (1991). ID L/L Teff K δL/L μmag νmax μHz Δν0 μHz Cross-ref. 8 9 10 2 18 50.8 50.2 48.2 46.4 45.8 4750 4772 4727 4727 4772 287 281 275 265 256 35.8 36.8 37.0 38.4 40.3 4.3 4.4 4.4 4.6 4.7 S1010/G2 S1084/– S1279/G7 S1074/– S1316/– 5 17 7 15 25.4 22.4 20.2 16.9 4815 4835 4854 4873 140 122 109 91 74.8 86.0 96.9 117.3 7.6 8.4 9.2 10.6 S1054/G9 S1288/– S989/G12 S1277/– 14 13 11.2 9.9 4945 4966 58 51 187.3 213.2 15.2 16.8 S1293/– S1305/– Results Mean levels in the Fourier spectra in the frequency interval 300–900 μHz, corresponding to white noise, reach 20 μmag for the stars with the lowest noise. In many stars we see apparently high levels of non-white noise, but the detailed temporal variation of the noise is unknown. We are therefore not able to clearly disentangle the noise and stellar signal in the analysis. However, we do see evidence of excess power in the Fourier spectra, shifting to lower frequencies for more luminous stars, consistent with expectations (Fig. 1; right panel). If the observed power excesses were due to stellar oscillations, this result would show great prospects for asteroseismology in stellar clusters. A more detailed analysis will be given by Stello et al. (2007). Acknowledgments. Australia. This paper has been supported by the Astronomical Society of References Brown T. M., Gilliland R. L., Noyes R. W., Ramsey L. W., 1991, ApJ, 368, 599 Gilliland R. L., Brown T. M., Thomson D. T., et al., 1991, AJ, 101, 541 Kjeldsen H., Bedding T. R., 1995, A&A, 293, 87 Montgomery K. A., Marschall L. A., Janes K. A., 1993, AJ, 106, 181 Sanders W. L., 1977, A&AS, 27, 89 Stello D., Arentoft T., Bedding T. R., et al., 2006, MNRAS, 373, 1141 Stello D., Bruntt H., Kjeldsen H., et al., 2007, MNRAS, in press Comm. in Asteroseismology Vol. 150, 2007 Core modes as a seismic probe of mixing beyond the convective core B. L. Popielski Warsaw University Observatory, Al. Ujazdowskie 4, 00-478, Warsaw, Poland The debate on the extent of mixing beyond the convective core is not yet settled. For intermediate mass stars, 1.2 – 2 M , where the convective core tends to grow, three mixing recipes must be considered. These are: the layered model (LY; Spruit 1992), which assumes no mixing, the semi-convective model (SC; Schwarzschild & Härm 1958), where moderate mixing occurs, and the overshooting model (OV), where the extent is the largest and may be suitably chosen. There is a subset of stochastically excited modes which is particularly useful for sounding the partially mixed layers above the core. I will refer to this subset as core modes because these modes are partially trapped in the g-cavity encompassing the inhomogeneous layers. The consecutive core modes (k = 1, 2, etc.) are nearly equidistant in period. The = 1 core modes are expected to have larger surface amplitudes compared to the modes of higher degree, not only near the avoided crossing frequency and hence should be easily detected. I tested whether the mixing recipes may be distinguished with the use of core modes. For testing I chose η Boo, for which the possible presence of core modes was suggested (Di Mauro et al. 2003). I looked for such modes in the rich oscillation spectrum from MOST (Guenther et al. 2005). Possible dipole modes were identified by their large departure from the = 1 p-mode ridge in the echelle diagram. I identified 7 possible dipole core modes. Only model calculations could be used to state which of these modes are dipole core modes. I calculated evolutionary models of η Boo for three mixing recipes. The 0.1 Hp overshooting distance was adopted. The models were constrained by the following non-seismic observables: effective temperature, Teff , luminosity, L, surface metallicity, (Z /X )s and two seismic parameters derived from the = 0 ridge in the echelle diagram: the mean large separation, D, and the width of the ridge, ΔνD . In these models there are core modes up to k = 3 (see Table 1). However, our identification procedure could have eliminated the core modes, whose frequencies were too close to the p-mode ridge, from the observed spectrum. Thus, we should expect at most 3 dipole core modes. The remaining peaks could be attributed to modes of higher or just artifacts. Identification of possible core modes was done using the Π − ΔΠ diagram, where Π stands for period and ΔΠ stands for the period difference between two consecutive modes. I identified 7 pairs of peaks as k = 1 or k = 2. If we assume that only two peaks correspond to core modes, we cannot exclude any of the mixing recipes considered because we don’t know which 5 peaks have to be rejected. On the other hand, if we assume that three peaks, found to be nearly equidistant in period, correspond to core modes, then the layered model (LY) is favoured. Of course, we don’t know which case we deal with. Clearly, the available data do not allow us to distinguish the mixing recipes. In part this is due to ambiguities in the mode identification, which may vanish for a much cleaner spectrum. In part it is due to rather LY SC OV0 α 2.10 1.95 1.95 t [Gyr] 2.384 2.402 2.244 15.44 18.42 23.16 Π1 , Π2 , Π3 [min] 21.58 28.33 25.80 33.22 32.22 39.49 Table 1: Parameters of central models reproducing the observables of η Boo for the three mixing recipes. In columns we find the values of the mixing-length parameter, age and periods for the first three dipole core modes. The models have identical mass of 1.71 M and common initial chemical composition, X0 = 0.73 and Z0 = 0.034. 152 Core modes as a seismic probe of mixing beyond the convective core poor constraints for models, which result in large uncertainties of Π and ΔΠ. This may be improved by reducing uncertainties of temperature, metallicity and oscillation frequencies. Acknowledgments. I thank W. A. Dziembowski for many valuable discussions. I also thank the European Helio- and Asteroseismology Network HELAS for financial support. References Di Mauro M. P., Christensen-Dalsgaard J., Kjeldsen H., Bedding T. R., Paternò L., 2003, A&A, 404, 341 Guenther D. B., Kallinger T., Reegen P., et al., 2005, ApJ, 635, 547 Schwarzschild M., Härm R., 1958, ApJ, 128, 348 Spruit H. C., 1992, A&A, 253, 131 Katrien Kolenberg on close inspection of a poster. Comm. in Asteroseismology Vol. 150, 2007 Two-scale mass-flux closure models for turbulence: p-mode amplitudes in solar-like stars K. Belkacem,1 R. Samadi,1 M.-J. Goupil,1 F. Kupka,2 M.-A. Dupret 1 2 1 Observatoire de Paris, LESIA, CNRS UMR 8109, 92195 Meudon, France Max-Planck-Institute for Astrophysics, Karl-Schwarzschild-Str. 1, 85741 Garching, Germany Abstract A new closure model has been developed, which takes into account both the skewness of the velocity distribution induced by the presence of two flows in the convection zone, and the effects of turbulence onto each flow (Belkacem et al. 2006a). Applied to the formalism of p-mode excitation, it has been possible to validate this theoretical model by a comparison with the observational excitation rates in the solar case using GOLF data (see Belkacem et al. 2006b). The next step is to consider α Cen A for which observations of the mode-damping rates are available. Results and conclusion A confrontation of the solar excitation rates using the closure model with plumes (CMP) has successfully been performed in the solar case, except at high frequency where uncertainties remain. In these proceedings we focus on α Cen A for which the best data are available (Bedding et al. 2004, Fletcher et al. 2006). These constraints are compared with new theoretical calculations as developed by Belkacem et al. (2006b). Figure 1 shows that the current observational constraints are not accurate enough to discriminate between the quasi-normal approximation (QNA) closure model (see Belkacem et al. 2006a) and the CMP although, as in the solar case, the CMP decreases the discrepancy between theoretical and observational excitation rates. Preliminary work tends to show that the asymmetry between the updrafts and the downdrafts does not change significantly between the few 3D simulations of main-sequence stars investigated in this work and that the CMP remains valid according to these 3D simulations. Hence, we expect that the difference between the effect on the excitation rates of the CMP model and that of the QNA remains constant for intermediately massive stars lying on the main sequence. This, however, needs to be confirmed using more 3D simulations and needs to be extended to other domains in the HR diagram. It emphasizes the need for more accurate seismic data to discriminate between the two closure models. The space based mission CoRoT is an asteroseismology mission that in the very near future will enable us to derive, for a large set of solar-like oscillating stars with different effective temperature and gravity, the rates at which energy is supplied to the modes by turbulent convection. The quality of those data is expected to be significantly higher than for current observations. References Bedding T. R., Kjeldsen H., Butler R. P., et al., 2004, ApJ, 614, 380 Belkacem K., Samadi R., Goupil M.-J., Kupka F., 2006a, A&A, 460, 173 Belkacem K., Samadi R., Goupil M.-J., Kupka F., Baudin F., 2006b, A&A, 460, 183 Fletcher S. T., Chaplin W. J., Elsworth Y., et al., 2006, MNRAS, 371, 935 154 Two-scale mass-flux closure models for turbulence: p-mode amplitudes in solar-like stars Figure 1: The dashed line corresponds to the constraints obtained from the observed spectrum derived by Bedding et al. (2004) for the amplitudes and the averaged mode line-widths derived by Fletcher et al. (2006). Dotted lines correspond to the estimated error interval of the observational data. The theoretical calculation based on the CMP is plotted as the solid line and the QNA closure based calculation as the dash-dotted line. Alexander Kaiser, Paul Beck, Patrick Lenz, Gerhard Hensler and Holger Pikall. Comm. in Asteroseismology Vol. 150, 2007 Discussion on solar-like oscillators and γ Doradus stars led by Douglas O. Gough Institute of Astronomy, University of Cambridge, Cambridge CB30HA, UK Gough: Perhaps we should go through what we’ve heard today, and see what issues were raised. Just one point (before I forget): the kind of precision that Günter succeeded so marvellously in obtaining for things like the ionization of helium in the Sun is much greater than the precision we can expect to get from other stars. The high precision enabled him, in particular, to distinguish (barely) between the subtleties of the fits of various formulae to the data. The issue especially for other stars is just how to model a seismic signature with an appropriate functional form, particularly when several different formulae appear to fit the less precise data equally well. If one wants to calibrate other stars and extract quantities like the helium abundance, Y , it is essential that Y is contained in the signature in the right way. One could simply fit stellar models using Y as one of the several parameters that have been chosen (often for computational convenience) to define them, but how does one know whether the outcome is biased by other, hidden, variables? I don’t think Günter stressed in his talk the importance of relating in a robust way the seismic signature directly to the physical quantities one wants to determine. Perhaps we should refresh our minds and get back to what we’ve learnt from γ Doradus stars. They are very useful because they are g-mode pulsators. One of the important issues is what excites them. This appears to be at least partially understood now, which I thought was great, but there remain some physical principles that aren’t understood. To be sure, there was modulation of the heat flux, and there were important contributions from convection; and one thing we heard today was that convection is very important, and those who ignore it, at their peril, get results that are at least suspect. But how could theorists improve the situation? We have theories - not very many - that attempt to address variations of the heat flux and the diagonal components of the Reynolds stress, but for g modes the non-diagonal components are also important, as Marc-Antoine said in his talk. As far as I am aware, to estimate those components in terms of the others in the theory requires the introduction of more parameters, a procedure which is always worrying. For then one must question whether the formalism is predictive? I don’t know how to answer this, but I am asking for comments on the theories, and how one might then carry out even a half-way meaningful calculation. Fritz has been absolutely silent on this issue; I wonder if you have anything to say? Kupka: The existing simulations (star-in-a-box) describe how a star evolves, which is not very useful in this case because convection occurs at a very small scale. We can’t resolve this in such simulations. The other case is a box-in-a-star where we resolve the up- and downflows. The problem with the g modes is that the size of the waves is much larger than the boxes. You will have to set artificial boundaries and take care to connect them properly in the case of these stars. So I don’t think it would be easy to make simulations that are useful for testing this idea. Kaye: The dynamical models, which are numerical models, and which are more than a sketch on a piece of paper, have not been around for that long. The reason for this is that we started with the frozen-in convection, simply because it was the easiest thing and in fact the only one that was available. As we progressed further and put in physics that must be included we thought that qualitatively that description is OK. I think this is what Marc-Antoine tried 156 Discussion on solar-like oscillators and γ Doradus stars to say. He did not say that we know everything and we understand all the frequencies and amplitudes etc. But what he did say, at a very qualitative level, is that we know what the basic driving mechanism is. And if you go back, say, five years, we couldn’t say that. Dupret: The time-dependent convection treatment I included in my non-adiabatic models is a perturbation of the mixing-length treatment, so of course there are approximations in this treatment. But what we saw is that if you include the effects of convective flux variations and turbulent pressure variations, this does not change significantly the driving. The basic mechanism remains the same: a periodic flux blocking at the base of the convective envelope driving the gravity modes. There is still the problem of how to model the non-diagonal components of the Reynolds stress variations. We have begun such work but the predictions depend strongly on unknown parameters, and it is not yet possible to conclude. It would be fine if we could get information on the coherent interaction between convection and pulsation from numerical simulations, but I am not sure how far this would be possible at this time. Montgomery: Here, the relevant time scales, the pulsational time scale and the convective turnover time scale, are of the same order. There are some stars where things should be somewhat easier. If you look at pulsating white dwarfs, the convective turnover times are of the order of a second and the pulsation periods are a few hundred seconds. Therefore you can treat the convection zone as instantly adjusting. Then all we need to care about is what is the thermal re-adjustment time in the convection zone. You can show that the dissipation due to the turbulent viscous pressure is small because the mixing is so rapid that the eigenfunctions are flat. So anyway there are regimes where you can test things and in which you don’t need a time-dependent model of convection in order to do convection in a pulsating star necessarily. So this is the opposite of frozen-in convection, this is the infinitely-easily-able-to-adjust-to-the-pulsation-conditions convection. Gough: Mike came to Cambridge as a man who was keen on using observations to understand the world. I seem to have converted him into a theorist, because his answer was: this problem is too difficult, don’t think about those stars; let’s go for something easy! Dupret: For γ Doradus stars, near the bottom of the convection zone the time scale of convection is close to the period of the pulsations and it is smaller in the upper layers. Therefore we cannot use just one approximation; between the two extreme cases is a complex region where we have no choice but using time-dependent convection models. Roxburgh: Two comments. First, qualitative agreement is not enough, we need quantitative agreement. We have quantitative frequencies and the properties of the oscillations in order to make inferences about the star. Qualitative is not enough. The other point is that if you want to test a theory, or a model, such as a time-dependent theory of convection, which can’t be tested in the the parameter domain of the real star, you can still test the concept against the numerical simulations in different parameter regions. Kaye: I agree that qualitative is not enough, but to be fair we need to give the theorists more than a few dozen stars that are uniquely identified and that have enough frequencies. Since they are all hovering at period of about 0.8 days (which is the mean), it’s extremely difficult and you simply must have spectroscopy to back it up. I never thought that, as I heard from Jaymie, we now have three stars that are both γ Dor and δ Scutis, but what are the chances that they are all Am and they are all single? It’s not fair to put higher burdens onto the theorists before we can provide them with sufficient data to work with. Gough: Perhaps we should move on, although still sticking with the γ Doradus stars. We’ve been talking about the frequencies, but we need to know what the modes are. The frequency ratio method (which should really be a period ratio method because it’s the periods that follow the simple asymptotic relations) is used by some people to fit the data. It is based on taking just the leading term in the asymptotic eigenperiod formula, and is analogous to what we did in helioseismology with p modes. What we found immediately is that in practice the use of such a crude approximation doesn’t work. To get anything right, or at least anything that looks like a correct result, one must take at least the next term in the asymptotic formula D. O. Gough 157 into account. Now for the g modes that comes from two integrals. The first depends on the sound speed and the acoustical cutoff frequency (which depends on the density scaleheight, not to mention the density itself via its influence on the gravitational potential); the second comes from the nature of the transition beween the radiative interior and the convection. So there are (at least) two important uncertainties in the extended formula, and these need to be inferred from the data, in preference to trying to fit the over-simple formula that is in current use. Kaye: The problem has been, really, the lack of concentrated, detailed spectroscopy. It’s easier (not easy) to combine photometric campaigns than to combine spectroscopic campaigns. The number of spectroscopic campaigns of γ Doradus stars that I am aware of and where mode identification was later tried used the moment method etc. But there was only one case where it was possible to model in detail the line profile variations and to go through various steps to do mode identification, and that was Conny’s work. Gough: Well, you are talking about a star that only has one, unidentified, period, and I am not sure how much we can learn from that. Conny has identified the surface structure of the mode, which is just what we need for learning about the structure of the star; of course, the so-called frequency ratio method is aiming at obtaining just that too, but more indirectly. The issue I am adressing now is whether there are some stars with several frequencies that are determined accurately enough for us to say something about their rightful positions in the spectrum. Weiss: Not yet. We know from MOST that the data are coming and there are several candidates for γ Dor/δ Scuti hybrids and for bona fide γ Dor stars. So maybe in two years from now we should have a γ Doradus conference. Gough: I look forward to that. Referring to the Sun again, we learnt an awful lot in the early days when we were struggling with understanding the broad Lorentz-like spectrum of global-scale observations. However, one of the principal observers came along with his interpretation that what was being observed was a spectrum of only = 0 modes, because to him that was the simplest thing to say, and in science simplicity rules. To some of us, that was evidently wrong even at the time, and indeed now we all agree on that. But I noticed that basically we heard exactly that this afternoon: ‘It’s probably a white-dwarf spectrum because all these stars must be the same’. Bedding: For the K giants, I’d like to take the opposite view that none of them are multiperiodic, but all that we see is a broad Lorentzian envelope. For every one of them, if you look at the power spectrum, they’re all the same. Gough: Just like the Sun! Bedding: Well, no. Like one mode in the Sun that you haven’t observed long enough. I think Artie was arguing that there is no K giant with a resolved frequency spectrum, unless we get many, many months of observations, which we will get from COROT and probably Kepler. I don’t think we have enough information to say that these stars do have multiple modes. Gough: I have one simple request: the single mode you are observing: please identify it! Matthews: On behalf of Thomas (Kallinger) and his poster on MOST observations of K giants, we tried to demonstrate that the multimode identification of the star HD 20884 is inconsistent with damped oscillations because the peaks aren’t following a Lorentzian profile. Conny and her students like Saskia Hekker have argued from line-profile variations that there is evidence for nonradial oscillations, so I think there is growing evidence for that. Beta Cephei and Slowly Pulsating B stars Conny Aerts and Werner Weiss. Comm. in Asteroseismology Vol. 150, 2007 The present day of asteroseismology of β Cephei stars: observations A. Pigulski Instytut Astronomiczny, Uniwersytet Wroclawski, Wroclaw, Poland Abstract Several successful campaigns on bright β Cephei-type pulsators were completed during the recent years yielding detections of many modes at a sub-millimag level. On the other hand, searches for β Cephei-type stars in massive photometric databases resulted in a multiplication of the number of known members of this group. These discoveries now allow much better statistical investigations of β Cephei stars as a group and a good selection of interesting targets for case studies for asteroseismology. We summarize the up-to-date achievements of asteroseismology of β Cephei stars and present the results of the searches for these stars in the OGLE, ASAS and MACHO databases. Introduction The great successes of global helioseismology in modelling the internal structure of the Sun, in particular its internal rotation (see, e.g., Christensen-Dalsgaard 2002 and references therein) led to a growth of interest in applying seismic methods to pulsating stars. The large problems we encounter in this work, however, are due mainly to the low number of detected modes in comparison with millions of modes observed at the solar surface and the difficulty of their proper identification in terms of the quantum numbers used to describe the geometry of pulsations. Since stellar disks are not yet resolved, the cancellation effects limit the detected modes to spherical degrees of ≤ 4 in photometric data. From the point of view of asteroseismology, not all types of pulsating stars are equally attractive. Depending on the number of global parameters that define the internal structure of a star, we need to observe a sufficiently large number of modes to constrain these parameters. This explains the advance of asteroseismology in the application to white dwarfs which have rich pulsation spectra consisting of modes that can be relatively easily identified. The observational and theoretical aspects of asteroseismology of different types of pulsating stars across the H-R diagram have been recently reviewed by Kurtz (2006), Handler (2006) and Michel (2006). A general conclusion from the above-mentioned reviews is that the application of asteroseismology to β Cephei stars, massive main-sequence pulsators, looks promising. These stars have relatively simple pulsation spectra, albeit not too simple. Typically, several modes, both radial and non-radial, are observed. Next, many β Cephei stars have modes identified and the methods of mode identification developed in the recent years are usually applicable to these stars. Consequently, the sample of β Cephei stars studied in detail by means of asteroseismology grows rapidly. We summarize the results of these studies in the next section. It was possible owing to the joint effort of many groups of observers that cooperate in observing the most interesting targets within multisite campaigns. Presently, the observational studies of β Cephei stars follow three main approaches: • Case study of selected targets consisting usually of a photometric and/or spectroscopic observing campaign followed by detailed asteroseismic modelling. • Searches for new β Cephei stars using mainly massive photometric surveys like OGLE, MACHO or ASAS. 160 The present day of asteroseismology of β Cephei stars: observations Table 1: A list of β Cephei stars that were the best targets of recent asteroseismic studies. Nhigh , Nlow , and Nid stand for the number of detected high-frequency, low-frequency modes and the number of modes with unambiguous identifications, respectively. As remarks, we indicate when photometric (PH) and spectroscopic (SP) data were used to find and identify modes. References to Star Nhigh + Nlow Nid observations mode id asteroseis. Remarks V836 Cen ν Eri 12 Lac θ Oph 6+0 12 + 2 10 + 2 7+0 6 11 5 3 (1) (4), (5), (7) (10) (11), (12) (2), (3) (6)–(8) (10) (11), (12) (2), (3) (8), (9) — — PH PH+SP PH PH+SP References: (1) – Aerts et al. (2004b), (2) – Aerts et al. (2003), (3) – Dupret et al. (2004), (4) – Handler et al. (2004), (5) – Aerts et al. (2004a), (6) – De Ridder et al. (2004), (7) – Jerzykiewicz et al. (2005), (8) – Pamyatnykh et al. (2004), (9) – Ausseloos et al. (2005), (10) – Handler et al. (2006), (11) – Handler et al. (2005), (12) – Briquet et al. (2005). • Observations of β Cephei stars in environments that have different chemical abundances, in particular, in Large and Small Magellanic Clouds and different regions of the Galaxy, including the Galactic field and young open clusters. In the subsequent sections, we will summarize the recent achievements of these three approaches. Case study of selected targets The main requirement for successful seismic modelling is the proper mode identification. Since there are some factors that can help to achieve this, we list them here as they are important in the context of selecting targets for the follow-up study. These helpful factors are the following: (i) the presence of a large number of modes, (ii) the presence of rotational splitting(s), (iii) large amplitudes, (iv) cluster membership. In addition, if a pulsating star is a component of an eclipsing and/or spectroscopic binary, some global parameters can usually be better constrained. For this reason, stars that show a large number of modes, especially such modes which are close in frequency and therefore suspected to be rotationally split, are preferred during the selection of targets for a detailed seismic study. Table 1 lists basic information for four stars that either were the subject of recent asteroseismic studies (V836 Cen, ν Eri) or the asteroseismic study is in progress for them (12 Lac, θ Oph). The schematic frequency spectra of these four stars are shown in Fig. 1. More β Cephei stars (δ Cet, β CMa, SY Equ) were observed recently, but they have a smaller number of modes detected or identifications are not available for some modes which means that the information that can be obtained from modelling these stars is rather limited. A lesson learnt from the first decade of asteroseismology of β Cephei stars is that we still need to study more stars before some general conclusions concerning the interiors of early B-type stars can be drawn. There is some indication of non-rigid rotation (faster in the core) coming from the studies of Dupret et al. (2004) and Pamyatnykh et al. (2004), but there are still problems in matching frequencies of all modes with a consistent model on the one hand and making them unstable on the other. If we really want to get such information as metallicity, overshooting parameter, mass, age, and rotation in the core from seismic modelling, we really need to have more modes in a single star detected and identified. 161 A. Pigulski 100 50 V836 Centauri 2 [mmag] 10 5 1 100 50 V amplitude 1 0(F) i Eridani 1 0(F) 10 5 1 1 2 1 100 50 1 1 10 5 12 (DD) Lacertae 0 2 2 1 100 50 e Ophiuchi 2 10 5 0 1 1 4 5 6 Frequency [d -1] 7 8 Figure 1: Schematic frequency spectra of four β Cephei stars with the largest number of detected modes. Modes that have their spherical degree identified are labelled with the corresponding value. Fortunately, new observing campaigns were initiated. In particular, three open clusters, NGC 3293 (Handler et al. 2007), NGC 6910 and χ Persei (Pigulski et al. 2007) were selected as targets in the ongoing campaigns. We already know over 20 β Cephei stars in these clusters. A preliminary analysis of the star WEBDA 18, a member of NGC 6910, already resulted in the detection of seven modes, but we can expect that more will be found in the final analysis. Additional constraints on the global parameters of the cluster members will surely help in their seismic modelling. Searches in massive photometric surveys Soon after the publication of the review paper on β Cephei stars by Stankov & Handler (2005), listing 93 certain members of this group, 19 new β Cephei stars were found by Pigulski (2005) and Handler (2005) in the published photometry of the All Sky Automated Survey (ASAS, Pojmański 2001). The main goal of this survey is to monitor the whole sky 162 The present day of asteroseismology of β Cephei stars: observations for variability. About 70% of the sky south of declination +28o is already monitored. The observations cover stars in the magnitude range between 7 and 14 mag in V. In a series of papers (Pojmański et al. 2005 and references therein), a catalogue of about 50 000 variable stars was published. All but two of these 19 new stars have semi-amplitudes larger than 35 mmag which is a rather large value for β Cephei stars. This was the consequence of using the dispersion vs. magnitude diagram for the selection of stars in the catalogue. On the other hand, the detection threshold in Fourier spectra for the brightest observed stars amounted to about 3–5 mmag. It became obvious that a large number of β Cephei stars could be discovered once the whole database of over 107 stars observed within the ASAS survey will be analysed by means of Fourier analysis. In the first step, we decided to select O and B stars from the existing catalogues and then analyse their ASAS photometry. The best way to select OB stars (and distinguish them from δ Scuti stars which partly overlap with β Cephei stars in period) is to use their spectral types and/or UBV photometry. A very homogeneous catalogue of spectral types for bright southern objects is the Michigan Spectral Survey catalogue published by N. Houk and her collaborators in five volumes (Houk & Swift 1999 and references therein). The catalogue provides MK spectral types for stars with HD numbers south of declination +5o . About 4,000 OB stars were selected from this catalogue. The sample is homogeneous and magnitude-limited. As a result of the analysis of the ASAS V-filter photometry of this sample, we found 102 new β Cephei stars (Pigulski & Pojmański, in preparation). A second sample of about 11,000 OB stars was selected from over 200 other catalogues. The analysis of this sample is underway; a preliminary check of the results indicates that we can expect to find another 100–150 new β Cephei stars. This finding triples the number of known β Cephei stars and shows the potential of all-sky surveys like ASAS in studying all types of variable stars. Figure 2 shows the amplitudes of the main modes for the 220 β Cephei stars that are currently known of which more than half were found using ASAS photometry. As mentioned above, this number will soon increase to over 300, once the analysis of the second sample of the ASAS data will be completed. It is also obvious that in the sample of 102 newly-discovered β Cephei stars we will find excellent targets for follow-up asteroseismic studies, as all these stars are bright; with a few exceptions, they fall in the range between 8 and 10 mag in V. Going back to the discussion on the selection of objects suitable for asteroseismology, we have in this sample: • Seven stars with modes equidistant (or almost equidistant) in frequency, presumably due to rotational splitting. In two stars, quadruplets, and in the other five stars, triplets were detected. As far as we are aware, these are the first β Cephei stars in which quadruplets are seen. This leads to the suspicion that we observe rotationally split = 2 mode in which one component was not detected. Since the detection threshold for these stars in the ASAS data is still high (3–5 mmag), follow-up campaigns should easily reveal more modes. • Many stars with large amplitudes. As can be seen from Fig. 2, over 20 stars discovered with ASAS have semi-amplitudes of the main mode larger than 30 mmag. These are mostly the stars discovered by Pigulski (2005) and Handler (2005), but in the discussed sample, another large-amplitude star, HD 173006, was found. • Many stars belonging to open clusters and OB associations. Although the ASAS photometry is not suitable for finding variable stars in clusters owing to its poor spatial resolution, we find some variables in some loose open clusters and in the outer regions of denser ones. • Four stars that are presumably the primary components of eclipsing binaries. Two, maybe three, are suspected to be double-lined spectroscopic binaries which will allow to derive their stellar parameters directly. 163 A. Pigulski BW Vul A V, main [mmag] 80 60 40 20 0 0.1 0.15 0.2 0.25 0.3 Pmain [d] Figure 2: V-filter semi-amplitudes of the main mode, AV,main , plotted as a function of the period of this mode, Pmain , for 220 β Cephei stars. Stars discovered in the ASAS data are shown with open circles, the other ones, as filled circles. ASAS is not the only survey in which β Cephei stars can be found. Narwid et al. (2006) found over 200 short-period variable stars in the OGLE-II photometry of Galactic fields. Without any doubts, many of them are β Cephei stars. With the available photometry, however, they cannot be presently distinguished from δ Scuti stars. The new UBV photometry we are going to carry out for these stars will surely solve the problem. This will enable us to compare the pulsational properties of the β Cephei stars located at larger distances and closer to the Galactic centre than the ASAS sample. The former stars are suspected to have higher metallicities than the latter which makes the comparison very attractive. Metallicity and pulsations of β Cephei stars The previous sentence brings us to the problem of the dependence of the pulsations of β Cephei stars on metallicity, predicted by theory. This dependence was already confirmed from the observations of Galactic open clusters (Pigulski et al. 2002), but later supported by the searches for β Cephei stars in the Magellanic Clouds using the OGLE-II data (Kolaczkowski et al. 2004, 2006). The Magellanic Clouds have much smaller overall metallicities than our Galaxy and indeed the incidence of β Cephei stars drops rapidly when going from our Galaxy to the Large (LMC) and then Small Magellanic Cloud. The study of these stars goes now to the spectroscopic work which should allow to establish observationally the lower limit of metallicity for the pulsations of β Cephei stars. Conclusions Summarizing, there is indeed a rapid growth of the number of excellent data for β Cephei stars that will allow statistical studies of these stars as a group. For example, there is a striking difference between the largest amplitudes of modes in β Cephei stars located in the solar neighbourhood and those in the LMC (Kolaczkowski 2004). While for Galactic β Cephei 164 The present day of asteroseismology of β Cephei stars: observations stars the semi-amplitudes reach 0.1 mag in V (Fig. 2), for all but two stars in the LMC they are smaller than 0.02 mag in I which translates into less than 0.03 mag in V. This may bring some clues for the long-standing problems of mode selection and amplitude limitation. Fortunately, some non-linear theoretical studies of β Cephei stars have been recently undertaken (see Smolec & Moskalik 2007). This and the growing number of asteroseismic studies can soon result not only in a better understanding of β Cephei stars, but also in knowledge of the interiors of early B-type stars and pulsations in general. Acknowledgments. This work was supported by the MNiI grant 1 P03D 016 27. Many results presented here were obtained in cooperation with G. Pojmański (Warsaw Univ. Observatory), Z. Kolaczkowski and A. Narwid (Astronomical Institute, Univ. of Wroclaw). The author is grateful to the EC for the establishment of the European Helio- and Asteroseismology Network HELAS, which made his participation at this workshop possible. References Aerts C., Thoul A., Daszyńska J., et al., 2003, Sci, 300, 1926 Aerts C., De Cat P., Handler G., et al., 2004a, MNRAS, 347, 463 Aerts C., Waelkens C., Daszyńska-Daszkiewicz J., et al., 2004b, A&A, 415, 241 Ausseloos M., Scuflaire R., Thoul A., Aerts C., 2004, MNRAS, 355, 352 Briquet M., Lefever K., Uytterhoeven K., Aerts C., 2005, MNRAS, 362, 619 Christensen-Dalsgaard J., 2002, Rev. Mod. Phys., 74, 1073 De Ridder J., Telting J. H., Balona L. A., et al., 2004, MNRAS, 351, 324 Dupret M.-A., Thoul A., Scuflaire R., et al., 2004, A&A, 415, 251 Handler G., 2005, IBVS, 5667 Handler G., 2006, Comm. Asteroseis., 147, 31 Handler G., Shobbrook R. R., Jerzykiewicz M., et al., 2004, MNRAS, 347, 454 Handler G., Shobbrook R. 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A., 2004, MNRAS, 350, 1022 Pigulski A., 2005, Acta Astron., 55, 219 Pigulski A., Kolaczkowski Z., Kopacki G., Jerzykiewicz M., 2002, in Aerts C., Bedding T. R., Christensen-Dalsgaard J., eds, ASP Conf. Ser. Vol. 259, Radial and Nonradial Pulsations as Probes of Stellar Physics. Astron. Soc. Pac., San Francisco, p. 146 Pigulski A., Handler G., Michalska G., et al., 2007, these proceedings Pojmański G., 2001, in Paczynski B., Chen W.-P., Lemme C., eds, ASP Conf. Ser. Vol. 246, Small Telescope Astronomy on Global Scales. Astron. Soc. Pac., San Francisco, p. 53 Pojmański G., Pilecki B., Szczygiel D., 2005, Acta Astron., 55, 275 Smolec R., Moskalik P., 2007, these proceedings Stankov A., Handler G., 2005, ApJS, 158, 193 A. Pigulski 165 DISCUSSION Mukadam: Do the high and low amplitude stars exhibit any other distinguishing properties? Pigulski: High-amplitude stars are those with amplitudes larger than 40 mmag, but there is no difference for instance in luminosity. All β Cephei stars have amplitudes lower than 0.1 mag. Frandsen: There is also the super-WASP survey going on these days. Pigulski: Yes, and there are other surveys, also in the Northern hemisphere and therefore I expect the amount of data and number of stars to increase rapidly over the next few years. Aerts: Would you do a spectroscopic study of the eclipsing binary β Cep stars, please? Pigulski: Yes, this will be one of the first things we will do. We even have two of those stars in the same cluster, so we can do both of them at the same time. How many astronomers does it take to run a powerpoint presentation? 166 Konstanze Zwintz already working on these proceedings. Comm. in Asteroseismology Vol. 150, 2007 Observational Asteroseismology of slowly pulsating B stars P. De Cat Koninklijke Sterrenwacht van België, Ringlaan 3, 1180 Brussels, Belgium Abstract We review the status of observational asteroseismology of slowly pulsating B (SPB) stars. Their asteroseismic potential is extremely good because the excited high-order g-modes probe the deep interior of these hot stars. To enable asteroseismic modelling, a sufficient amount of well-identified modes is mandatory. To reach this goal with ground-based observations, dedicated long-term and preferably multi-site campaigns are needed to increase the number and the accuracy of detectable frequencies. The first results for SPB stars based on observations obtained with the asteroseismic space-mission MOST are very promising, guaranteeing the success of missions like CoRoT, launched in December 2006. These results also indicate that high-precision observations are needed to detect and to study low-amplitude SPB stars. Although SPB pulsations are not restricted to slow rotators, there is some observational evidence for an amplitude drop towards high values of the projected rotational velocity. For several SPB stars, close frequency multiplets are observed. In some cases, the observed frequencies might be components of a rotationally split mode, but in other cases an alternative explanation is needed. Magnetic fields of a few hundred Gauss, that recently have been detected for fourteen confirmed members, can cause such frequency shifts. SPB stars can no longer be considered as non-magnetic stars and magnetic fields should be included in the theoretical models. We argue that mode identification of g modes still remains one of the main obstacles, although progress has been made in this field recently. Asteroseismic potential After conducting a systematic study of variability amongst B type stars, Waelkens (1991) introduced the slowly pulsating B (SPB) stars as an independent class of stars pulsating in high-order, low degree gravity modes (g modes) with typical periods of the order of days. These modes are excited by the opacity mechanism acting on the metal-bump. They are trapped deep in the interior of these hot stars, making them very interesting from an asteroseismic point of view. On the other hand, they are very difficult targets for in-depth asteroseismic studies because the theoretical frequency spectra of SPB stars are very dense, the observed amplitudes are low (cf. Fig. 4), and most of the currently known SPBs are multi-periodic, giving rise to beat periods of the order of months or even years. Currently, at least 51 confirmed and 65 candidate galactic SPB stars are known, of which 15 are in open clusters. Thanks to the OGLE-II and MACHO databases, extra-galactic SPBs were recently found: 59 in the LMC and 11 in the SMC (Kolaczkowski et al. 2006). For the SPB stars observed in the Geneva photometric system, the effective temperatures and surface gravities were determined with the code CALIB in the same way as described by De Cat et al. (2007). As shown in Fig. 1, these stars cover the (young) part of the theoretical SPB instability strip. This figure also illustrates the existence of a common part of the theoretical instability strip of the β Cep and SPB stars. At least 6 β Cep/SPB hybrids are currently known: 53 Psc (LeContel et al. 2001), ι Her (Chapellier et al. 2000), ν Eri (Jerzykiewicz et al. 2005), HD 886 (Chapellier et al. 2006), HD 13745, and HD 19374 (De Cat et al. 2007). Since they simultaneously pulsate in low-order p/g modes and high-order g modes probing both the outer layers and the deep interior of these stars, they are ideal asteroseismic targets. 168 Observational Asteroseismology of slowly pulsating B stars Figure 1: Position in the (log(Teff ),log g )-diagram of the candidate (open symbols) and confirmed (full symbols) SPB stars for which Geneva photometry is available. The triangles indicate the hybrid β Cep/SPB stars. The stars with a detected magnetic field are given in black. The lower and upper dotted lines show the ZAMS and TAMS, respectively. The dashed lines denote evolution tracks for stars with M= 15, 12, 9, 6, and 3 M . The dash-dot-dot-dotted and dash-dotted lines represent the theoretical instability strips for β Cep and SPB modes provided by De Cat et al. (2007). A typical error bar is given in the lower left corner. Observations For a successful asteroseismic study, the observation of a large number of well identified modes is mandatory. The detection of frequency multiplets is advantageous. Unfortunately, long-term monitoring with dedicated telescopes has not been enough to provide these basic needs so far. Currently, the best data-sets consist of several hundreds of (mostly) photometric observations spread over some 15 years. Because it concerns single-site data, the frequency analysis suffers from strong aliasing. Moreover, the maximum number of independent frequencies detected with ground-based data, i.e. 8 for HD 160124 (Waelkens 1991), is low. Although there is evidence for frequency multiplets for some stars, the results of the mode identification are still inconclusive for a lot of the observed modes (see below). The organization of (unrealistic) long-term simultaneous photometric and spectroscopic multi-site campaigns is needed to overcome these problems. Space-based observations can be an alternative solution. Recently, new variable B-stars were discovered thanks to the white-light data obtained in observation campaigns of some 30 consecutive days with the MOST satellite. HD 163830 is a new SPB star for which 20 frequencies below 2 d−1 are detected (Fig. 2, left panel). The two lowest frequencies are interpreted as rotation modulation. It has been shown that the remaining frequencies are compatible with unstable = 1 and/or 2 modes (Aerts et al. 2006). HD 163868 is an SPB emission star for which the 60 observed frequencies below 3.8 d−1 are attributed to prograde g modes or to r modes (Walker et al. 2005). HD 163899 is the prototype of a new class of SPB supergiants. The 48 observed frequencies below 2.8 d−1 are post-TAMS g modes (Saio et al. 2006). Although MOST already has shown the capability of dedicated space-missions to detect a large number of frequencies, the lack of colour information makes the identification of the modes impossible. Hence, the lack of accurate mode identifications currently prevents us to start asteroseismic modelling for SPB stars. P. De Cat 169 Figure 2: Amplitude spectrum of HD 163830 (left: MOST data; Aerts et al. 2006) and HD 21071 (right: Geneva B data; De Cat et al. 2007). The frequencies given in grey are attributed to rotation and those in black to high-order g modes. The spacings between the three observed frequencies of HD 21071 indicated with an arrow are compatible with those expected for a rotationally split = 1 mode. Figure 3: Distributions of the observed SPB frequencies. Left: based on the ground-based observations of confirmed members (black) and on the MOST observations of HD 163830 (dark grey), HD 163868 (light grey), and HD 163899 (white). Right: based on the ground-based observations of the galactic (black) and the extra-galactic (LMC: dark grey; SMC: light grey) candidate members. Frequencies The distribution of the observed frequencies of the confirmed and candidate SPB stars are given in the left and right panel of Fig. 3, respectively. For the confirmed SPB stars, the majority of the observed frequencies lies below 1.5 d−1 , which is compatible with the frequency range of the theoretically predicted unstable SPB modes (e.g. Dziembowski et al. 1993). The distribution peaks around 0.65 d−1 and has a long tail towards higher frequencies. The distribution of the candidate SPB stars is flatter, peaks around 1.10 d−1 , and extends up to 3 d−1 . It is not clear whether or not the difference in these distributions is significant. Past experience with follow-up observations for a sample of 27 candidate SPB stars selected by Aerts et al. (1999) and Mathias et al. (2001) taught us that we can expect that about 20% of the remaining SPB candidates are misclassified because the SPB-like frequency observed in photometry is due to either binarity or rotational modulation (De Cat et al. 2000, Briquet et al. 2004). High-resolution spectroscopic follow-up data are needed to clarify this issue. In any case, distributions shown for candidate SPB stars should be interpreted with caution. Amplitudes The distributions of the observed photometric amplitudes of the confirmed and candidate SPB stars are given in the left and right panels of Fig. 4, respectively. Although it is not obvious to compare the distributions in the different panels because they are based on observations in different photometric filters, it is clear that the observed amplitudes are at maximum a 170 Observational Asteroseismology of slowly pulsating B stars Figure 4: Distributions of the observed SPB amplitudes in photometry. Left: based on the Geneva V observations of confirmed members (top) and on the MOST observations of HD 163830 (bottom, dark grey) and HD 163899 (bottom, light grey). Right: based on the Hipparcos Hp observations of candidate galactic members (top) and the OGLE-II observations of candidate members in the LMC (bottom, dark grey) and the SMC (bottom, light grey). few hundredths of a magnitude. In radial velocity, the amplitudes are below ∼10 km s−1 (not shown). Also the main difference between ground- and space-based observations is well illustrated: while no modes with amplitudes below ∼1 mmag are observed from Earth due to the current detection limits of our ground-based equipment (Fig. 4 top left, top right, and bottom right panels), the MOST observations are dominated by low amplitude modes (Fig. 4 bottom left panel). This indicates that there is a clear need for high-precision observations both to detect and to study the variations of SPB stars in full detail. Hence, space-missions like e.g. CoRoT (launched in December 2006) will provide a gold mine for g-mode research. Chemical composition Niemczura (2003) determined the metallicity for a sample of 34 reference and 20 SPB stars based on low-resolution IUE spectra. She found no significant difference between the nonpulsating and pulsating B stars. The average SPB metallicity of [m/H] -0.20 or Z 0.013 was considered as low at the time, but it helped to explain the instability of some of the observed low frequency modes in SPB stars (De Cat et al. 2004). Recently, it became clear that this mean value is close to the “new” solar metallicity (Asplund et al. 2005). A large project based on high-resolution CORALIE spectra (390–682 nm) with the aim to determine in a self-consistent way the physical parameters (Teff and log g ) and the NLTE abundances for the majority of the confirmed SPB stars is ongoing in Leuven. Briquet & Morel (2007) report the first results. For HD 85953, the abundances of the considered chemical elements are, within the errors, indistinguishable from those of OB dwarfs in the solar neighbourhood. For HD 3360, a clear nitrogen excess is found, which is similar to what has been observed for four β Cep stars (Morel et al. 2006). It is too early for general conclusions. P. De Cat 171 Figure 5: The results of the photometric mode identification for ν1 = 1.1569(6) d−1 of HD 24587. For each theoretical model within the observed range of log(Teff ) and log g (cf. Fig. 1), the theoretical amplitude ratios for modes with = 1, 2, 3, and 4 are represented with a grey dashed, dash-dotted, dotted, and dash-dot-dot-dotted line, respectively, in the panels from left to right. The black dots indicate the observed amplitude ratios and their standard error. The most probable value for is 1. Figure 6: Overview of the most probable values of the spherical degree for the observed modes of confirmed (black) and candidate (grey) SPB stars with more than 20 observations in the Geneva photometric system. There is a clear dominance of = 1 modes (left) and no dependence of on the observed frequency is found (right). Mode identification For the identification of the modes, different techniques can be used. In case multi-colour photometric observations are available, constraints on the spherical degree can be obtained by comparing observed and theoretical amplitude ratios (e.g., Dupret et al. 2003). For all the observed frequencies of SPB stars with more than 20 observations in the 7 filters of the Geneva photometric system, we applied this method in the same way as De Cat et al. (2007). In this procedure, the modes with eigenfrequencies for = 1, 2, 3, and 4 that are the closest to the observed frequency are selected for each model within the observed (log(Teff ),log g ) error box of a pre-calculated grid of main-sequence models with the “new” solar composition to calculate the theoretical amplitude ratios relative to the Geneva U filter. A representative illustration of the results is given in Fig. 5. For the main frequency of HD 24587, the theoretical amplitude ratios of = 1 and 4 modes are compatible with the observed ones. Although the results are inconclusive, = 1 is considered as the most probable solution because the relative number of compatible = 1 modes is higher. Moreover, = 4 modes are less likely to be observed in photometry due to cancellation effects. The global results of the photometric identification exercise are given in Fig. 6. There is a clear dominance of = 1 modes (left panel) which is compatible with theoretical expectations (Townsend 2003). No evidence for a dependence of the value on the observed frequency is found (right panel). High-resolution spectroscopy can provide constraints on additional parameters including the azimuthal number m, the projected rotational velocity v sin i , and the inclination i . In the moment method, a comparison is made between the first three normalized velocity moments 172 Observational Asteroseismology of slowly pulsating B stars of a time-series of observed line-profiles and theoretical ones computed for a large grid of parameters (Briquet & Aerts 2003). This method performs best in the case of low-degree modes observed in sufficiently slow rotators. Unfortunately, this method generally leads to several equivalent solutions. After calculation of the corresponding time-series of synthetic line-profiles, additional tests may help in selecting the best moment solutions: (1) by comparing phase diagrams of higher order (even) velocity moments derived from the observed and synthetic line-profiles, and (2) by comparing the amplitude and phase variations across the observed and synthetic line-profiles for both the observed frequency and its first harmonic. This identification scheme has already been applied successfully to mono-periodic SPB stars, leading to a unique identification as a prograde dipole mode in four cases (De Cat et al. 2005). The application to multi-periodic SPB stars is ongoing (De Cat et al., in preparation). Recently, the Fourier parameter fit method has been introduced by Zima (2006) in which the zeropoints, amplitudes and phases across the observed line-profiles for each detected frequency are fitted in a statistically justified way to those derived from synthetic line-profiles. Contrary to the moment method, the best performance is found in the case of higher-degree modes observed in sufficiently rapid rotators. Moreover, it is complementary to the photometric identification because it is able to put severe constraints on m. The first results of its application to multi-periodic SPB stars are presented by Zima et al. (2007). It is clear that mode identification for g modes is very difficult. The best results are found when both photometric and spectroscopic techniques are simultaneously applied. Rotation In Fig. 7, we show the distribution of the projected rotational velocity (v sin i ) for the confirmed (left) and candidate (right) SPB stars. It is clear that SPB pulsations are not restricted to slow rotators. For rapid rotators, significant frequency shifts with respect to those in a nonrotating star are expected for non-zonal modes (m = 0). This argument has already been used to explain the high frequencies observed for e.g. HD 121190: ν1 = 2.6831(4) d−1 , ν2 = 2.6199(4) d−1 , and ν3 = 2.4713(7) d−1 (Aerts & Kolenberg 2005). The corresponding modes have either = 1 or 2. The combination of v sin i = 118(3) km s−1 and R = 1.7(3) R leads to a projected rotational frequency Ω sin i = 1.37(24) d−1 . In case of retrograde g modes, the frequencies in the co-rotating frame are at least 0.7 d−1 lower, which moves them towards the theoretically expected range of unstable modes. This also indicates that the results of mode identification should be treated with caution and that inclusion of rotation in asteroseismic modelling is needed. We also investigated whether or not the Hipparcos Hp amplitudes depend on rotation. An amplitude drop towards high v sin i is seen for the confirmed SPB stars (Fig. 7, left panel). Because the slowest rotators were chosen first for follow-up spectroscopic studies, this might be a selection effect. Since rapidly rotating candidate SPB stars with high photometric amplitudes do exist (Fig. 7, right panel), additional observations are needed to confirm or reject them as pulsating stars. For several stars, close frequency multiplets are observed. In the right panel of Fig. 2, we give the example of HD 21071, for which four frequencies are observed in Geneva data: ν1 = 1.18843(1) d−1 , ν2 = 1.14934(2) d−1 , ν3 = 1.41968(7) d−1 , and ν4 = 0.95706(9) d−1 (De Cat et al. 2007). The most probable identification is = 1 for the four observed modes. It is possible that ν4 , ν1 , and ν3 (indicated with arrows in Fig. 2) are components of a rotationally split = 1 mode because Ω sin i = 0.45(12) d−1 , which leads to a frequency spacing that is very close to the observed one. Rotational splitting cannot be responsible for the close frequency pair (ν1 , ν2 ). Such frequency spacings are compatible with those of modes with either the same degree but a subsequent radial order n or with different values. P. De Cat 173 Figure 7: Distribution of the projected rotational velocity (v sin i ) for the confirmed (left) and candidate (right) SPB stars. The dots with error bars denote the amplitudes of the observed frequencies in the Hipparcos Hp filter. Magnetic fields HD 37151 is the first SPB star for which four magnetic field measurements were carried out (Borra 1981), but the results were compatible with a zero field (North & Paltani 1994). HD 3360 is an SPB star with a rotational period PΩ = 5.37 d and a pulsation frequency of 0.64 d−1 for which Neiner et al. (2003) detected a polar magnetic field of Bpol = 335+120 −65 G. Its longitudinal component varies sinusoidally with PΩ . In the case of a simple dipolar configuration, a polar field of 120 G on the surface corresponds to a polar field of 110 kG in 1 -mode the vicinity of the convective core, which causes a frequency splitting of 1% for a g20 (Hasan et al. 2005). Hence, magnetic fields are a valuable alternative explanation for the very close frequency multiplets observed in several SPB stars since longitudinal magnetic fields of a few hundred G have been detected recently in another thirteen SPB stars (Hubrig et al. 2006). The SPB stars with a confirmed magnetic field are given in black in Fig. 1. The inclusion of magnetic fields in theoretical models is needed because it concerns a significant fraction of the known members. From a comparative study between pulsating SPB stars and non-pulsating Bp stars, Briquet et al. (2007) conclude that the group of SPB stars is younger and has a weaker longitudinal magnetic field than the group of Bp stars. Conclusions The potential of seismology of SPB stars is excellent, and the potential of β Cep/SPB hybrids is even better since they probe both the deep stellar interior and the outer layers. Before we can move on to in-depth asteroseismic modelling of SPB stars, we need (1) long-term multisite and/or space-based data, (2) accurate mode identification techniques for g modes, and (3) the inclusion of magnetic fields and rotation in the theoretical models. Acknowledgments. I am very grateful to Z. Kolaczkowski for making the observed frequencies and amplitudes in the candidate SPB stars in the LMC and the SMC available for this review. References Aerts C., De Cat P., Kuschnig R., et al., 2006, ApJ, 642, L165 Aerts C., De Cat P., Peeters E., et al., 1999, A&A, 343, 872 Aerts C., Kolenberg K., 2005, A&A, 431, 615 Asplund M., Grevesse N., Sauval A. J., 2005, in Barnes T. G. III, Bash F. N., eds, ASP Conf. Ser. Vol. 336, Cosmic Abundances as Records of Stellar Evolution and Nucleosynthesis. Astron. Soc. Pac., San Francisco, p. 25 174 Observational Asteroseismology of slowly pulsating B stars Borra E. F., 1981, ApJ, 249, L39 Briquet M., Aerts C., 2003, A&A, 398, 687 Briquet M., Hubrig S., De Cat P., et al., 2007, A&A, in press (astro-ph/0702111) Briquet M., Morel T., 2007, these proceedings Briquet M., Aerts C., Lüftinger T., et al., 2004, A&A, 413, 273 Chapellier E., Le Contel D., Le Contel J. M., Mathias P., Valtier J.-C., 2006, A&A, 448, 697 Chapellier E., Mathias P., Le Contel J. M., et al., 2000, A&A, 362, 189 De Cat P., Aerts C., De Ridder J., et al., 2000, A&A, 355, 1015 De Cat P., Briquet M., Aerts C., et al., 2007, A&A, 463, 243 De Cat P., Briquet M., Daszyńska-Daszkiewicz J., et al., 2005, A&A, 432, 1013 De Cat P., Daszyńska-Daszkiewicz J., Briquet M., et al., 2004, in Kurtz D. W., Pollard K. R., eds, ASP Conf. Ser. Vol. 310, Variable Stars in the Local Group, IAU Colloquium 193. Astron. Soc. Pac., San Francisco, p. 195 Dupret M.-A., De Ridder J., De Cat P., et al., 2003, A&A, 398, 677 Dziembowski W. A., Moskalik P., Pamyatnykh A. A., 1993, MNRAS, 265, 588 Hasan S. S., Zahn J.-P., Christensen-Dalsgaard J., 2005, A&A, 444, L29 Hubrig S., Briquet M., Schöller M., et al., 2006, MNRAS, 369, L61 Jerzykiewicz M., Handler G., Shobbrook, R. R., et al., 2005, MNRAS, 360, 619 Kolaczkowski Z., Pigulski A., Soszyński, I., et al., 2006, Mem. Soc. Astron. Ital., 77, 336 Le Contel J.-M., Mathias P., Chapellier E., Valtier J.-C., 2001, A&A, 380, 277 Mathias P., Aerts C., Briquet M., et al., 2001, A&A, 379, 905 Morel T., Butler K., Aerts C., Neiner C., Briquet M., 2006, A&A, 457, 651 Neiner C., Geers V. C., Henrichs H. F., et al., 2003, A&A, 406, 1019 Niemczura E., 2003, A&A, 404, 689 North P., Paltani S., 1994, A&A, 288, 15 Saio H., Kuschnig R., Gautschy A., et al., 2006, ApJ, 650, 1111 Townsend R. H. D., 2003, MNRAS, 343, 125 Waelkens C., 1991, A&A, 246, 453 Walker G. A. H., Kuschnig R., Matthews J. M., et al., 2005, ApJ, 635, L77 Zima W., 2006, A&A, 455, 227 Zima W., De Cat P., Aerts C., 2007, these proceedings DISCUSSION Handler: As Mike Breger has pointed out in his talk, there are some fundamental limits to frequency analysis. One of them is the resolution of the data set, so you can only resolve frequencies to 1.5/T . If you look at the frequencies of the MOST data for some of these B stars, about two thirds of them are not resolved. So I would like to discourage theorists to model individual frequencies of these stars; frequency ranges are still OK. The other thing that worries me is that MOST observes about 30 cycles of the variations of those stars and then finds about 60 frequencies in these data, which is also a little incredible in my view. Dziembowski [to Handler]: It is very difficult to discourage theorists from interpreting data that are so interesting. [To De Cat:] Would you say that the current data are consistent with the hypothesis that all B-type stars in the proper range of the HR diagram are pulsating? De Cat: I can’t say because the higher the precision, the lower amplitudes you can find. Dziembowski: But is the trend consistent with the idea that pulsation in this part of the HR diagram is a universal phenomenon? De Cat: I think so, but I can’t be sure. Comm. in Asteroseismology Vol. 150, 2007 Oscillations in main sequence B-type stars - challenges to theory W. A. Dziembowski Warsaw University Observatory and Copernicus Astronomical Center, Warsaw, Poland Abstract The current status of our understanding of the diversity of B-star pulsation is presented with an emphasis on unsolved problems. Not all detected modes are found unstable in standard models. The proposed way of extending the instability by invoking an iron accumulation in the driving zone is not free of difficulties. There are still controversies regarding the excitation of slow modes in Be stars. Nonlinear modelling of radial pulsations in β Cephei stars results in much higher amplitudes than observed. There must be hidden modes involved but we may only speculate about their nature. Introduction Not long after the driving mechanism for pulsation in stars of the Cepheid instability strip has been identified, efforts were made to explain the origin of pulsations in β Cephei stars. For about two decades this constituted the greatest challenge to stellar pulsation theory. While theorists were still searching the explanation for β Cep pulsation, new types of periodic B-star variability were discovered by observers. Interestingly, the new variables, though less luminous than β Cep stars, had longer periods. The first such objects were discovered by Smith (1977) by means of spectroscopy. These were rapid rotators and their variability was detected in line profiles. The term Slowly Pulsating B-type (SPB) stars denoting all mid to late B-type long period variables was defined 14 years later by Waelkens (1991), who discovered many such objects in his photometric survey. These discoveries added a new problem to the long-standing challenge of explaining the origin of hot star pulsation. The answer that came in the early 1990ties thanks to sophisticated calculations of stellar opacities by the OPAL team (Iglesias et al. 1992) was not unexpected. In fact, Simon’s (1982) call for a revision of stellar opacity data was motivated by the problem of the driving mechanism for β Cep pulsation. Shortly after the OPAL opacities became available for stellar modelling, the first papers demonstrating that there are unstable modes in B stars with periods consistent with observations were published (Cox et al. 1992; Kiriakidis et al. 1992; Moskalik & Dziembowski 1992; Dziembowski & Pamyatnykh 1993; Gautschy & Saio 1993; Dziembowski et al. 1993). In the latter three papers the instability of high order g-modes responsible for slow pulsation was demonstrated. The puzzle was solved. The driving effect is caused by the classical κ-mechanism acting in the layer of the local opacity maximum arising primarily due to the line opacities of ionized iron. This maximum occurs at a temperature of about 2 × 105 K and is often referred to as the Fe-bump or Z-bump. The identification of the driving mechanism did not stop the interest in B-star pulsation. In recent years, the main effort was focused on applications of seismic sounding, which required collecting more data on the excited modes. There have been fruitful ground-based campaigns on selected β Cep stars. Very interesting data on various B-type pulsators were obtained with the MOST space telescope. The new data not only led to valuable constraints on stellar models and internal rotation but also revealed that our understanding of B-star pulsation is by far not satisfactory. 176 Oscillations in main sequence B-type stars - challenges to theory The opacity mechanism in B stars The occurrence of two distinct types of B-type pulsators is a consequence of the existence of two distinct types of modes which have large amplitudes in the Z-bump layer and have periods matching the thermal relaxation time of that layer. With these two conditions satisfied, the driving effect may be strong enough to overcome the damping occurring outside this layer. The first type encompasses p- and g-modes of the lowest radial orders n and angular degrees . In the outer layers, the properties of such oscillations are determined by the frequency ω, and are nearly independent of . These modes are unstable in somewhat evolved main sequence stars of spectral types earlier than B4. The simultaneous excitation of p- and g-modes is important for seismic diagnoses because their frequencies are sensitive to the deep interior stellar structure. The instability extends to high- modes trapped in the envelope. The second type of B star pulsations encompasses g-modes of high orders. The instability range depends on the value of ( + 1)/ω 2 which determines the depth dependence of the pulsation amplitude and separately on ω, which determines the time-scale matching. At low s, the period match occurs for objects of lower masses and later spectral types than β Cep stars. This explains the occurrence of the SPB domain in the main sequence band. The instability of the high-n modes occurs in wider ranges of stellar parameters. However, in models of more massive stars it was originally found only for high- modes, which are not easily detectable in light variations. Thus, we have thought that the β Cep-type and SPB-type pulsation are mutually exclusive. Observations taught us that we have been wrong. The driving mechanism in all B-type pulsators is the same. It is the κ-mechanism in its cleanest form and there is no role for convection. This is not true for main sequence F-type stars. This is why the slowly pulsating γ Doradus stars cannot be regarded as an SPB star analog. The role of convection in the former stars is essential, while it is only secondary in the somewhat brighter and much more rapidly pulsating δ Scuti stars. True analogs of the two types of main sequence B-type pulsators were found among the sdB stars and were explained with the same driving mechanism (Fontaine et al. 2003). Does iron accumulate in the driving zone of β Cephei stars? ν Eridani is perhaps the most thoroughly studied β Cephei star. Recent observational campaigns (Aerts et al. 2004, Handler et al. 2004, Jerzykiewicz et al. 2005) on this object have been very rewarding. New modes were found and for most of them unique identifications were found (De Ridder et al. 2004). The data were used for seismic model construction which led to implications regarding the global parameters of the star, internal mixing and rotation (Pamyatnykh et al. 2004, Ausseloos et al. 2004) and stellar opacities (Daszyńska-Daszkiewicz et al. 2005). However, the models were not totally successful as they predict mode instability only in the 4 to 6 c/d range while in ν Eri’s oscillation spectrum there is a number of peaks in the 6 to 8 c/d range and a peak at 0.42 c/d. The explanation proposed by Pamyatnykh et al. (2004) was that the iron abundance in the driving layer is significantly enhanced due to selective radiation pressure. The required enhancement to destabilize high frequency modes was somewhat less than a factor of four and somewhat larger for the low-frequency mode. The proposal was based on Charpinet et al.’s (1996) solution of the driving problem for the sdB pulsators, but it was not clear then whether or not this applies because of huge difference in properties between the two types of objects. Detailed calculations of element segregation due to diffusion and radiative pressure for main sequence B-stars were made by Seaton (1999), but only for stars with a mass up to 4.5M , which is about half of ν Eri’s mass. These calculations, which were made assuming no microscopic mixing, showed that a significant iron accumulation in the Z-bump may indeed take place. However, the enhancement should occur also in the atmosphere and should thus be visible. Calculations for a model appropriate for ν Eri (Bourge et al. 2007) show W. A. Dziembowski 177 a higher iron enhancement in the atmosphere which is consistent with the trend seen in Seaton’s results. In main sequence stars with masses less than 3M and in sdB stars, the iron enhancement may be hidden because there is a region between the Z-bump layer and the photosphere where gravitational settling of iron dominates over selective radiation pressure. Since there is no spectroscopic evidence for iron enhancement in ν Eri, the proposed solution seems invalidated. Paradoxically, as Turcotte and Richard (2005) pointed out, none of the HgMn stars - the only B stars showing evidence of diffusive element segregation - is known as a pulsator. Another problem is the neglect of rotational mixing. In the case of ν Eri it might be justified because of its unusually slow equatorial velocity of some 6 km/s. However, this is not the only object, which is a hybrid β Cep/SPB pulsator. The oscillation spectrum of 12 Lac (Handler et al. 2006) is strikingly similar, but its rotational velocity is much higher. How rotation affects slow modes The nature of the variability with periods in the range from one half to a few days observed in Be stars has been a subject of controversy. The interpretation in terms of slow modes, first proposed by Baade (1982), is partially supported by linear stability calculations. On the other hand, Balona (1995) argues that the observed periodic light variability may be explained by spots on the rotating stellar surface. The ambiguity is caused by the fact that the rotation periods of Be stars and the periods of unstable modes are similar. This coincidence implies that rotation cannot be regarded as a small perturbation and that the angular dependence of the modes cannot be described by individual spherical harmonics. Two approaches have been adopted to treat the large effects of rotation. One developed by Lee and Saio (1989) relies on a truncated expansion of the longitudinal mode dependence into Legendre functions. The other, which relies on the traditional approximation, allowing for a separation of the angular dependence in terms of the Hough functions, has been used for instance by Townsend (2005) in his extensive survey of slow-mode instability in B-stars. The traditional approximation greatly facilitates the stability analysis because the effect of rotation essentially reduces to replacing ( + 1) with a λ parameter, which for specified angular orders depends only on Ω/ω - the ratio of angular velocity rotation to mode frequency. Townsend (2005) showed that rotation has only a small effect on the extent of the SPB domain in the HR diagram. The effect on the frequency range of unstable modes in the inertial system and on mode visibility may be much more significant. The oscillation spectrum of the Be star HD 163868, determined from MOST data by Walker et al. (2005), is far the richest for an object of this type. The spectrum shows three abundant groups of peaks: one below 0.5 c/d, one centred near 1.5 c/d, and one near 3 c/d. The authors could explain the two latter groups in terms of unstable modes in an appropriate stellar model. Only for the highest-frequency peaks of the first group they could find counterparts among unstable modes. Repeating the stability analysis for the same model but using the traditional approximation, we (Dziembowski et al. 2007) obtained a somewhat different result. In particular, we had no difficulty in explaining all low frequency peaks in terms of unstable retrograde g-modes of the lowest angular order and we could account for mode selection taking into account the visibility dependence on the aspect and assuming i ≈ 90o . With i ≈ 55o , as adopted by Walker et al. (2005), we could not obtain any consistent interpretation of the observed oscillation spectrum. Beyond linear theory Linear stability calculations provide only a partial answer to the question which modes may be excited and do not predict pulsation amplitudes. From observations, we know that the typical form of B-star pulsation consists of the excitation of many modes with low amplitudes. 178 Oscillations in main sequence B-type stars - challenges to theory There are only three β Cep stars with a V amplitude exceeding 0.08 mag. Surprisingly, two of the three stars were discovered only very recently (Pigulski 2007). Typical amplitudes of known modes in B-type pulsators are much lower. Why this form of pulsation is chosen may be answered only by going beyond linear theory. Recent nonlinear modelling of radial pulsations of β Cep stars by Smolec and Moskalik (2007) predicts light amplitudes that are significantly higher than even in these three highamplitude and apparently single-mode pulsators. These authors conclude that there must be hidden modes involved in the pulsations of these stars. Indeed, their results suggest that saturation of the instability by a single-mode is unlikely. Although in most cases they find single-mode pulsation as the limit cycle, they also find cases of sustained double mode (DM) pulsation involving the fundamental and first overtone modes. The DM pulsation occurred either due to properties of saturation (non-resonant DM pulsation) or due to the resonance 2ωIov ≈ ωfund + ωIIov . The first two involved modes were linearly unstable, while the second overtone is stable. What was found rather rare in models that know only about radial modes should be common in a realistic situation. The non-resonant DM behaviour found by Smolec and Moskalik (2007) occurs in the intermediate Teff -range between the first overtone and fundamental mode domains. Since modes differing in in narrow frequency ranges have similar saturation coefficients, we expect that the domain of stable single-mode pulsation may totally disappear. Moreover, there are many more possibilities for resonant coupling. At the lowest order in amplitude of radial modes there is a possibility of parametric excitation of nonradial modes with the same and opposite m values with frequencies whose sum is close to the radial mode frequency, ω. If the sum is close to 2ω, then the parametric excitation may occur due to a higher order effect, similar to that responsible for the resonant DM pulsation found by Smolec and Moskalik (2007). The effect requires higher amplitude, but nonlinear coupling is stronger between modes of higher frequencies, which all have large amplitude in the outer envelope. Amplitude growth may be terminated in two distinct ways. One is through induced changes in the mean stellar structure and the other is through a resonant excitation of stable (parasite) modes. In the first case, the discrepancy could be blamed to the presence of undetected nonradial modes. Especially those of high may indeed contribute to saturation and have disc-averaged light amplitudes below the detection threshold. In the absence of resonance, the lowest order equations for the evolution of mode amplitudes may be written in the form K X dAj αjk A2k ), = γj (1 − dt k=1 where Aj denotes surface-averaged amplitudes, γj the linear growth rates, and αjk are introduced ad hoc saturation coefficients, which are assumed greater than zero. For Aj we may choose the r.m.s. value of δR/R but as long as αjk remains unspecified the choice does not matter. Around each radial mode, there are always many unstable nonradial modes of similar frequencies PK and, 2hence, similar saturation coefficients. At a steady limit cycle we should have k=1 αjk Ak = 1. Compared with the single-mode case, we may expect, crudely, a factor K −1/2 reduction of the r.m.s. amplitude of individual modes. If the -values of the excited modes are larger than 2, the modes most likely remain undetectable in light variations. Amplitudes may be further reduced if high-order g-modes are excited. Such modes are unstable in β Cep stars in a certain range of values but we cannot assume for them similar saturation coefficients as for p-modes. If we assume that only p-modes take part in the saturation of the instability, then we may rule out this effect as the sole cause of amplitude limitation. If this were the case, then, assuming again that excited modes have similar frequencies, the r.m.s. velocity fluctuation should be of the same order as the radial velocity amplitude determined by Smolec and W. A. Dziembowski 179 Moskalik (2007) for radial pulsation. These authors found values up to 450 km/s. Thus, if the undetected modes are responsible for most of the instability saturation in β Cep stars, we should expect line broadening corresponding to macroturbulence at a level of 100 km/s, which is not observed. We must conclude that the instability in β Cep stars is not saturated by p-modes. Still, we should consider a possible role of unstable high-order g-modes. Since no nonlinear calculations have been done on such modes, we have to rely on a guess, which seems reasonable, that the mode contribution to saturation is determined by the amplitude of δTeff . Adopting a linear relation between δTeff and the pulsation velocity component, we may compare the r.m.s. velocities at saturation by g- and p-modes. My linear calculations showed that in the g-mode case the velocities are by factors between three and four lower, but still too high. Thus, it seems that the instability is not saturated and that the excess of work is consumed by parasite modes. Challenges that remain The puzzle of B-star pulsation has been solved at the beginning of the 1990ties. The classical opacity mechanism was shown to drive the whole variety of modes seen in B stars. New data that came after, though not shaking our basic understanding of the driving effect, point to a need for further work on better understanding pulsation in these stars. This is timely because if we do not understand an important aspect of stellar pulsation it means that we do not understand something important in stellar physics. There are problems on the level of linear theory. Not all modes that are detected are found unstable. With present microscopic physics data it seems impossible to explain the wide frequency range of modes in the two β Cep stars ν Eri and 12 Lac. Perhaps there is a need for further refining stellar opacity data. The data from the Independent Project (Seaton 2005, for the latest version), though confirming the gross features of the Z-bump, led to somewhat different astrophysical predictions (e.g. Daszyńska-Daszkiewicz et al. 2005). The interpretation of frequency spectra of Be stars is complicated by the large effects of rotation. Contradicting results of modelling the rich oscillation spectrum of HD 163868 might suggest we still need improvement in our treatment of linear oscillations in the case of fast rotation or again for improving the opacity data. The mechanism responsible for Be star activity varying on long time scales is still unknown. It is interesting to enquire about the possible role of the opacity driven oscillation. The answer requires going beyond linear theory. There are more such questions regarding B stars, for instance, what determines the main peak amplitude and its harmonics, or what causes temporal amplitude changes seen in many β Cep stars. Unfortunately, nonlinear modelling of B-star pulsation is still in its infancy phase. All modelling done so far assumed spherical symmetry. The lesson we learnt from recent studies of radial pulsation is that the detected modes cannot saturate the instability and thus they must represent only a small subset of the excited modes. What is the rest of the modes? Linear stability calculations show that there are many unstable high- modes, which may contribute to saturation but not to the observed variability. However, the presence of such modes should manifest itself in spectral line broadening which cannot be easily hidden. However, a quantitative assessment of this effect is still ahead of us. Acknowledgments. I am grateful to the SOC for the invitation to this workshop. My participation was supported by the HELAS project. The preparation of my presentation and of this paper was supported by the Polish MNiI grant No. 1 P03D 021 28. 180 Oscillations in main sequence B-type stars - challenges to theory References Ausseloos M., Scuflaire R., Thoul A., Aerts C., 2004, MNRAS, 355, 352 Aerts C., de Cat P., Handler G., et al., 2004, MNRAS, 347, 463 Baade D., 1982, A&A, 105, 65 Balona L. A., 1995, MNRAS, 306, 407 Bourge P.-O., Théado S., Thoul A., 2007, these proceedings Charpinet S., Fontaine G., Brassard P., Dorman B., 1996, ApJ, 471, L103 Cox A. N., Morgan S. M., Rogers F. J., Iglesias C. A., 1992, ApJ, 393, 272 Daszyńska-Daszkiewicz J., Dziembowski W. A., Pamyatnykh A. A., 2005, A&A, 441, 641 De Ridder J., Telting J. H., Balona L. A., et al., 2004, MNRAS, 351, 324 Dziembowski W. A., Pamyatnykh A. A., 1993, MNRAS, 262, 204 Dziembowski W. A., Daszyńska-Daszkiewicz J., Pamyatnykh A. A., 2007, these proceedings Dziembowski W. A., Moskalik P., Pamyatnykh A. A., 1993, MNRAS, 265, 588 Fontaine G., Brassard P., Charpinet S., et al., 2003, ApJ, 597, 518 Gautschy A., Saio H., 1993, MNRAS, 262, 213 Handler G., Shobbrook R. R., Jerzykiewicz M., et al., 2004, MNRAS 347, 454 Handler G., Jerzykiewicz M., Rodrı́guez E., et al., 2006, MNRAS, 365, 327 Jerzykiewicz M., Handler G., Shobbrook R. R., et al., 2005, MNRAS, 360, 619 Iglesias C. A., Rogers F. J., Wilson B. G., 1992, ApJ, 397, 717 Kiriakidis M., El Eid M. F., Glatzel W., 1992, MNRAS, 255, 1P Lee U., Saio H., 1989, MNRAS, 237, 875 Moskalik P., Dziembowski W. A., 1992, A&A, 256, L5 Pamyatnykh A. A., Handler G., Dziembowski W. A., 2004, MNRAS, 350, 1022 Pigulski A., 2007, these proceedings Seaton M., 1999, MNRAS, 307, 1008 Seaton M., 2005, MNRAS, 362, L1 Simon N. R., 1982, ApJ, 260, L87 Smith M. A., 1977, ApJ, 215, 574 Smolec R., Moskalik P., 2007, these proceedings Turcotte S., Richard O., 2005, in Alecian G., Richard O., Vauclair S., eds, Element Stratification in Stars: 40 Years of Atomic Diffusion. EAS Pub. Ser., Vol. 17, EDP Sciences, Les Ulis, p. 357 Townsend R. H. D., 2005, MNRAS, 360, 465 Walker G. A. H., Kuschnig R., Matthews J. M., et al., 2005, ApJ, 635, L77 Waelkens C., 1991, A&A, 246, 453 Comm. in Asteroseismology Vol. 150, 2007 Candidate SPB and γ Doradus stars from microlensing surveys A. Narwid, Z. Kolaczkowski and A. Pigulski Astronomical Institute, University of Wroclaw, Kopernika 11, 51-622 Wroclaw, Poland Abstract From the analysis of the database of 200 000 variable candidates in the OGLE-II Galactic fields we have extracted about 600 stars showing periodic low-amplitude brightness variations. Many of them are multiperiodic. From their location in the colour-magnitude diagram we conclude that they are good candidates for slowly pulsating B and γ Doradus stars. The data and analysis Using data from the catalogue of 200 000 variable stars candidates we searched short-period low-amplitude pulsators. This photometry was accumulated during the OGLE–II project carried out in the years 1997–2000 in the 49 fields located near the centre of the Galaxy (Woźniak et al. 2002). The analysis consisted of an automatic extraction of up to five periodic terms for all stars in the catalogue with consecutive prewhitening followed by an automatic classification based upon the periods, amplitudes and Fourier coefficients (for stars with detected harmonics or subharmonics). Then, for stars selected in this way, a detailed analysis was performed in an interactive way. The analysis yielded a lot of candidates for β Cephei and δ Scuti stars (Narwid et al. 2006). In addition, we detected a sample of over 600 low-amplitude variable stars with periods in the range between 0.5 and 6 days. We suspect that the sample consists mainly of a mixture of SPB and γ Doradus stars. For 270 of the variables, we were able to combine the OGLE-II data with the photometry available from the MACHO survey. The analysis of the combined photometry resulted in better resolution, lower detection threshold and practically removed the ambiguity in the frequencies of the detected periodicities. No transformations were performed before data combination. The results and conclusions The results we obtained can be summarized in the following way. The position in the colourmagnitude diagram (CMD) clearly suggests that these stars are main-sequence pulsators. Their V magnitudes range from 12 to 18 mag. The distribution of periods shows that most of these stars have periods in the range between 0.55 and 1.5 d; for periods longer than 2.5 d the number of variables decreases with increasing period. The I-filter semi-amplitudes of the variables are typically below 20 mmag, but there are stars with semi-amplitudes of up to 90 mmag. The brightness variability with periods from the aforementioned range is typical for candidate SPB and γ Doradus stars. Thus, we suppose that our sample consists mainly of a mixture of these two types of pulsators. This conclusion is supported by the fact that about 400 stars in our sample show multiperiodic behaviour. Up to seven modes in a single star were found in the combined OGLE-II and MACHO data. In the long-period range contamination from the other types of variability, e.g. α2 CVn stars or ellipsoidal binaries, cannot be excluded. In a few stars we also revealed periodicities with periods shorter than 0.5 d. Such periods are more typical for δ Scuti or β Cephei-type 182 Candidate SPB and γ Doradus stars from microlensing surveys variability. These stars are therefore good candidates for hybrid γ Doradus/δ Scuti stars similar to HD 8801 (Henry & Fekel 2005). Another possibility is that they are hybrid SPB/β Cephei stars. The periods, amplitudes and the position in the CMD are not sufficient to distinguish SPBs from γ Doradus stars. Therefore we are going to gather UBV photometry and/or low-resolution spectroscopy for stars from our sample, which will allow us to improve the classification of these stars. Acknowledgments. This work was supported by the MNiI grant No. 1 P03D 016 27. The authors are grateful to the EC for the establishment of the European Helio- and Asteroseismology Network HELAS, which made their participation at this workshop possible. References Henry G. W., Fekel F. C., 2005, AJ, 129, 2026 Narwid A., Kolaczkowski Z., Pigulski A., 2006, Mem. Soc. Astron. Ital., 77, 342 Woźniak P. R., Udalski A., Szymański M., et al., 2002, Acta Astron., 52, 129 Comm. in Asteroseismology Vol. 150, 2007 An abundance analysis of slowly pulsating B stars M. Briquet,1 T. Morel 1,2 1 Instituut voor Sterrenkunde, Katholieke Univ. Leuven, Celestijnenlaan 200 D, B-3001 Leuven, Belgium 2 European Space Agency (ESA) postdoctoral external fellow Abstract We present the methodology and the first results of a study aimed to determine in a selfconsistent way the physical parameters Teff and log g as well as NLTE abundances of the majority of all confirmed slowly pulsating B stars (hereafter SPBs). Observations High-resolution optical spectra of more than 30 SPBs were obtained with the CORALIE echelle spectrograph attached to the 1.2-m Leonard Euler telescope at La Silla during many observing runs dedicated to this class of pulsating B stars. In order to minimize the impact of the pulsations, several time-resolved spectra were co-added. Methods of analysis We made use of the latest versions of the NLTE line formation codes DETAIL and SURFACE (K. Butler, private communication), along with plane-parallel, fully line-blanketed LTE Kurucz atmospheric models. The physical parameters are estimated using an iterative scheme. The effective temperature is derived from the silicon ionization balance, the gravity from fitting the collisionallybroadened wings of the Balmer lines and the microturbulence from requiring the individual abundances given by the O II lines to be independent of the line strength. Once the atmospheric parameters above are known, the abundances are derived by matching the observed and predicted equivalent widths of a set of carefully-selected, unblended spectral lines. For consistency, direct integration is used in both cases. First results The derived abundances of two SPBs of early spectral type are given in Table 1. For HD 3360, the abundances of all considered chemical elements are indistinguishable from the values reported for early B dwarfs in the solar neighbourhood within the errors, except for nitrogen. Indeed, we clearly detect a nitrogen excess in this B2 star, as has recently been discovered in four β Cephei stars studied by Morel et al. (2006). Similarly to these latter stars, HD 3360 shows a strong boron depletion (Proffitt & Quigley 2001), has a detected magnetic field and is slowly rotating (Neiner et al. 2003). We refer to Morel et al. (these proceedings) for further discussion on the interpretation of these results. For HD 85953, all derived abundances are solar. Acknowledgments. MB is a Postdoctoral Fellow of the Fund for Scientific Research, Flanders. We thank all the observers from the Institute of Astrophysics of the University of Leuven who gathered the spectroscopic data. 184 An abundance analysis of slowly pulsating B stars Table 1: Atmospheric parameters, NLTE abundances and the resulting metallicity. By convention, log (H) = 12. The number of used lines is given in brackets. We define [N/C] and [N/O] as log[(N)/(C)] and log[(N)/(O)], respectively. For comparison purposes, we also give the typical values found for OB dwarfs in the solar neighbourhood (Daflon & Cunha 2004), the standard solar composition of Grevesse & Sauval (1998) and the solar abundances recently derived from 3-D hydrodynamical models (Asplund et al. 2005). Teff (K) log g ξ (km s−1 ) He/H log (C) log (N) log (O) log (Mg) log (Al) log (Si) log (S) log (Fe) Z [N/C] [N/O] HD 3360 22000±1000 3.7±0.15 1±1 0.084±0.027 (10) 8.16±0.08 (6) 7.97±0.13 (20) 8.38±0.30 (18) 7.57±0.16 (1) 6.15±0.16 (4) 7.28±0.30 (6) 7.22±0.18 (7) 7.31±0.16 (18) 0.010±0.002 −0.19±0.15 −0.41±0.32 HD 85953 21000±1000 3.8±0.15 1±1 0.070±0.012 (9) 8.16±0.14 (9) 7.66±0.20 (11) 8.41±0.32 (16) 7.62±0.11 (1) 6.14±0.13 (3) 7.25±0.30 (6) 7.26±0.16 (6) 7.40±0.23 (12) 0.010±0.002 −0.50±0.24 −0.75±0.37 OB stars Sun 1-D Sun 3-D ∼0.10 ∼8.2 ∼7.6 ∼8.5 ∼7.4 ∼6.1 ∼7.2 ∼7.2 ∼7.4 ∼0.01 ∼−0.6 ∼−0.9 0.085±0.001 8.52±0.06 7.92±0.06 8.83±0.06 7.58±0.05 6.47±0.07 7.55±0.05 7.33±0.11 7.50±0.05 0.017±0.001 −0.60±0.08 −0.91±0.08 0.085±0.002 8.39±0.05 7.78±0.06 8.66±0.05 7.53±0.09 6.37±0.06 7.51±0.04 7.14±0.05 7.45±0.05 0.012±0.001 −0.61±0.08 −0.88±0.08 References Asplund M., Grevesse N., Sauval A. J., 2005, in Barnes T. G. III, Bash F. N., eds, ASP Conf. Ser. Vol. 336, Cosmic Abundances as Records of Stellar Evolution and Nucleosynthesis. Astron. Soc. Pac., San Francisco, p. 25 Daflon S., Cunha K., 2004, A&A, 617, 1115 Grevesse N., Sauval A. J., 1998, Space Sci. Rev., 85, 161 Morel T., Butler K., Aerts C., Neiner C., Briquet M., 2006, A&A, 457, 651 Neiner C., Geers V. C., Henrichs H. F., et al., 2003, A&A, 406, 1019 Proffitt C. R., Quigley M. F., 2001, ApJ, 548, 429 Thierry Morel, Wolfgang Zima and Harry Shipman concentrating on a talk. Comm. in Asteroseismology Vol. 150, 2007 Temperature gradients in the core overshooting region M. Godart Institut d’Astrophysique et de Géophysique, Université de Liège, Belgium Abstract The term overshooting is used to describe two situations: the chemical mixing induced by the convective elements crossing the boundary given by Schwarzschild’s criterion (overshooting), or, in addition to that mixing, the change in the temperature gradient in the overshoot region when convection is efficient enough (penetration; Zahn 1991). We show that for models with the same mass of the mixed central region the oscillation frequencies are sensitive to the kind of overshoot treatment adopted. This effect is especially obvious for SPB stars and is high enough to be detected by CoRoT long run observations. That would imply the possibility of disentangling penetration from overshooting. HR diagram and internal structure For a given value of the overshooting parameter, different overshooting treatments yield different convective and mixed core mass fractions. For instance, an overshooting parameter of αov = 0.2 with the penetration treatment results in a mixed core 3% smaller than the computed one with the classic overshooting treatment. As a consequence, in the case of the classic treatment the main sequence evolutionary tracks are longer and more luminous than in the penetration case. The larger the overshooting parameter is, the greater the effect will be. In order to have the same mixed mass fraction we have to decrease αov down to 0.175 in models computed with overshooting. Effect on the frequencies We study the impact of different overshooting treatments on the oscillation frequencies in order to possibly use asteroseismology as a tool to disentangle penetration from overshooting at the top of a convective core. In the extra-mixed region, the Brunt-Väisälä (BV) frequency is positive in models computed with overshooting while it is zero in models computed with penetration. This difference matters for modes that propagate in the deep radiative interior. These include low-order g- and p-modes, which are excited in β Cep stars, and high-order g-modes, which are excited in SPB stars (Figs. 1 and 2). Fig. 1 shows the difference in normalized frequencies for a 10M star along the main sequence phase. For the g2 mode, it is of the order of 1.3%, which means 0.4 μHz, larger than the frequency resolution of CoRoT (0.08 μHz). Fig. 2 represents the period spacings of typical SPB frequencies for models computed with overshooting and penetration. The asymptotic R values of the period spacing (∼ ( (N/r )dr )−1 ) are different by about 150 s. Furthermore the discrepancies between the period spacing computed with different overshooting treatments are of the order of 1550 s at P ∼ 1.2 × 105 s, which could be detected by CoRoT. In conclusion, even if the overshooting parameters are chosen to produce overshooting and penetration models with the same central mixed mass fraction, the temperature gradient in their central regions is different. As a result g-mode and low order p-mode frequencies may be affected. These effects of overshooting treatments on the frequencies are within the reach of current asteroseismic observations. 186 Temperature gradients in the core overshooting region |1nl, rad - 1nl, ad|/1nl, rad (%) 1.6 p2 p1 g1 10M0 l=1 1.4 g2 1.2 1 0.8 0.6 0.4 0.2 a. 0 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 Xc p Figure 1: Difference between p-mode and g-mode normalized frequencies Ωnl = 2πνnl R 3 /GM (=1) of modes for 10M stellar models computed with the different overshooting treatments. 10 penetration overshooting 9 6P(103s) 8 7 5M0 Xc=0.5 l=1 b. 6 5 3 <6Ppene.> (10 s) <6Pov.> (103s) 4 0 50 100 150 P(103s) 200 250 300 Figure 2: Period spacings (ΔP = |Pn − Pn−1 |) for 5M models computed with overshooting and penetration. < ΔP > stands for the asymptotic value of the period spacing. Acknowledgments. The author thanks J. Montalban for numerous fruitful discussions. References Zahn J.-P., 1991, A&A, 252, 179 Comm. in Asteroseismology Vol. 150, 2007 A comparative study of B-type pulsators and non-pulsating chemically peculiar Bp stars M. Briquet,1 S. Hubrig,2 P. De Cat,3 C. Aerts,1 P. North,4 M. Schöller 2 1 Instituut voor Sterrenkunde, Katholieke Universiteit Leuven, Belgium European Southern Observatory, Casilla 19001, Santiago 19, Chile Koninklijke Sterrenwacht van België, Ringlaan 3, B-1180 Brussel, Belgium 4 Laboratoire d’astrophysique, Ecole Polytech. Fédérale de Lausanne, Observatoire, Sauverny, Switzerland 2 3 Abstract We carry out a comparative study between a sample of confirmed and well-studied B-type pulsators and a sample of well-studied Bp stars with known periods and magnetic field strengths. Our study indicates that the group of Bp stars is younger than the group of SPB stars and that stars with stronger magnetic fields have much lower pulsation amplitudes. Star samples and parameter determination We selected our sample of magnetic Bp stars from the recent catalogues of Bychkov et al. (2003, 2005) and Hubrig et al. (2006a). We considered stars with masses between 3 and 9 M , for which the rotation periods and magnetic field strengths are known. The list of confirmed SPB stars was retrieved from De Cat (2002). The only consistent way to determine the position of the stars of both samples in the H-R diagram is to use Hipparcos parallaxes. We retained stars with sufficiently accurate parallaxes, i.e. where σ(π)/π < 0.2, and with available Geneva or Strömgren photometry. Our sample consists of 24 Bp stars and 24 SPB stars. Explanations on the determination of the fundamental parameters can be found in Hubrig et al. (2000). Evolutionary state and magnetic field strength comparisons The cumulative distribution of log g for the Bp stars and SPB stars in our sample is shown in Fig. 1. A Kolmogorov-Smirnov test shows that the distribution of the values of log g for the Bp stars differs from the distribution for SPB stars at a significance level of 98.3 %. We consequently conclude that the group of Bp stars is younger than the group of SPB stars. It is well-known that magnetic fields are observed in most Bp stars. Recently, Hubrig et al. (2006b) performed a systematic search for magnetic fields in B-type pulsators with the FORS 1 instrument at the VLT. The histogram in Fig. 1 clearly shows that longitudinal magnetic fields in pulsating B stars are rather weak in comparison to the fields detected in Bp stars. This indicates that very strong magnetic fields are not co-existent with oscillations, or that stars with stronger magnetic fields have much lower pulsation amplitudes. Acknowledgments. Flanders. MB is Postdoctoral Fellow of the Fund for Scientific Research, 188 A comparative study of B-type pulsators and non-pulsating chemically peculiar Bp stars 1.0 8 Number of stars Cumulative fraction 0.8 0.6 0.4 6 4 2 0.2 0.0 0 3.6 3.8 4.0 log g 4.2 4.4 0 1 2 <Bl> [kG] 3 4 Figure 1: Left: Cumulative distribution of log g for the Bp stars (full line) and the SPB stars (dotted line). Right: Distribution of the longitudinal magnetic field values Bl for the Bp stars (full line) and the SPB stars (dotted line). References Bychkov V. D., Bychkova L. V., Madej J., 2003, A&A, 407, 631 Bychkov V. D., Bychkova L. V., Madej J., 2005, A&A, 430, 1143 De Cat P., 2002, in Aerts C., Bedding T. R., Christensen-Dalsgaard J., eds, ASP Conf. Proc. Vol. 259, Radial and Nonradial Pulsations as Probes of Stellar Physics. Astron. Soc. Pac., San Francisco, p. 196 Hubrig S., North P., Mathys G., 2000, ApJ, 539, 352 Hubrig S., North P., Schöller M., Mathys G., 2006a, AN, 327, 289 Hubrig S., Briquet M., Schöller M., et al., 2006b, MNRAS, 369, 61 Comm. in Asteroseismology Vol. 150, 2007 Mode identification of multi-periodic Slowly Pulsating B-stars: results and problems W. Zima,1 P. De Cat,2 C. Aerts 1 1 Instituut voor Sterrenkunde, K.U. Leuven, Celestijnenlaan 200D, 3001 Leuven, Belgium 2 Koninklijke Sterrenwacht van België, Ringlaan 3, 1180 Brussel, Belgium Abstract We report results from mode identifications (MI) for four selected multi-periodic Slowly Pulsating B-stars (SPB) using the Fourier parameter fit (FPF) method. Problems related to the pulsational nature of these objects which hamper a correct identification are discussed. For a present day status of knowledge about SPB stars we refer to De Cat (2007, this issue). Introduction De Cat et al. (2000), De Cat (2001), and De Cat & Aerts (2002, hereafter DA02) carried out a large photometric and spectroscopic monitoring program including 13 SPB stars to provide a better understanding for this class of variables. Their frequency analysis and mode identification are based on 7-colour Geneva-photometry, Hipparcos measurements, and timeseries of high-resolution, high signal-to-noise spectra. We selected four multi-periodic SPB stars, HD 26326, HD 74195, HD 85953, and HD 138764, which are promising targets for successful seismic modelling, to perform MI. We applied the Fourier parameter fit (FPF) method (Zima 2006) to their data by which we fit the observed zeropoint, amplitude and phase across an absorption line profile for each detected frequency with corresponding values from synthetic line profiles to determine the pulsational geometry. For each separate case we selected the deepest unblended line of the Siii-triplet. Results HD 26326: DA02 detected three frequencies from multi-colour photometry and the first three normalized velocity moments of the λ4128 Å Siii profiles: 0.534, 0.172 and 0.763 d−1 . By using amplitude ratios (Dupret et al. 2003) in seven passbands of the Geneva photometric system, the dominant frequency f1 was identified as =1 or 2 (De Cat et al., in preparation). By applying a Fourier analysis and least-squares fitting for each pixel across the λ4128 Å Siii profile we detected f1 and f2 in agreement with DA02, but the value of a third frequency (f3 =0.7559 d−1 ) differs significantly for reasons unknown, yet. We identified f1 with high significance as a prograde sectoral dipole-mode ( = m = 1) and constrained the azimuthal order for f3 to m = 1. For f2 , the results of the MI are ambiguous. HD 74195: For this object, DA02 report four frequencies between 0.3 and 0.4 d−1 . All four periodicities can be seen in the velocity moments with radial velocity amplitudes between 1.3 and 3.2 km s−1 . We detected only two of them in the intensity variations across the λ4128 Å Siii profile: f1 =0.357 d−1 and f2 =0.350 d−1 . We identified the azimuthal order of f1 as m = 1, but an ambiguity in the determination of remained. By also considering the photometric MI ( =1) we conclude that this is a sectoral dipole-mode. The best fits for f2 are achieved with ( ,m) = (3, −2) and (3,+1), not in agreement with the photometric MI of =1. 190 Mode identification of multi-periodic Slowly Pulsating B-stars: results and problems HD 85953: The mean line profile shows a clear asymmetry which may be caused by a composite profile due to a visual component. We therefore carried out the MI in two steps: first by considering the zeropoint profile, which sets strong constraints on v sin i , the intrinsic line width and the equivalent width, and second by only fitting amplitude and phase across the profile and omitting the zeropoint profile. It turned out that for both frequencies a better fit can be achieved with the second approach resulting in a narrower zeropoint profile and a lower v sin i value of 18 km s−1 , compared to 29 km s−1 when considering the zeropoint profile. This might indicate that we are indeed dealing with a composite profile which increases the width of the line. The best identification for f2 yields ( = 4, m = −3). For f1 large ambiguities prevent a clear identification. HD 138764: This star is multi-periodic with at least two periodicities (DA02). A dominant frequency at 0.794 d−1 with a radial velocity amplitude of 3.6 km s−1 is found from photometry and spectroscopy. The velocity moments show a second frequency at 0.637 d−1 with a much lower radial velocity amplitude of 0.8 km s−1 . Our analysis of the pixel-intensity variations of the λ4130 Å Siii line revealed f1 =0.794 d−1 , f2 =0.637 d−1 and an additional frequency at f3 =0.589 d−1 . By means of the FPF method f1 is clearly identified as a sectoral mode with =1, m=1, which is in good agreement with the photometric results and the identification from the moment method (De Cat et al., in preparation). The best fit to the Fourier parameters of this mode indicates an inclination angle of 30◦ and a v sin i of 21 km s−1 , implying an equatorial rotational velocity of 42 km s−1 and a rotational frequency of 0.32 d−1 . The amplitude and phase of f2 and f3 across the profile are strongly distorted due to the relatively large amplitude of f1 , therefore no reliable MI could be achieved for these two modes. Conclusions Mode identification of SPB stars is very challenging due to the large horizontal velocities, which hamper the identification of the azimuthal order of the pulsation modes. For some pulsation modes and m can be constrained but the uncertainty in the determination of the stellar inclination is for most stars too large to derive reliable frequency values in the stellar rotation frame of reference. The knowledge of these frequency values are very important for theoretical modelling. All identifications point towards low-degree and low-order pulsation modes. In many cases the dominant frequency is a sectoral dipole-mode. Recently, Hubrig et al. (2006) detected longitudinal magnetic fields with strengths up to a few hundred G for a set of SPB stars. An improved model of the line profile variations by also considering the effects of a magnetic field and non-uniform surface element abundances will be necessary for a better understanding of these objects. Acknowledgments. WZ and CA are supported by the Research Council of Leuven University, under grant GOA/2003/04. References De Cat P., Aerts C., De Ridder J., et al., 2000, A&A, 355, 1015 De Cat P., 2001, PhD Thesis, Katholieke Universiteit Leuven, Belgium De Cat P., Aerts C., 2002, A&A, 393, 965 Dupret M.-A., De Ridder J., De Cat P., et al., 2003, A&A, 398, 677 Hubrig S., Briquet M., Schöller M., et al., 2006, MNRAS, 369, 61 Zima W., 2006, A&A, 455, 227 Comm. in Asteroseismology Vol. 150, 2007 The ongoing 2005 – 2006 campaign on β Cephei stars in NGC 6910 and χ Persei (NGC 884) A. Pigulski,1 G. Handler,2 G. Michalska,1 Z. Kolaczkowski,1 G. Kopacki,1 A. Narwid,1 E. Vanhollebeke,3 M. Stȩślicki,1 K. Lefever,3 K. Gazeas,4 W. De Meester,3 J. Vanautgaerden,3 A. Leitner,2 J. De Ridder,3 V. Van Helshoecht,3 C. Gielen,3 B. Vandenbussche,3 S. Saesen,3 M. D. Reed,5 J. R. Eggen,5 G. A. Gelven,5 M. Desmet,3 E. Puga Antolı́n,3 C. Aerts,3 E. Schmidt,2 R. Huygen,3 D. Lorenz,2 M. Vučković,3 E. Broeders,3 E. Bauwens,3 T. Verhoelst,3 P. Deroo,3 P. Lenz,2 S. Dehaes,3 D. Ladjal,3 B. Steininger,2 G. Davignon,3 P. Beck,2 K. Yakut,3,6 R. Drummond,3 J.-N. Fu,7 X.-J. Jiang,8 C. Zhang,7 J. Provencal,9 L. Decin 3 1 Instytut Astronomiczny, Uniwersytet Wroclawski, Wroclaw, Poland Institute of Astronomy, University of Vienna, 1180 Vienna, Austria Instituut voor Sterrenkunde, Katholieke Universiteit Leuven, Belgium 4 Department of Astrophysics, Astronomy and Mechanics, Univ. of Athens, Greece 5 Department of Physics, Astronomy and Material Science, Missouri State University, USA 6 Ege University, Department of Astronomy and Space Sciences, Turkey 7 Beijing Normal University, Beijing, China 8 National Astronomical Observatories, Chinese Academy of Sciences, Beijing, China 9 Department of Physics and Astronomy, University Delaware, USA 2 3 Abstract We announce the discovery of eight new β Cephei stars and several other interesting variable stars as the preliminary result of the ongoing campaign on two northern open clusters, NGC 6910 and χ Persei. The results The recent progress in asteroseismic studies of some bright β Cephei stars prompted us to study stars in open clusters, where at least two β Cephei members were known. The main advantage of observing stars in clusters is that we can simultaneously obtain photometry for many objects and that the members share many properties (e.g., age and metallicity) which can be used in subsequent modelling. Three open clusters were selected for observations: NGC 3293 in the southern hemisphere, where eleven β Cephei stars were known (Handler et al. 2007), and two clusters in the northern sky, NGC 6910 and χ Persei (NGC 884). In NGC 6910 four β Cephei stars were discovered by Kolaczkowski et al. (2004), while in the central part of χ Persei two variables of this type were known from the study of Krzesiński & Pigulski (1997). The observations of the two northern clusters started in 2005 but the main campaign is occurring during this season (2006). Three telescopes, the 120-cm Mercator in La Palma, the 80-cm vlt in Vienna and the 60-cm in Bialków, were dedicated for the 2005 – 2006 campaign in the summer-autumn time and nine other observatories have contributed data as well. The campaign involves almost 60 observers at twelve sites. In 2005, observations were obtained from five sites (TUG, Bialków, Vienna, Mt. Cuba and La Palma). In total, about 470 hours of observations, 230 for NGC 6910 and 240 for χ Persei, were gathered. In 2006, we already (by September 15, 2006) acquired 700 hours of observations for both clusters, but the number is growing rapidly and we expect to have at least twice as many. From the preliminary analysis of a part of the Bialków 2005 data 192 Campaign on β Cephei stars in NGC 6910 and χ Persei we found new low-amplitude modes for the known β Cephei stars and discovered eight new pulsators of this type. Three of them (WEBDA1 25, 34, and 41) are in NGC 6910 and five [Oo 2085, 2444, 2488, 2566, and 2572 (Oosterhoff 1937)] belong to χ Persei. Oo 2444 was already suspected to be variable by Krzesiński (1998). Moreover, some eclipsing binaries, including possible members, WEBDA 30 in NGC 6910 and Oo 2433 in χ Persei, were found. Our analysis indicates that from the whole data set of the campaign we can expect to detect modes with semi-amplitudes as small as 0.1 – 0.3 mmag. Consequently, from the final analysis we should discover many new modes in the known β Cephei stars and new variables of this type. This makes the prospects for applying asteroseismology to pulsators in both clusters very promising. Acknowledgments. The authors are grateful to the EC for the establishment of the European Helio- and Asteroseismology Network HELAS, which made the participation of some of them at this workshop possible. References Handler G., Tuvikene T., Lorenz D., et al., 2007, these proceedings Kolaczkowski Z., Pigulski A., Kopacki G., Michalska G., 2004, Acta Astron., 54, 33 Krzesiński J. 1998, in Bradley P. A., Guzik J. A., eds, ASP Conf. Ser. Vol. 135, A Half Century of Stellar Pulsation Interpretation. Astron. Soc. Pac., San Francisco, p. 157 Krzesiński J., Pigulski, A., 1997, A&A, 325, 987 Oosterhoff P.T., 1937, Ann. van de Sterrewacht te Leiden, 17, 1 1 See http://obswww.unige.ch/webda/ for the numbering system used in NGC 6910. Comm. in Asteroseismology Vol. 150, 2007 Pulsating variables in NGC 3293, the open cluster with the most β Cephei stars known G. Handler,1 T. Tuvikene,2 D. Lorenz,1 S. Saesen,3 J. L. Provencal,4 R. R. Shobbrook,5 M. Pagani,6 B. Quint,6 M. Desmet,3 C. Sterken,2 A. Kanaan,6 C. Aerts 3,7 1 Institute of Astronomy, University of Vienna, Austria 2 Vrije Universiteit Brussel, Belgium Instituut voor Sterrenkunde, K. U. Leuven, Belgium 4 University of Delaware and Mt. Cuba Observatory, USA 5 Research School of Astronomy and Astrophysics, Australian National University 6 Universidade Federal de Santa Catarina, Brazil 7 Department of Astrophysics, Radboud University Nijmegen, The Netherlands 3 Abstract We carried out an extensive CCD photometry campaign of the open cluster NGC 3293 that contains eleven known β Cephei stars. Preliminary results indicate that none of these is singly periodic. Several objects are among the most multiperiodic of these massive pulsators, giving us strong hope to perform precision asteroseismology in an open cluster for the first time. We also report a peculiar group of variables in NGC 3293 that is located near the lowluminosity end of the β Cephei instability strip. The variability periods of these stars are too long for classical β Cephei pulsation, but too short for binarity or rotational effects, or for SPB-type pulsation. In addition, we discovered about a dozen δ Scuti stars in the field. Introduction Pigulski (2007) most recently reviewed the initial successes of asteroseismology of β Cephei stars, where first constraints on interior stellar structure such as differential rotation, were obtained. As only stars in the centre of the β Cephei instability strip could be investigated so far, the asteroseismically available parameter space in the HR diagram needs to be extended, i.e. stars of lower and higher mass are to be examined. The open cluster NGC 3293 seems ideal for this purpose because it contains eleven known β Cephei stars, many of which belong to the most massive representatives of the group. In addition, other advantages of open cluster asteroseismology (assumption of same metallicity, many targets in the same field) can be exploited. Therefore, we carried out a massive CCD photometry campaign of NGC 3293, involving six sites in the Southern Hemisphere. More than 700 hours of high-quality UBV photometry were obtained from January to May, 2006. First results From a frequency analysis of the 32 nights of U data collected by the first author at the South African Astronomical Observatory (SAAO), we find that all ten β Cephei stars in the centre of the cluster are multiperiodic, with a maximum of five frequencies (V378 Car) detected in these data so far. Several stars, including the eclipsing binary V381 Car, show four pulsation frequencies in these data. V406 Car exhibits an equally spaced frequency triplet. Given the large amount of data we collected, we expect that our final detection level for pulsation modes will be better than 0.5 mmag. Combining this with the expected clean spectral window due 194 Pulsating variables in the open cluster NGC 3293 Figure 1: Light curves of the two mid B-type variables NSV 18451 (upper curve) and NSV 18457 (lower curve) from our campaign. The filled circles are SAAO data, the open circles are CTIO measurements. Complicated variability is evident. Figure 2: Amplitude spectra of the two δ Scuti stars BVC 183 (left panel) and BVC 363 (right panel) in the field of NGC 3293 (B data from CTIO). The identification numbers are from Baume et al. (2003). to our multisite coverage, we are optimistic that our observational results for the β Cephei stars will enable detailed asteroseismic modelling. There is a second group of B-type variables in this cluster. These stars are 1 − 2 magnitudes fainter than the β Cephei stars, their variability occurs on longer time scales (∼8 to 12 hr), and often seems multiperiodic (see Fig. 1 for some examples). The variability time scales of these stars is shorter than those of known SPB stars, according to the on-line compilation of De Cat (2004), in most cases shorter than the critical rotation period of mid B stars (about 10 hours), but longer than the time scale expected for β Cephei-type pulsation (see Stankov & Handler 2005). The variability of these stars may be connected to their rapid rotation. Moving down the HR diagram of NGC 3293 to fainter magnitudes, one would also suspect the presence of δ Scuti stars in this cluster. Indeed, we found over a dozen candidates of this type of variables; some of them are foreground objects, however. Amplitude spectra of two confirmed δ Scuti stars are shown in Fig. 2. The presence of both β Cephei and δ Scuti stars in NGC 3293 may result in a useful test of stellar opacities (Pamyatnykh, private communication). References Baume G., Vazquez R. A., Carraro G., Feinstein A., 2003, A&A, 402, 549 De Cat P., 2004, http://www.ster.kuleuven.ac.be/∼peter/Bstars/ Pigulski A., 2007, these proceedings Stankov A., Handler G., 2005, ApJS, 158, 193 Comm. in Asteroseismology Vol. 150, 2007 A spectroscopic study of the β Cephei star 12 (DD) Lacertae M. Desmet,1 M. Briquet,1 P. De Cat,2 C. Aerts,1,3 G. Handler,4 J. Krzesinski,5 H. Lehmann,6 S. Masuda,7 P. Mathias,8 D. E. Mkrtichian,9 J. H. Telting,10 K. Uytterhoeven,11 S. L. S. Yang12 1 Institute of Astronomy - KULeuven, Celestijnenlaan 200D, 3001 Leuven, Belgium 2 Koninklijke Sterrenwacht van België, Ringlaan 3, 1180 Brussel, Belgium Department of Astrophysics, University of Nijmegen, PO Box 9010, Nijmegen, The Netherlands 4 Institut für Astronomie, Universität Wien, 1180 Wien, Austria 5 Mt. Suhora Observatory, Cracow Pedagogical University, Ul. Podchorazych 2, 30-084 Cracow, Poland 6 Karl-Schwarzschild-Observatorium, Thüringer Landessternwarte, 7778 Tautenburg, Germany 7 Okayama Astrophysical Obs., National Astronomical Obs., Kamogata, Okayama, Japan 8 Observatoire de la Côte d’Azur, Dpt. Gemini, UMR 6203, 06103 Grasse, France 9 Astronomical Observatory of Odessa National University, Marazlievskaya 1v, 65014 Odessa, Ukraine 10 Nordic Optical Telescope, Apartado 474, 38700 Santa Cruz de La Palma 11 Brera Astronomical Observatory, Via E. Bianchi 46, 23807 Merate (LC), Italy 12 Department of Physics and Astronomy, University of Victoria, Victoria, BC V8W 3P6, Canada 3 Abstract We present first results of a spectroscopic multisite campaign for 12 (DD) Lacertae (hereinafter 12 Lac). This star is one of the best observed β Cephei stars. It has a large number of known oscillation frequencies but a lack of identified m-values for its detected modes. In our data set we find seven independent frequencies together with combination frequencies. In addition, two of these modes are identified: one radial mode and one prograde dipole mode. Data The data originate from a spectroscopic multisite campaign for 12 Lac. We also added the data set from Mathias et al. (1994). Almost two thousand high-resolution spectra were gathered with 8 different telescopes, which were evenly spread over the northern continents to reduce aliasing of the frequencies. All spectra include the Siiii triplet centred on 4560 Å and were collected during a time span of 12 years, from September 1990 until July 2004. Frequency analysis The Siiii line profiles around 4560 Å were subjected to a detailed line profile analysis. We computed the first three normalized velocity moments v , v 2 and v 3 (for a definition see Aerts, De Pauw & Waelkens 1992). The summation limits were determined dynamically for each individual line profile to avoid the noisy continuum. We applied Period04 (Lenz & Breger 2005) to search for frequencies in v , which is the centroid velocity. We also performed a two-dimensional frequency search (across the line profile) in order to find additional frequencies. In total we found seven independent frequencies, together with some combination frequencies. We clearly recovered the five main frequencies which had already been discovered spectroscopically in the past (e.g., Mathias et al. 1994). Even without the inclusion of the data set by Mathias et al. (1994), these frequencies are present. We also found two other additional independent frequencies, which have also been detected in photometric data by Handler et al. (2006): 0.35529 ± 0.00001 cd−1 (1.8 ± 0.1 km s−1 in v ) and 7.40637 ± 0.00001 cd−1 (0.6 ± 0.1 km s−1 in v ). The peaks in the periodogram corresponding to these two frequencies exceed an amplitude signal-to-noise ratio of 4 and thus they are significant (e.g., Breger et al. 1999). 196 A spectroscopic study of the β Cephei star 12 (DD) Lacertae Mode identification The main strength of mode identification techniques based on high-resolution spectroscopy is that they are able to derive the azimuthal order m of the pulsation modes. Therefore, we adopt the values for the spherical degree of the pulsation modes provided by unique identifications based on multi-colour photometry (Handler et al. 2006) and use our data to derive m. This technique has already been proven successful in the case of θ Ophiuchi (Briquet et al. 2005). Our conclusions are based on three different spectroscopic identification techniques. As a first result, we showed that one of the frequencies (5.334229 ± 0.000004 cd−1 , 2.8 ± 0.1 km s−1 in v ) must be a radial or a dipole mode by means of the amplitude and phase variation across the line profile (Telting & Schrijvers 1997, Schrijvers et al. 1997). This corroborates the identification of Handler et al. (2006), who concluded that this frequency corresponds to a radial mode. Secondly, to identify as many modes as possible, we are currently applying two additional state-of-the-art methods, namely the moment method (Briquet & Aerts 2003) and the Fourier parameter fit (FPF) method (Zima 2006). In the moment method, the wavenumbers ( ,m) and some other continuous velocity parameters are computed in such a way that the theoretically computed first three moment variations best fit the observed ones. In the FPF method, the mode identification is performed by a χ2 minimization, using the observed zero point, amplitude and phase across the line profile and their theoretically modelled counterparts. Our preliminary results, based on the moment method and the FPF method, show that the frequency with the largest amplitude in the first moment (5.178960 ± 0.000001 cd−1 , 14.3 ± 0.1 km s−1 ) corresponds to a prograde dipole mode (( , m) = (1, 1)). Future work The ultimate goal is to construct stellar models which show oscillations in accordance with all the observed modes of 12 Lac, and thus constrain unknown stellar parameters. To this end, we will calculate an extensive grid of stellar models using the evolutionary code CLES (Code Liégeois d’Evolution Stellaire, written by R. Scuflaire). Acknowledgments. MD, MB and CA are supported by the Research Fund, K.U. Leuven under the Grant GOA/2003/04. MB is Postdoctoral Fellow of the Fund for Scientific Research, Flanders. References Aerts C., De Pauw M., Waelkens C., 1992, A&A, 266, 294 Breger M., Garrido R., Handler G., et al., 1999, A&A, 349, 225 Briquet M., Aerts C., 2003, A&A, 398, 687 Briquet M., Lefever K., Uytterhoeven K., Aerts C., 2005, MNRAS, 362, 619 Handler G., Jerzykiewicz M., Rodrı́guez E., et al., 2006, MNRAS, 365, 327 Lenz P., Breger M., 2005, Comm. Asteroseis., 146, 53 Mathias P., Aerts C., Gillet D., Waelkens C., 1994, A&A, 289, 875 Schrijvers C., Telting J. H., Aerts C., Ruymaekers E., Henrichs H. F., 1997, A&AS, 121, 343 Telting J. H., Schrijvers C., 1997, A&A, 317, 723 Zima W., 2006, A&A, 455, 227 Comm. in Asteroseismology Vol. 150, 2007 Asteroseismology of the β Cephei star KP Per S. Saesen,1 M. Briquet,1 J. Cuypers,2 P. De Cat,2 K. Goossens 1 1 Instituut voor Sterrenkunde, Katholieke Universiteit Leuven, Celestijnenlaan 200D, Leuven, Belgium 2 Koninklijke Sterrenwacht van België, Ringlaan 3, 1180 Brussel, Belgium Abstract We investigated the oscillations of the β Cephei star KP Per (HD 21803, B2IV, V = 6.41) using Geneva photometry. We performed a detailed frequency analysis and a mode identification by means of photometric amplitude ratios. Then we confronted our deduced observational oscillation spectrum with that predicted by theory in order to determine a range for some stellar parameters, such as the mass and radius of KP Per. The observational oscillation spectrum The data were taken with the P7 photometer mounted on the 1.2 m Mercator telescope located in the Roque de los Muchachos Observatory at La Palma (Spain). KP Per was monitored between December 2001 and September 2004. We gathered 338 high-quality photometric measurements in the seven colours of the Geneva system. We carried out a frequency analysis by means of Phase Dispersion Minimization (Stellingwerf 1978), the Lomb-Scargle Fourier method (Lomb 1976, Scargle 1982) and by multifrequency least-squares fitting. We solved alias problems (especially for f3 ) by combining photometric data from the literature with each other and with our data set. We disentangled three frequencies: f1 = 4.95575 cd−1 , f2 = 5.04846 cd−1 and f3 = 4.40346 cd−1 , which were already reported by Jarzebowski et al. (1981). After prewhitening the remaining standard deviation is 10 to 12 mmag in the different Geneva filters, so probably more frequencies are present. For the mode identification we deduced the degree by comparing the theoretical amplitude ratios with the observed ones (Dupret et al. 2003). This comparison is shown in Figs. 1 and 2. f1 and f2 unambiguously correspond to dipole modes ( = 1). The larger error bars hampered a unique identification for f3 : both a dipole and a quadrupole ( = 2) mode are possible. Figure 1: The amplitude ratios scaled to the Geneva U-filter for f1 . The filled circles with error bars denote the observed amplitude ratios and their uncertainties, the black bands indicate the theoretical predictions for these. The outcome for f2 is similar. 198 Asteroseismology of the β Cephei star KP Per Figure 2: Same as Fig. 1 but for f3 . The amplitude ratios are scaled to the Geneva B-filter. The theoretical oscillation spectrum We used a grid of equilibrium models calculated by Clés (Code Liégeois d’Évolution Stellaire, written by R. Scuflaire). The models were characterized by their mass, age, initial hydrogen abundance, initial metallicity and overshoot parameter. Information on the used input physics can be found on http://astrotheor3.astro.ulg.ac.be/files/scuflaire/. The frequencies for these models were computed by a standard adiabatic pulsation code (Boury et al. 1975). We also checked the excitation of the modes by means of the non-adiabatic pulsation code mad (Dupret et al. 2003). The modelling We compared the observational oscillation spectrum with the theoretical one. We wanted to find out which models can explain the observations in order to reveal the radial order n of the frequencies and in order to constrain some physical parameters, such as the mass, radius, age and angular rotational frequency of KP Per. As a first result of seismic modelling, we deduced that f1 and f2 belong to the same triplet. We then required the reproduction and excitation of f1 as zonal dipole mode and of f3 as dipole or quadrupole mode and we found stellar models that qualify and fall into the 3σ-error box of KP Per in the HR diagram. For more details on these models, we refer to Saesen et al. (in preparation). The choice of the zonal mode of the triplet is unimportant: modelling with f1 , f2 or (f1 + f2 )/2 gives consistent results. Acknowledgments. This work was based on observations obtained with the P7 photometer attached to the 1.2 m Mercator telescope (La Palma, Spain). These data will be published with our forthcoming article on KP Per. MB is a Postdoctoral Fellow and SS is an Aspirant Fellow of the Fund for Scientific Research, Flanders (FWO). References Boury A., Gabriel M., Noels A., Scuflaire R., Ledoux P., 1975, A&A, 41, 279 Dupret M.-A., De Ridder J., De Cat P., et al., 2003, A&A, 398, 677 Jarzebowski T., Jerzykiewicz M., Rı́os Herrera M., Rı́os Berumen M., 1981, Rev. Mex. A&A, 5, 61 Lomb N. R., 1976, Ap&SS, 39, 447 Scargle J. D., 1982, ApJ, 263, 835 Stellingwerf R. F., 1978, ApJ, 224, 953 Comm. in Asteroseismology Vol. 150, 2007 Nitrogen excess in slowly-rotating β Cephei stars: deep mixing or diffusion? T. Morel,1,2 K. Butler,3 C. Aerts,1,4 C. Neiner,1,5 M. Briquet 1 1 3 Instituut voor Sterrenkunde, Katholieke Universiteit Leuven, Belgium 2 European Space Agency (ESA) postdoctoral external fellow Universitäts-Sternwarte München, Scheinerstrasse 1, D-81679 München, Germany 4 Department of Astrophysics, University of Nijmegen, The Netherlands 5 GEPI, UMR 8111 du CNRS, Observatoire de Paris-Meudon, France Abstract We present the results of an NLTE abundance study of a small sample of β Cephei stars, which point to the existence of a population of slowly-rotating B-type pulsators exhibiting a significant amount of nitrogen-enriched material at their surface. Although the origin of this nitrogen excess remains unclear, an overabundance preferentially occurring in stars with a detected magnetic field seems to emerge at this stage. Full details can be found in Morel et al. (2006). An abundance study of β Cephei stars Precise knowledge of the fundamental parameters and metallicity of the β Cephei stars is essential for a correct theoretical interpretation of their oscillation spectrum. This has prompted us to launch a detailed NLTE abundance analysis of nine prime targets for seismic modelling (γ Peg, δ Cet, ν Eri, β CMa, ξ 1 CMa, V836 Cen, V2052 Oph, β Cep and 12 Lac) using the line formation codes DETAIL/SURFACE and high-resolution optical spectra covering in most cases the entire oscillation cycle of the stars. A standard, iterative scheme is used to self-consistently derive the atmospheric parameters: Teff is determined from the silicon ionization balance, log g from fitting the collisionally-broadened wings of the Balmer lines and the microturbulence from requiring the abundances yielded by the O II features to be independent of the line strength. All stars under study are slow rotators and curve-of-growth techniques were used to derive the abundances of He, C, N, O, Mg, Al, Si, S and Fe. On the existence of N-rich β Cephei stars The abundances of all the chemical elements (and as a result the metallicity) are indistinguishable from the values previously reported using similar techniques for early B-type dwarfs in the solar neighbourhood (e.g., Daflon & Cunha 2004). The only notable exception is nitrogen, which appears enhanced in four targets by up to 0.6 dex. Evolutionary models including the effects of fast rotation predict that an increase of the N surface abundance arising from the dredge up of core-processed material should be accompanied by a strong boron depletion. Such a trend is clearly observed for the seven stars with boron data and indeed suggests that we are witnessing the results of deep mixing (see Fig. 1). However, the rotational velocities needed to account for the abundance patterns of the N-rich stars (200–300 km s−1 ) appear well in excess of the values found from seismic or line-profile variation studies (< 60 km s−1 ). 200 Nitrogen excess in slowly-rotating β Cephei stars: deep mixing or diffusion? Figure 1: Ratios of the abundance of C, N and O ([N/C] and [N/O]), as a function of the NLTE boron abundances taken from the literature (Mendel et al. 2006; Proffitt & Quigley 2001; Venn et al. 2002). These data are compared with the theoretical predictions of Heger & Langer (2000) for a 12 M star and three different values of the rotational velocity on the ZAMS: 99 (left-hand panels), 206 (middle panels) and 328 km s−1 (right-hand panels). The locus in each panel (dashed line and open squares) defines an age sequence with the time elapsed from the ZAMS increasing leftwards from t=0 to 15 Myrs (t=0 to 12.5 Myrs for ΩRZAMS =99 km s−1 ) in steps of 2.5 Myrs (see upper right panel). Conclusions Our abundance study of several well-studied β Cephei stars reveals in some targets an unexpected nitrogen excess systematically accompanied by a marked boron depletion. In spite of being the typical signature of rotationally-induced mixing, the existence of core-processed material brought up by this mechanism is difficult to envision for such largely unevolved, slowly-rotating objects. Alternatively, diffusion effects might be invoked (Bourge et al., these proceedings). An important clue to the origin of this phenomenon may lie in the fact that several N-rich stars have a detected magnetic field of up to a few hundreds Gauss (e.g., Hubrig et al. 2006). Indeed, preliminary results also suggest similar abundance patterns in some magnetic, slowly pulsating B stars (e.g., ζ Cas; Briquet & Morel, these proceedings). Acknowledgments. TM acknowledges financial support from the European Space Agency through a Postdoctoral Research Fellow grant and from the Research Council of Leuven University through grant GOA/2003/04. MB is Postdoctoral Fellow of the Fund for Scientific Research, Flanders. References Daflon S., Cunha K., 2004, ApJ, 617, 1115 Heger A., Langer N., 2000, ApJ, 544, 1016 Hubrig S., Briquet M., Schöller M., et al., 2006, MNRAS, 369, L61 Mendel J. T., Venn K. A., Proffitt C. R., Brooks A. M., Lambert D. L., 2006, ApJ, 640, 1039 Morel T., Butler K., Aerts C., Neiner C., Briquet M., 2006, A&A, 457, 651 Proffitt C. R., Quigley M. F., 2001, ApJ, 548, 429 Venn K. A., Brooks A. M., Lambert D. L., et al., 2002, ApJ, 565, 571 Comm. in Asteroseismology Vol. 150, 2007 An abundance study of the B-type targets for the asteroseismology programme of the CoRoT mission T. Morel,1,2 C. Aerts 1,3 1 3 Katholieke Universiteit Leuven, Instituut voor Sterrenkunde, B-3001 Leuven, Belgium 2 European Space Agency (ESA) postdoctoral external fellow Department of Astrophysics, University of Nijmegen, 6500 GL Nijmegen, The Netherlands Abstract We present the very first results of a project aimed at deriving the detailed chemical composition of the B-type stars in the eyes of CoRoT, focusing here on the two primary targets HD 170580 and HD 180642. Setting the stage for the CoRoT observations of B-type stars The French-European satellite CoRoT will soon monitor with extremely high photometric precision and time sampling a vast number of B-type stars during the course of its asteroseismology programme. Accurate estimates of the fundamental parameters and metallicity of these targets is essential to constrain the theoretical models and to allow for a proper interpretation of the space data. We are engaged in a project whose objectives are a homogeneous determination of both the atmospheric parameters (Lefever et al., in prep.) and the chemical composition (Morel et al., in prep.) of all the B stars in the eyes of CoRoT with high-resolution optical spectra secured as part of the ground-based preparatory campaign (GAUDI database; Solano et al. 2005). Most key chemical elements significantly contributing to the metallicity are considered: C, N, O, Mg, Al, Si, S and Fe. Only Ne is missing at this stage, but work is currently underway to determine the abundance of this important element in the context of asteroseismological studies. First abundance results for two primary B-type targets Here we report on our analysis of two primary targets which will be observed during the first long runs of the mission: HD 170580 (B2 V) and HD 180642 (B1.5 II–III). The latter is a largeamplitude pulsator with three frequencies already detected from ground-based photometric data (Aerts et al., in prep.). The FEROS spectrum of HD 170580 is extracted from the GAUDI database, while the analysis of HD 180642 is based on 11 FEROS spectra taken in May 2006 with the ESO/MPI 2.2m Telescope at la Silla. See Morel et al. (2006) for details on the methodology used to derive the NLTE chemical abundances. Table 1 presents the results which can be compared with literature data for early B-type dwarfs in the solar vicinity (Daflon & Cunha 2004). Two points are worth mentioning: (a) there is some indication that HD 170580 is He weak; (b) there is also a hint that HD 180642 is N-rich, as observed in other slowly-rotating β Cephei stars (Morel et al. 2006), but the boron data which could be used to confirm the occurrence of deep mixing are unfortunately not available for this star. Considering the large number of B stars in the GAUDI database and the fact that most of them are fast rotators, semi-automated spectral synthesis techniques must be developed. On the other hand, the majority of these objects are much cooler than the stars already analysed (see Fig. 1), which will require the definition of new line lists, computation of a grid of NLTE synthetic spectra down to Teff ∼10 kK, etc. Finally, model atmosphere codes taking into account the stellar wind shall be used for the (super)giants suffering substantial mass loss. 202 An abundance study of the B-type targets for the asteroseismology programme of the CoRoT mission Table 1: Atmospheric parameters (ξ is the microturbulence velocity and vT is the total amount of rotational and pulsational broadening), mean NLTE abundances (on the scale in which log [H]=12) and metallicity, Z , of HD 170580 and HD 180642. The number of used lines is given in brackets. The last column gives the typical abundance values found for early B dwarfs in the solar neighbourhood (Daflon & Cunha 2004). We define [N/C] and [N/O] as log[(N)/(C)] and log[(N)/(O)], respectively. Teff (K) log g ([cgs]) ξ (km s−1 ) vT (km s−1 ) He/H log (C) log (N) log (O) log (Mg) log (Al) log (Si) log (S) log (Fe) Z [N/C] [N/O] a HD 170580 20 000±1000 4.10±0.15 1+5 −1 10 0.048±0.021 (10) 8.13±0.16 (4) 7.87±0.27 (14) 8.42±0.39 (10) 7.45±0.43 (1) 6.23±0.24 (3) 7.22±0.36 (7) 7.28±0.21 (12) 7.37±0.25 (9) 0.0095±0.0030 –0.26±0.32 –0.55±0.48 HD 180642 24 500±1000 3.45±0.15 12±3 44 0.088±0.018 (4) 8.21±0.10 (9) 8.00±0.19 (21) 8.53±0.14 (25) 7.34±0.20 (1) 6.22±0.15 (3) 7.19±0.19 (7) 7.10±0.34 (4) 7.34±0.21 (21) 0.0106±0.0016 –0.21±0.22 –0.53±0.24 B dwarfs ∼0.085 ∼8.2 ∼7.6 ∼8.5 ∼7.4 ∼6.1 ∼7.2 ∼7.2 ∼7.3a ∼0.0099 ∼–0.6 ∼–0.9 Taken from Morel et al. (2006). Figure 1: Breakdown by spectral type of the 190 B-type stars with spectra available in the GAUDI database at the time of writing (excluding the known Be stars). Acknowledgments. Many thanks to Katrien Uytterhoeven for providing us with the FEROS spectra of HD 180642. T. M. acknowledges financial support from the European Space Agency through a Postdoctoral Research Fellow grant and from the Research Council of Leuven University through grant GOA/2003/04. References Daflon S., Cunha K., 2004, ApJ, 617, 1115 Morel T., Butler K., Aerts C., Neiner C., Briquet M., 2006, A&A, 457, 651 Solano E., Catala C., Garrido R., et al., 2005, AJ, 129, 547 Comm. in Asteroseismology Vol. 150, 2007 Effects of diffusion in β Cephei stars P.-O. Bourge, S. Théado, A. Thoul Institut d’Astrophysique, Allée du 6 Août, 17, B-4000 Liège, Belgium Abstract We investigate the effects of the radiatively-driven diffusion of Fe, C, N and O in β Cephei stellar models. Computations As suggested by Cox et al. (1992) and by Pamyatnykh et al. (2004), radiatively-driven diffusion and consequently the accumulation of iron affect the excitation of the pulsation modes of β Cephei stars, increasing the number of excited modes. We have shown in a previous study that the accumulation of iron occurs near the opacity bump (Bourge & Alecian 2006, Bourge et al. 2006) and that it excites several higher order radial pulsation modes. We present here the results of our latest fully evolutionary calculations. We have computed a 10 M stellar model with the initial mass fractions X0 = 0.7392, Z0 = 0.0122. We do not introduce overshooting but the helium convection zone is extended to the surface. The stellar model is evolved using cles v.18.11 (Scuflaire 2005) modified to include radiative forces and mass loss. The diffusion velocities are computed by solving Burgers’ equations (Burgers 1969). The radiative forces are computed using adapted routines and tables from opcd v.2.1 (Seaton 2005). The mass loss is computed according to the theoretical formula of Vink et al. (2000, 2001), scaled down by 1 dex (see Puls et al. 2006). During the main sequence phase of evolution, the local radiative accelerations on Fe are always higher than the local gravity (except in the central regions, where diffusion is insignificant). We can thus expect an accumulation of iron where the gradient of the radiative accelerations is positive (i.e. where log T ≈ 6.2, 5.2 and near the surface). Iron stratification results from the competition between microscopic diffusion (dominated by the radiative forces), convection and mass loss. During the main sequence, the mass loss increases by more than one order of magnitude (≈ 5 × 10−11 to 10−9 M /yr). On the first half of the main sequence, the radiative forces dominate and the accumulation of iron occurs in the iron convection zone (enhancement by a factor of about 2) and at the surface. When the central hydrogen mass fraction reaches 0.3, the mass loss starts to dominate and the iron overabundances decrease, to finally disappear at the TAMS. Our results show that for a 10 M stellar model the introduction of microscopic diffusion including radiative forces and mass loss leads to a significant accumulation of iron in the metal opacity bump. As shown by Pamyatnykh et al. (2004), Bourge & Alecian 2006, Bourge et al. (2006) and Miglio et al. (2007), this leads to an increase of the range of excited frequencies and of the width of the instability strip. This could also provide an explanation for the existence of low metallicity β Cephei stars, as in the SMC and LMC (Pigulski et al. 2002, Kolaczkowski et al. 2006). Similarly we also followed the evolution of the abundances of C, N, O. Near the surface, the radiative force on N is larger than the ones on C and O, and larger than the local gravity. This leads to a slight enrichment in nitrogen at the surface. Rotational mixing is usually used as an explanation for the N-enrichment observed in early B-type stars. Our results show that the radiative forces could also contribute to this N-enrichment, at least in the case of some β Cephei stars (see Morel et al. 2006, 2007, Morel & Aerts 2007), most of which are known to be slow rotators. Complete evolutionary calculations are still in progress. 204 Effects of diffusion in β Cephei stars Acknowledgments. POB is supported by the Belgian IAP grant P5/36; ST by ESAPRODEX ’CoRoT Preparation to exploitation I’ grant C90197. AT is Chercheur Qualifié au Fond National de la Recherche Scientifique Belgium. References Bourge P.-O., Alecian G., 2006, in Sterken C., Aerts C., eds, ASP Conf. Ser. Vol. 349, Astrophysics of Variable Stars. Astron. Soc. Pac., San Francisco, p. 201 Bourge P.-O., Alecian G., Thoul A., Scuflaire R., Théado S., 2006, Comm. Asteroseis., 147, 105 Burgers J. M., 1969, Flow Equations for Composite Gases, New York: Academic Press Cox A. N., Morgan S. M., Rogers F. J., Iglesias C. A., 1992, ApJ, 393, 272 Kolaczkowski Z., Pigulski A., Soszyński, I., et al., 2006, Mem. Soc. Astron. Ital., 77, 336 Miglio A., Bourge P.-O., Montalbán J., Dupret M.-A., 2007, these procedings Morel T., Aerts C., 2007, these proceedings Morel T., Butler K., Aerts C., Neiner C., Briquet M., 2006, A&A, 457, 651 Morel T., Butler K., Aerts C., Neiner C., Briquet M., 2007, these proceedings Pamyatnykh A. A., Handler G., Dziembowski W. A., 2004, MNRAS, 350, 1022 Pigulski A., Kolaczkowski Z., 2002, A&A, 388, 88 Puls J., Markova N., Scuderi S., 2007, in de Koter A., Smith L., Waters R., eds, ASP Conf. Ser., Mass loss from stars and the evolution of stellar clusters. Astron. Soc. Pac., San Francisco, in press Scuflaire R., 2005, cles: see http://www.astro.ulg.ac.be/∼scuflair Seaton M. J., 2005, MNRAS, 362, L1 Vink J. S., de Koter A., Lamers H. J. G. L. M., 2000, A&A, 362, 295 Vink J. S., de Koter A., Lamers H. J. G. L. M., 2001, A&A, 369, 574 Clockwise from the left: Michael Bazot, Alfred Tillich, Mélanie Godart, Stéphane Charpinet, Christoffer Karoff, Pierre-Olivier Bourge and Marc-Antoine Dupret, with Suzanna Randall and Don Kurtz discussing in the background. Comm. in Asteroseismology Vol. 150, 2007 Amplitude Saturation in β Cephei Models - Preliminary Results R. Smolec, P. Moskalik Copernicus Astronomical Centre, Bartycka 18, 00-716 Warsaw, Poland We present preliminary results concerning amplitude saturation in β Cephei models. Using a nonlinear approach we have investigated the amplitude limitation mechanism in β Cephei stars. In our approach radial modes have been treated as representative for all acoustic oscillations. We have studied pulsation properties of several models (7–20 M , Z = 0.02, 0.015) using radiative Lagrangian hydrocodes (essentially those of Stellingwerf 1974, 1975). Nonlinear limit cycles (monoperiodic full-amplitude oscillations) have been calculated through Stellingwerf’s (1974) relaxation technique, which also provides information about limit cycle stability. In our main survey (Z = 0.02) only the fundamental and the first overtone modes are linearly excited. Nonlinear growth rates have been used to determine the modal selection (see e.g., Stellingwerf 1975). We found that fundamental mode pulsation is dominant. First overtone pulsation is restricted to intermediate masses and to the vicinity of the blue edge. The first overtone and the fundamental mode pulsation domains are separated by either-or or narrow double-mode domains. Predicted single-mode saturation amplitudes have been compared to amplitudes observed for monoperiodic β Cephei variables (Fig. 1, left). Predicted amplitudes are significantly higher. The amplitudes may be lowered by decreasing the metal abundance of the models, Z . We have found that for Z = 0.015, the decrease of model amplitudes is not sufficient. At the same time the instability strip shrinks and leaves a lot of stars beyond the blue edge. By lowering Z we are not able to match simultaneously the observed amplitudes and the instability strip. The predicted amplitudes may be easily lowered to the observed level if one assumes collective saturation of the pulsation instability, by n similar acoustic modes.√In this hypothetical multimode solution, amplitudes of individual modes are a factor of ∼ n lower than in the single-mode solution. Using linear code of Dziembowski (1977) we have determined the number of linearly unstable acoustic modes for models of different masses, located in the centre of the main sequence band. This number doesn’t vary much along an evolutionary track and thus, was assumed to be representative for all models of a given mass. The number of unstable modes is much higher than the number of detected modes in the multiperiodic β Cephei variables. Nonlinear simulations (Nowakowski 2005) also show that not all unstable modes take part in the saturation process. Thus, we have arbitrarily assumed that only one third of the linearly unstable modes take part in the saturation. Amplitudes rescaled under the assumption of collective saturation are presented in Fig. 1 (right). Using only part of the linearly unstable acoustic modes, we have lowered the theoretical amplitudes to the observed level. Thus, we argue that collective instability saturation is sufficient to explain the observed amplitudes of the β Cephei pulsators. A possible difficulty of this model is that the predicted pulsation-induced broadening of spectral lines might be higher than observed. We discuss this problem in Smolec & Moskalik (2007). In several of our radiative models we have found numerically robust, double-mode behaviour, with radial fundamental and first overtone modes simultaneously excited. This form of pulsation is encountered only in intermediate mass models (10 – 11 M ). Depending on the specific model, the origin of double mode pulsation can be traced to one of two different mechanisms: either to the non-resonant coupling of the two excited modes, or to the 2ω1 ω0 + ω2 parametric resonance. 206 Amplitude Saturation in β Cephei Models - Preliminary Results Figure 1: Predicted single-mode saturation amplitudes (left) and amplitudes assuming collective saturation by several acoustic modes (right). For comparison, amplitudes of monoperiodic (open circles) and multiperiodic (full circles) β Cephei stars are plotted. Full results of this analysis (including a discussion of non-uniform filling of the theoretical instability strip by β Cephei variables and detailed study of the double-mode models) are presented by Smolec & Moskalik (2007). Acknowledgments. The authors are grateful to the EC for the establishment of the European Helio- and Asteroseismology Network HELAS, which made their participation at this workshop possible. This work has been supported by the Polish MNiI Grant No. 1 P03D 011 30. References Dziembowski W. A., 1977, Acta Astron., 27, 95 Nowakowski R., 2005, PhD Thesis, Copernicus Astronomical Center, Warsaw Smolec R., Moskalik P., 2007, MNRAS, in press (astro-ph/0702406) Stellingwerf R. F., 1974, ApJ, 192, 139 Stellingwerf R. F., 1975, ApJ, 195, 441 Comm. in Asteroseismology Vol. 150, 2007 The Beta Cephei instability domain for the new solar composition and with new OP opacities A. A. Pamyatnykh,1,2,3 W. Ziomek 4 1 2 Copernicus Astronomical Center, Bartycka 18, 00-716 Warsaw, Poland Institute of Astronomy, Pyatnitskaya Str. 48, 109017 Moscow, Russia 3 Institute of Astronomy, University of Vienna, 1180 Vienna, Austria 4 Astronomical Institute, Kopernika 11, 51-622 Wroclaw, Poland The recent revision of the solar chemical composition (A04: Asplund et al. 2005) leads to a decrease of about 40% in the C, N, O, Ne abundances and to a ∼ 20 % decrease of Fe and some other metal abundances in comparison with older abundances (GN93: Grevesse & Noels 1993), as shown in Fig. 1. H He O C N Ne Mg Si Fe S Na Al Ar Ca Ni Cr H He C N O NeNaMgAl Si S Ar Ca Cr Mn Mn Fe Ni Figure 1: The new solar abundances in comparison with the older ones. We tested the effects of these modifications of the heavy element abundances on the instability of β Cephei models. For opacities, the newest data from the Opacity Project (Seaton 2005) were used. Fig. 2 shows that the β Cephei instability domain in the HRD, when computed with new data for Z = 0.012 (revised solar value), is very similar to the instability domain computed with the OPAL opacities (Iglesias & Rogers 1996) for older solar metallicities and Z = 0.02. For the older data and assuming Z = 0.012, we obtain only weak β Cep instability (Pamyatnykh 1999). Two effects are responsible for stronger instability when using the new data: (i) The metal opacity bump in the OP case is located slightly deeper in the star than that in the OPAL case, which results in more effective driving; (ii) at a fixed Z value, the new Fe-group abundances are higher than the older ones because the Z value is determined mainly by the abundances of C, N, O, and Ne (see Fig. 1). 208 The Beta Cephei instability domain for the new solar composition and with new OP opacities Figure 2: The new β Cephei instability domain in the main-sequence band (OP opacity, A04 mixture, Z = 0.012) compared with the older one (OPAL GN93, Z = 0.02, see Pamyatnykh 1999). 29 bright variables from Stankov & Handler (2005) with mV < 6.0 and well-measured Hipparcos parallaxes are plotted. Acknowledgments. AAP acknowledges partial financial support from the HELAS project and from the Polish MNiI grant No. 1 P03D 021 28. References Asplund M., Grevesse N., Sauval A. J., 2005, in Barnes III T. G., Bash F. N., eds, ASP Conf. Ser. Vol. 336, The Solar Chemical Composition. Astron. Soc. Pac., San Francisco, p. 25 Grevesse N., Noels A., 1993, in Pratzo N., Vangioni-Flam E., Casse M., eds, Origin and Evolution of the Elements. Cambridge Univ. Press, Cambridge, p. 15 Iglesias C. A., Rogers F. J., 1996, ApJ, 464, 943 Pamyatnykh A. A., 1999, Acta Astron., 49, 119 Seaton M. J., 2005, MNRAS, 362, L1 Stankov A., Handler G., 2005, ApJS, 158, 193 Comm. in Asteroseismology Vol. 150, 2007 Instability strips of main sequence B stars: a parametric study of iron enhancement A. Miglio,1 P.-O. Bourge,1 J. Montalbán,1 M.-A. Dupret 2 1 Institut d’Astrophysique, Allée du 6 Août, 17, B-4000 Liège, Belgium 2 LESIA, Observatoire de Paris, F-92195 Meudon, France Abstract The discovery of β Cephei stars in low metallicity environments, as well as the difficulty to theoretically explain the excitation of the pulsation modes observed in some β Cephei and SPB stars, suggest that the iron opacity “bump” provided by standard models could be underestimated. We investigate, by means of a parametric study, the effect of a local iron enhancement on the location of the β Cephei and SPB instability strips. The excitation of the pulsations of the β Cephei and SPB stars is challenging current theoretical models, since the latter cannot satisfactorily reproduce the observations of β Cep stars in low metallicity environments (e.g. Kolaczkowski et al. 2006), the excitation of the observed pulsation modes in some β Cep stars (Pamyatnykh et al. 2004, Ausseloos et al. 2004, Handler et al. 2005), the excitation of hybrid SPB and β Cep pulsators, and the observations of SPB-type pulsations in “cool” B-type stars (Antonello et al. 2006, Bruntt et al. 2006). As discussed by Miglio et al. (2007), the current uncertainties on opacity calculations, and on the assumed metal mixture, have a significant impact on the excitation of modes in both β Cep and SPB stars. Nonetheless, these uncertainties may not be sufficient to explain the whole discrepancy between theoretical predictions and observations. Figure 1: Instability strips represented in a log Teff -log P diagram. In each panel, the two regions of unstable modes represent β Cep- and SPB-type pulsations. 210 Instability strips of main sequence B stars: a parametric study of iron enhancement We therefore investigate another possible solution to the problem: we follow the suggestion by Cox et al. (1992) and Pamyatnykh et al. (2004) and carry out a parametric study of the effect of local iron enhancement on the stability of SPB and β Cep stars. We base our parametric description on Fe accumulation profiles as found in models of A–F stars with diffusion and radiative accelerations (Richard et al. 2001; see also Bourge et al. 2006a,b for B stars). At each time step in the evolution we increase the Fe mass fraction in the chemical mixture. The increase is described by a Gaussian function centred at log T ∼ 5.2, where this value is justified by calculations of radiative accelerations using the OP web server (see also Bourge et al. 2007). We calculate the opacity by interpolating between several OPAL tables computed with different mass fractions of Fe in the chemical mixture. Although the results depend on the Fe accumulation rate, we find (see Fig. 1) that the SPB/β Cep instability strips becomes wider (in particular the SPB-type instability occurs also at lower Teff ), higher frequency modes are excited in β Cep models and a larger number of β Cep models is found to be excited for Z =0.01. Acknowledgments. A. M. and J. M. are supported by the PRODEX 8 COROT grant C90199, P.-O. B. by the Belgian IAP grant P5/36 and M.-A. D. by the CNRS. A. M. and J. M. also acknowledge E. Antonello and L. Mantegazza for their valuable collaboration and suggestions. References Antonello E., Mantegazza L., Rainer M., Miglio A., 2006, A&A, 445, L15 Ausseloos M., Scuflaire R., Thoul A., Aerts C., 2004, MNRAS, 355, 352 Bourge P.-O., Alecian G., 2006a, in Sterken C., Aerts C., eds, ASP Conf. Ser. Vol. 349, Astrophysics of Variable Stars. Astron. Soc. Pac., San Francisco, p. 201 Bourge P.-O., Alecian G., Thoul A., Scuflaire R., Théado S., 2006b, Comm. Asteroseis., 147, 105 Bourge P.-O., Théado S., Thoul A., 2007, these proceedings Bruntt H., Southworth J., Torres G., et al., 2006, A&A, 456, 651 Cox A. N., Morgan S. M., Rogers F. J., Iglesias C. A., 1992, ApJ, 393, 272 Handler G., Jerzykiewicz M., Rodrı́guez E., et al., 2006, MNRAS, 365, 327 Kolaczkowski Z., Pigulski A., Soszyński I., et al., 2006, Mem. Soc. Astron. Ital., 77, 336 Miglio A., Montalbán J., Dupret M.-A., 2007, MNRAS, 375, L21 Pamyatnykh A. A., Handler G., Dziembowski W. A., 2004, MNRAS, 350, 1022 Richard O., Michaud G., Richer J., 2001, ApJ, 558, 377 Comm. in Asteroseismology Vol. 150, 2007 Asteroseismology of the β Cephei star ν Eridani using differentially-rotating models J. C. Suárez,1 R. Garrido,1 M. J. Goupil 2 1 Instituto de Astrofı́sica de Andalucı́a, CP-3004, Granada, Spain 2 Observatoire de Paris-Meudon, LESIA, UMR, France Abstract This work is focused on asteroseismic modelling of B stars using differential rotation in both the equilibrium models and the oscillation computations. We discuss the possibility of inferring information on the internal structure from the analysis of asymmetries of rotationally split modes. In particular we present some preliminary results on the well-known β Cephei star ν Eridani for which at least three triplets have been identified as g1 , p1 and p2 ( = 1), respectively. Introduction A seismic analysis of the oscillation spectrum of ν Eridani was performed by Pamyatnykh et al. (2004). In that work only three frequencies were fitted and they fail to predict the mode excitation of the broad observed frequency range due to the presence of the ( = 1, p2 ) mode. Nevertheless, Pamyatnykh et al. (2004) also inferred some properties of the internal rotation rate using the values of rotational splittings of two dipoles ( = 1) identified as g1 and p1 . In particular, their results suggest that the mean rotation rate in the μ-gradient zone is about three times higher than in the envelope for their two standard models fitting the three aforementioned frequencies. Motivated by these results, we aim at performing a complete modelling of ν Eridani taking into account the effect of rotation up to the second order and, using a radial differential rotation (shellular rotation) described by Suárez, Goupil & Morel (2006). In addition, the list of observed frequencies and mode identifications is taken from the updated work of Jerzykiewicz et al. (2005). The seismic model & analysis of multiplet asymmetries Models were computed assuming two types of rotation profiles: uniform rotation (the total angular momentum is globally conserved during evolution), and differential rotation (with the hypothesis of local conservation of the angular momentum). The models were assumed to rotate with v ∼ 7 km s−1 at the surface. Adiabatic oscillation spectra were computed using the adiabatic code Filou (Tranh Min & Léon, 1999; Suárez, 2002), which corrects the eigenfrequencies up to second-order effects of rotation (including near degeneracy) and takes a radial variation of the rotation profile (shellular rotation, Suárez et al. 2006) into account. The search for models that fit the observed frequencies (∼ 5% of error in frequency match) yields a mass of M = 7.13 M , a metallicity of Z = 0.019, and an overshoot parameter of dov = 0.28. In order to place the model in the photometric error box and to obtain instability of the observed modes, we use a metallicity of Z = 0.019 in which we consider a non-standard central hydrogen abundance of X = 0.50 (see Ausseloos et al. 2004). The oscillation frequencies and the identified (g1 , = 1), and (p1 , = 1) triplets were fitted by such models with an age around 16.2 Myr, and considering rotational velocities (at the surface) ranging from 5 to 7 km s−1 . In addition to this, a supplementary (p2 , = 1) triplet 212 Asteroseismology of the β Cephei star ν Eridani using differentially-rotating models is also identified. The differentially-rotating models are found to show a mean rotation rate in the core about 2.5 – 3 times faster than on the surface, supporting the predictions given by Pamyatnykh et al. (2004). Analysis of asymmetries of the rotational split = 1 triplets, reveals significant differences when assuming uniform or differential rotation. As expected, the variations of the rotation profile near the core and the μ gradient zone, affects principally the g1 triplets. Indeed, the comparison with the observed asymmetries indicates that the differentially rotating model would reproduce the asymmetries for the three triplets better than the uniformly rotating one. However, for such a low rotation velocity, the observed asymmetries are very small and then, model discrimination becomes difficult. Thus, in order to better examine the behaviour of these asymmetries, further work for fast rotators is then required (Suárez et al., in preparation). References Ausseloos M., Scuflaire R., Thoul A., Aerts C., 2004, MNRAS, 355, 352 Jerzykiewicz M., Handler G., Shobbrook R. R., et al., 2005, MNRAS, 360, 619 Pamyatnykh A. A., Handler G., Dziembowski W. A., 2004, MNRAS, 350, 1022 Suárez J. C., 2002, PhD Thesis, Universitée Paris 7, France Suárez J. C., Goupil M.-J., Morel P., 2006, A&A, 449, 673 Trahn Minh F., Léon L., 1995, Phys. Process Astrophys., 219 Some people are busy working even between the sessions: Hans Kjeldsen, Peter Reegen, Karen Pollard and Laszlo Kiss with their laptops. Comm. in Asteroseismology Vol. 150, 2007 Interpretation of the Be star HD 163868 oscillation spectrum based on the MOST observations W. A. Dziembowski,1,2 J. Daszyńska-Daszkiewicz,1,3 A. A. Pamyatnykh 1,4 2 1 Copernicus Astronomical Center, Bartycka 18, 00-716 Warsaw, Poland Warsaw University Observatory, Al. Ujazdowskie 4, 00-478 Warsaw, Poland 3 Astronomical Institute, Kopernika 11, 51-622 Wroclaw, Poland 4 Institute of Astronomy, Pyatnitskaya Str. 48, 109017 Moscow, Russia On the basis of MOST photometry, Walker et al. (2005) detected a large number of significant peaks in the oscillation spectrum of HD 163868 and provided an interpretation for some of them in terms of high-order g modes. However, after conducting a stability survey for low degree modes in a model that seems appropriate for the star they were unable to explain the low frequency part of the spectrum, where the amplitudes are the highest. In the observed frequency spectrum, shown in the upper panel of Fig. 1, we see three groups of modes. According to Walker et al. (2005), the highest frequency group may be explained by excitation of prograde = 2, m = 2 g modes and the group at intermediate frequencies by prograde = 1 g modes. Because individual modes are no longer described by single spherical harmonics, the values are used only for mode identification. These authors found a large number of unstable modes in these two frequency ranges. They also found an instability of retrograde m = −1 r modes in the frequency range which extends down to 0.43 c/d, thus encompassing part of the lowest frequency group. In their study they rely on the truncated Legendre expansion. We made our stability survey for nearly identical model but relying on the traditional approximation. Our results, presented in the lower panel of Fig. 1, differ significantly from those of Walker et al. (2005). We do not find any unstable prograde = 1 g mode, instead we find many other unstable modes in the whole frequency range. Taking into account visibility conditions, which depend on mode geometry and the aspect angle, i , we found that occurrence of peaks in the three separate frequency ranges may be understood if i ≈ 90o . Then our interpretation of the highest frequency group is = 2, m = 2 (the same as proposed by Walker et al.), of the intermediate frequency group is = 2, m = 0 and m = −2, and of the lowest frequency group is = 1, m = −1. The best fit is obtained assuming a rotation velocity of about 270 km/s, that is somewhat lower than used in Fig. 1. If i ≈ 55o , as Walker et al. (2005) adopted, then there would be no explanation for the gap around the frequency of 1 c/d, where we would expect to see the = 1, m = 0 modes, which are unstable and have good visibility at this aspect. A detailed description of our calculations has been published elsewhere (Dziembowski et al. 2007). Acknowledgments. The authors acknowledge partial financial support from the HELAS project and from the Polish MNiI grant No. 1 P03D 021 28. References Dziembowski W. A., Daszyńska-Daszkiewicz J., Pamyatnykh A. A., 2007, MNRAS, 374, 248 Walker G. A. H., Kuschnig R., Matthews J. M., et al., 2005, ApJ, 635, L77 214 Interpretation of the Be star HD 163868 oscillation spectrum based on the MOST observations 12000 A [ppm] 10000 8000 6000 4000 2000 0 0.3 l = 2 m= 0 l = 2 m= +1 l = 2 m= +2 l = 2 m= -1 l = 2 m= -2 l = 1 m= 0 l = 1 m= +1 l = 1 m= -1 Vrot=300 km/s r, m= -1 r, m= -2 0.2 d 0.1 0.0 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 iobs [c/d] Figure 1: Top: Frequency spectrum of HD 163868. Bottom: Normalized growth rates, η (η > 0 means instability), for low-degree modes in the model of HD 163868. Comm. in Asteroseismology Vol. 150, 2007 g-modes in the late-type Be star β CMi detected by the MOST satellite1 H. Saio,2 C. Cameron,3 R. Kuschnig,3 G. A. H. Walker,4 J. M. Matthews,3 J. F. Rowe,3 U. Lee,2 D. Huber,5 W. W. Weiss,5 D. B. Guenther,6 A. F. J. Moffat,7 S. M. Rucinski,8 D. Sasselov 9 2 Astronomical Institute, Tohoku University, Sendai, Japan Dept. of Physics and Astronomy, University of British Columbia, Canada 4 1234 Hewlett Place, Victoria, BC V8S 4P7, Canada 5 Institut für Astronomie, Universität Wien, Austria 6 Dept. of Astronomy and Physics, St. Mary’s University Halifax, Canada 7 Dépt. de physique, Univ. de Montréal, and Obs. du Mont Mégantic, Canada 8 Dept. of Astronomy & Astrophysics, David Dunlap Obs., Univ. of Toronto, Canada 9 Harvard-Smithsonian Center for Astrophysics, Cambridge, MA 02138, USA 3 Abstract The Microvariability and Oscillations of Stars (MOST) satellite has detected low-amplitude light variations (Δm ∼1 mmag) in the late-type Be star β CMi (B8Ve). The photometric variations have periods of ∼ 0.3 days. This is consistent with high-order, prograde (m = −1) g modes of a nearly critically rotating 3.5M model. Results β CMi is one of the latest spectral type Be stars located near the cool boundary of the SPB instability region in the HR diagram (Pamyatnykh 1999). The MOST detection of multiple pulsations in β CMi is the first detection of photometric variations of this star and, more importantly, is the first detection of nonradial g modes in a Be star later than B6, leading to the possibility that pulsations are excited in all Be stars. There are two significant frequency detections of 3.257 and 3.282 c/d and some marginal evidence for other frequencies (see Saio et al. 2007 for further details). The top panel of Fig. 1 shows theoretical frequencies versus growth rates for the pulsations excited in a rapidly rotating 3.5 M model. The model is from Saio et al. (2007); a slightly faster rotation rate is adopted to obtain better agreement with observations. In this model only prograde high-order g modes of m = −1 are excited by the κ-mechanism at the Fe-bump of opacity at T ∼ 2 × 105 K. Since the frequencies of high-order g modes in the co-rotating frame are much smaller than the rotation frequency, the frequencies in the inertial frame group in a frequency range slightly higher than the rotation frequency. This phenomenon is typical of SPBe-type pulsations first observed in HD 163868 by Walker et al. (2005). In that case, an additional group of frequencies (for m = −2) appears around twice the rotation frequency. Figure 1 shows that the closely spaced frequencies observed in β CMi are consistent with high overtone g modes in a rapidly rotating star and that the identified frequencies lie in roughly the same frequency region as the theoretically excited g modes. 1 Based on data from the MOST satellite, a Canadian Space Agency mission, jointly operated by Dynacon Inc., the University of Toronto Institute of Aerospace Studies and the University of British Columbia with the assistance of the University of Vienna. 216 g-modes in the late-type Be star β CMi detected by MOST Figure 1: Observed frequencies versus amplitudes (bottom panel) and theoretical frequencies versus growthrates for excited prograde dipole g modes of a rapidly rotating model (top panel). References Pamyatnykh A. A., 1999, Acta Astron., 49, 119 Saio H., Cameron C., Kuschnig R, et al., 2007, ApJ, 654, 544 Walker G. A. H., Kuschnig R., Matthews J. M., et al., 2005, ApJL, 635, L77 Comm. in Asteroseismology Vol. 150, 2007 Discussion on β Cephei and SPB stars led by Conny Aerts1,2 2 1 Institute of Astronomy - KULeuven, Celestijnenlaan 200D, 3001 Leuven, Belgium Department of Astrophysics, University of Nijmegen, PO Box 9010, Nijmegen, The Netherlands Aerts: It makes me happy that we have the largest number of posters in this session. Wojtek gave a great range of topics for us to discuss, for instance the Be stars. I have also seen some evolution over the past 10 years, in the good interaction between observers and theorists on the subject which I think is very important. Is there anybody who would like to address a questions on these topics to the speakers or to the poster authors or to the audience? Christensen-Dalsgaard [to Dziembowski]: What do you see in the foreseeable future as the prospect for a realistic and reliable and accurate, and maybe even physically correct, treatment of rapid rotation and pulsation? Dziembowski: There are two approaches and they give different answers. There is the traditional approximation, and the expansion into the associated Legendre functions. Each of them has advantages. The traditional one is easier and this is why we are using it. I think that we need a numerical 2D models of linear adiabatic pulsations in rotating stars. Furthermore, our models ignore centrifugal distortion. One important consequence of including this effect of distortion is a nonuniform distribution of the temperature across the surface. The result is that you may have driving only in the equatorial regions which, in this case, will cause some modes to be preferred. This is important and I encourage young people to work on this problem. Roxburgh: I should point out that at least to me, there was impressive progress on the modelling of adiabatic oscillations - so far only polytropes - by Daniel Reese, Francois Ligniéres and Michel Rieutord. What they show, essentially from full 3-D modelling of oscillations, is that the perturbation approximation breaks down at rotational velocities of the order of 50 km/s for models of the δ Scuti type. For very many stars we therefore need to go beyond linear calculations, and these authors’ recipes can be extended to realistic models of stars. Dziembowski: Fortunately, significant nonadiabatic effects arise only in the outer layers where the plane-parallel approximation applies. Therefore for determining the mode geometry the adiabatic treatment is likely sufficient. Reed: Looking at multicolour observations, I’m curious to know how well the observations are constraining the modes and by how much they are matched by the models. Aerts: The stars that have been modelled so-called successfully, are all slow rotators. The reason is that they are easier for the reasons just mentioned. Then we have a frequency spectrum that’s not very dense for β Cephei stars (in contrast to the SPB stars, for instance). So in that sense we have very good matches with the frequency values, but we do have excitation problems as Wojtek clearly tried to explain. This is very important to be solved. I think that, for the moment, we have very good data on β Cephei pulsations, we know quite well how to model the slowly rotating ones, but we are missing frequency matches and this tells us about missing physics. We need more theoretical work on the mode selection mechanism. We do not understand how this works and it would be great to know if someone told us that. Reed: How many of these stars have good mode identifications? Aerts: Between two to five, but more is coming up. There are data sets where the identification is still ongoing, but in addition to the photometry we do need the spectroscopy. 218 Discussion on β Cephei and SPB stars Paparo: It happened that different data sets led to different mode identifications. Are these single data sets for all stars or are the observations repeated over several seasons? The problems usually come when there are more and more observations. For example, the δ Scuti star XX Pyxidis was regarded as simple and when more data became available it became more and more complicated. I expect this will be similar for your β Cephei and other B-type stars. Christensen-Dalsgaard: It’s wonderful that you got all the data that Andrzej talked about for β Cephei stars. But how are we going to address the issues of follow-up that will be required - and of course I am going to use this as an advertisement for the talk by Frank Grundahl tomorrow on the SONG network - to be able to analyse these stars in detail and see the problems with them? Aerts: For the two to five stars where we have this information, we have very long-term monitoring. Our multisite campaigns lasted five to six months and we can add data from season to season. The data that Wojtek showed for ν Eri imply that we have stable modes. For 12 Lac, we see the same main six frequencies as were seen in 1978 and 1991. For B stars it’s therefore much easier than for δ Scuti stars because the modes stay and that helps a lot. Pigulski: What about Spica? Aerts: This is a binary, it’s an ellipsoidal variable, it’s a high-degree pulsator and it’s moderately rapidly rotating. So we have it all, as far as complications are concerned, and it’s a magnificent laboratory. So I agree we should do it. We have very concrete plans already for this star with the MOST team. Breger: I really love this discussion. Ten to fifteen years ago there was a lot of criticism when someone concentrated on one or two objects to really find out what is going on. And now you show that this is just the approach that allowed you to discover what is really happening in β Cephei stars. In some way this answers Margit’s comment as well. She said that you need more than one data set to detect the complexity of real stars. There are two explanations for detected changes: first, the star has changed and second, you over-interpreted your first data set. Therefore, I would like to make a plea to those of you who referee papers to support the immense efforts that go into observing single objects. Aerts: I would like to add to the remark made by Gerald this morning on the MOST photometry where lots of frequencies were claimed and perhaps that’s a bit optimistic. I can tell you that I was guilty of that. It is true that only if you go back season to season to have trustworthy values to give to the theoreticians. So even with high-quality data from space we do need long-term monitoring. Bedding: This also applies to solar-like stars. But I would like you to tell us about strange modes... Dziembowski: This concept was introduced in the context of very nonadiabatic pulsation in luminous (high L/M ratio) stars. There are two different definitions of strange modes. First, I will tell you the one that I like and then I will tell you the one I don’t like. The one I like is that if a mode does not have its adiabatic counterpart it is a strange mode. What is the adiabatic counterpart? You can scale down nonadiabatic effects, for instance by gradually increasing stellar mass. If you land on an adiabatic mode, in the sense that the difference between the adiabatic and the nonadiabatic mode frequency is small, then this is an ordinary pulsational mode for me. If you land on a thermal non-oscillatory mode, this is a strange mode. Some people, however, call a mode strange if it is trapped in a near-surface cavity around the hydrogen or helium ionization zones. Bedding: As an observer, what should I observe to see a strange mode? Dziembowski: There is no way of identifying modes by pure observational means. Gough [to Bedding]: May I add to that? If you observe modes that have dynamical importance, and if we know what they are, theorists can use that to learn something about the structure of the star and its dynamics, and that’s important. Whether or not some theorist classifies it as a strange mode is really not relevant. So it’s not really an important question to you. What is important to you is that you measure modes that are dynamically interesting. C. Aerts 219 Aerts: There is a poster by Hideyuki Saio on a MOST data set on a supergiant SPB. That one is located between the Wolf-Rayet/LBV-type stars and the much easier β Cephei stars. There are lots of frequencies detected (never mind whether they are resolved or not, but they are there), and this star is just an extension of the SPB star instability strip to the upper part of the HR diagram. These are not strange modes to me, but maybe by someone else they would be termed like that. I find that extremely interesting because it will allow us to calculate the upper part of the HR diagram. This is a little related to your question because it’s related to nonradial oscillation modes in supergiant stars. Dupret: I agree that much work has to be done to study the interaction between rotation and oscillations in rapid rotating stars. However I stress that many β Cep stars are slow or moderate rotators. For some of them observed in multi-site campaigns (e.g. HD 129929, θ Oph, ν Eri) rotational splitting is clearly seen. Their study allows to probe internal rotation, without the theoretical difficulties and uncertainties associated with fast rotation. This is very interesting as it allows to test theories of angular momentum transport. So it is time to include these transport mechanisms in our stellar evolution codes, we can constrain them now! Kepler: I would like to point out the difference between frequencies and modes. Sometimes, especially in white dwarfs, you have hundreds of combination frequencies which are not modes. You may want to make a clear distinction between frequencies and modes to avoid an over-interpretation of data. Matthews: I agree. We constantly look at and identify combination frequencies. We certainly recognize that distinction and when we make an identification we don’t use the term ”modes” unless there is some theoretical match. Kepler: Sometimes combination frequencies do excite real modes, by resonance. We must also be very careful not to throw away all combination frequencies because sometimes they are real modes. I’m just saying we must be very careful in separating modes and frequencies. Breger: This is an important problem. I would like to advertise a new paper by Katrien Kolenberg and myself which shows that there actually exists a case where a combination frequency excites a mode separated by a minuscule amount of 0.7 nHz. We had to combine photometry covering several decades to obtain the required frequency resolution. This shows that combination frequencies are extremely important. We also find that positive combinations (sum of frequencies) usually have higher amplitude than their negative counterparts. Gough [to Kepler]: I would like to add to your comment. The existence of harmonics and combination frequencies are indications of the existence of nonlinearity, which is extremely interesting. For the analysis, we not only need to know the amplitudes of the combination frequencies, but also their relative phases. May I make a plea to observers to publish relative phases in addition to the amplitudes? Dziembowski: There is no easy way to make a distinction between the cases of resonant mode excitation and a simple harmonic light curve distortion. The reason is that there is a phase-lock induced by nonlinear mode coupling, which cancels the departure from the exact resonance (frequency mismatch). As a result, in the frequency domain we see a simple harmonic. The only way to say there is a resonance is an abnormal enhancement of amplitude at the harmonic frequency. This is what we see in the case of Bump Cepheids, where the second overtone has frequency close (but not equal) to twice that of the fundamental mode. Bourge: To drive all the modes observed in β Cephei stars, one must increase the iron abundance in the driving zone. But one doesn’t see the abundance patterns expected on the surface, as Wojtek Dziembowski said in his talk. We spoke about mixing, but this is not the only process modifying the chemical abundances. In my models, when I include mass loss, I find this has a big influence on the chemical composition even in the driving region. But we do not include that in the current ”standard” models. Aerts: Then I have one final comment to make. Can anyone tell us how one can discriminate between convection and rotational mixing? With that I would like to thank you very much for this discussion. Pulsating white dwarf and sdB stars Comm. in Asteroseismology Vol. 150, 2007 Observational white dwarf seismology S. O. Kepler Instituto de Fı́sica, Universidade Federal do Rio Grande do Sul, Porto Alegre, RS - Brazil Abstract After the Sun, the stars with the most detected pulsation modes are the white dwarfs. From the hot PG 1159 stars, through the pulsating DBs near 25000 K, to the more numerous DAVs around 12000 K, we now know of around 150 pulsating white dwarf stars, but they are still all in the nearby thin disk of our Galaxy. As the white dwarf models are simple and the details of the initial conditions are washed out when the stars reach the DBV and the DAV instability strips, seismology does give structural information with detail and precision, and even allows us to measure evolutionary timescales. Taking into account that around 97% of all stars evolve to white dwarfs, we measure the records of Galactic history, which is a powerful tool to study physics at high energies. Introduction Asteroseismology of white dwarf stars is a strong tool for probing high energy and high density physics, such as the study of neutrinos (weak interaction - Kawaler 1997; O’Brien et al. 1998; Winget et al. 2004), axions (the best candidate for cold dark matter, Córsico et al. 2001), crystallization (cool white dwarf stars are quantum crystals, Winget et al. 1997; Córsico et al. 2004, 2005; Kanaan et al. 2005) and even the determination of the C(α, γ) cross section (Metcalfe, Salaris & Winget 2002; Metcalfe 2003; Metcalfe, Montgomery & Kawaler 2003) essential in the study of type Ia supernovae. In terms of stellar structure and evolution, the observed pulsations can be used to evaluate the total mass, the layers and even core masses, rotation periods, magnetic fields, differential rotation (Kawaler, Sekii & Gough 1999), and also a real measurement of the evolutionary time scales, dR/dt (Costa et al. 2003) and dT /dt (Stover et al. 1980; Kepler et al. 1982, 2005b; Mukadam et al. 2003), which in turn can be used to measure the age of the Galaxy (Winget et al. 1987; Hansen et al. 2002). The changes in pulsation periods of white dwarf stars can also be used for the detection of extra-solar planets, complementing the search space not easily available for radial velocity measurements (Winget et al. 2003). The pre-white dwarf PG 1159 stars around 75 000 K to 170 000 K have the largest number of modes detected. With the first class of pulsating stars to be predicted theoretically before discovery, the DBVs around 22 000 K to 29 000 K, and the first pulsating white dwarf stars to be discovered, serendipitously, back in 1968, the DAVs around 10 850 K to 12 270 K, the 150 pulsating white dwarf stars known are all in the thin disk of our Galaxy, just because they are intrinsically faint. They form the most numerous class of variable stars. As their structure is simple, seismology does give structural information with detail and precision. Because of their high densities and internal temperatures, they are tools to study physics at high energies, where quantum effects are dominant, but post-Newtonian corrections are still not dominant. All the pulsating white dwarf stars are non-radial g-mode pulsators, and the eigenmodes are described by three indices: the number of radial nodes (k), the total number of nodes across the surface ( ), and the number of azimuthal nodes (m). With the mode identification via multiplets for pulsating PG 1159 stars and DBVs, or via chromatic amplitudes changes from ultraviolet to optical (Kepler et al. 2000; Castanheira et al. 2004, 2005), or line profile 222 Observational white dwarf seismology variations (Clemens, van Kerkwijk, & Wu, 2000; Kotak et al. 2002, 2003; Kotak, van Kerkwijk & Clemens 2002, 2004; Thompson et al. 2003), for DBVs and DAVs, we have been successful in applying seismology to estimate the mass, and total luminosity via the mass-radius relation, and consequently the distance, but also the thickness of the composition layers, including the core composition, and rotation periods. Nearly all the modes identified up to today have = 1 or 2. Yeates et al. (2005) propose to use the amplitudes of the combination peaks to identify = 1, using the amplitude equations of Wu (2001). Hydrogen-atmosphere white dwarf stars (DAs) comprise ∼ 90% of all white dwarf stars; helium dominated DOs and DBs total close to the remaining 10% (Eisenstein et al. 2006). Pulsating PG 1159 stars The instability strip of the pulsating PG 1159 stars, or GW Vir stars (McGraw et al. 1979), around Teff 170 000 K to 75 000 K and log g = 5.7 to 7.5, include both the DOVs (McGraw et al. 1979, Bond et al. 1984), without evidence of surrounding planetary nebulae, and the PNNVs (Grauer & Bond 1984), both with detectable evidence of ongoing mass loss. Their atmospheres are mainly composed of He, C and O, and the pulsators also have strong lines of N (Dreizler 1998). These hydrogen deficient stars are probably the evolutionary remnants of a born again episode, triggered by a late helium thermal pulse after the star has left the AGB (Fujimoto 1977; Schönberner 1979; Iben 1982; and Althaus et al. 2005). There are 11 pulsators known, and their periods change slowly with time due to variations in both temperature, probably dominant, and radius dP dT dR =a +b dt dr dt (Winget, Hansen & van Horn 1983; Winget et al. 1985; Kawaler et al. 1986; Costa et al. 1999). The pulsation periods range from 7 to 50 minutes, being longer for the PNNVs (Vauclair, Solheim & Østensen 2005) and, for the prototype, have been detected even in X-ray (Barstow et al. 1986). The period spacings for this class of variables are mainly given by asymptotic theory, as they are high-k pulsators. Presently, the largest uncertainty in the mass determination from the period spacings is coming from uncertainty in the theoretical models (Kawaler et al. 1995, 2004), not due to observational precision. So an effort in accurate modelling is necessary and hopefully in progress. Note that the accuracy in the mass determination from the period spacings, even with the uncertainty in the models, of the order of ΔM 0.02 M (Costa et al. 2003), is at least an order of magnitude more accurate than the determinations from spectral fitting. As convection is negligible in these stars, the κ − γ mechanism at the C and O partial ionization zones are the main drivers, as originally proposed by Starrfield et al. (1983) and confirmed by Bradley & Dziembowski (1996), and more accurately with the evolutionary models of Quirion et al. (2004, 2005, 2006, 2007), Córsico & Althaus (2005, 2006) and Córsico, Althaus & Miller Bertolami (2006). DBVs The class of pulsating DB stars, also called V777 Her after their progenitor GD 358, discovered by Winget et al. (1982a), with an atmosphere of helium, has 13 pulsators known (+4 strong candidates - Nitta et al. 2005). The instability strip is located around Teff 29 000K to 22 000 K, with an uncertainty around 2 000 K due to uncertainties in the temperature determination from spectral fitting (Beauchamp et al. 1999; Castanheira et al. 2006a). The excitation is due to the κ − γ mechanism in the He partial ionization zone, as proposed by Winget et al. (1982b), and is the first class of variable stars predicted theoretically. The pulsation spectra, in general, show a large number of harmonics and combination periodicities, S. O. Kepler 223 consistent with a thick convection zone distorting the eigenmodes that enter the base of the convection zone (Ising & Koester 2001; Montgomery 2005, 2006). The prototype and brightest known member, GD 358, shows hundreds of combination peaks in the Fourier transform of the light curve, and shows strong amplitude changes on timescales of weeks and months (Winget et al. 1994; Vuille et al. 2000; Kepler et al. 2003). The periods range from 140 to around 1000 s and the uncertainties in temperatures, coupled with the contamination of a small amount of hydrogen, if any, in the spectra of a few DBs, makes the analysis of the purity of the DB instability strip difficult. DAVs The DAVs or ZZ Ceti class of pulsating white dwarf stars, with 126 known members in November 2006 (Mukadam et al. 2004; Mullally et al. 2005; Kepler et al. 2005a; Gianninas et al. 2005; Voss et al. 2006; Castanheira et al. 2006bc), was the first observed, when Arlo Landolt (1968) was studying the photometric standard star HL Tau 76 and found variations of up to 0.3 mag on time scales around 12 minutes. Soon afterwards, Lasker & Hesser (1969) found G44-32, with periods around 10 and 13.7 minutes, followed by R 548 = ZZ Ceti, with periods of 213s and 271s (Lasker & Hesser 1971). Warner & Robinson (1972) and Chanmugam (1972) proposed the pulsations were non radial g-modes, as both the radial pulsations and p-modes should have much shorter periods in white dwarf stars. The class was first studied by McGraw & Robinson (1976). Robinson, Nather & McGraw (1976) first detected rotational splittings, in R 548, and McGraw (1979) and Robinson, Kepler & Nather (1982) showed the light variations were dominated by changes in temperatures caused by g-mode pulsations. The filter mechanism that selects which modes get excited to observable amplitudes, mode trapping, was studied by Winget et al. (1981) and Córsico et al. (2002). Some pulsators have small amplitudes and sinusoidal light curves (Stover et al. 1980; Kepler et al. 1982, 1983; Kepler 1984), while others are high amplitude pulsators, with many harmonics and combination peaks detected (McGraw & Robinson 1975; Robinson et al. 1978; Kleinman et al. 1998; Vuille 2000; Dolez et al. 2006). The nonadiabatic models of Dziembowski (1977), Keeley (1979), Dziembowski & Koester (1981), Dolez & Vauclair (1981) and Winget et al. (1982b) concluded the excitation was due to the κ−γ mechanism in the hydrogen partial ionization zone, but in recent calculations with OP and OPAL opacities, the models indicate that the convection zone is carrying about 90% of the flux even at the blue edge, and totally dominates the driving, i.e. convective driving in the convection zone caused the partial ionization zone, as proposed by Brickhill (1991) and Goldreich & Wu (1999). The question of the purity of the ZZ Ceti instability strip also depends on the accuracy of the determination of the effective temperatures and gravities, as the instability strip ranges only around 1200 K in Teff and depends on gravity. With high SNR spectra for the bright sample, Bergeron et al. (1995, 2004) and Gianninas, Bergeron & Fontaine (2005, 2006) find a pure instability strip, while there are ∼ 20 stars inside the same instability strip if one uses the less accurate determinations of surface parameters for the fainter SDSS variables, and the relatively high detection limits of Mukadam et al. (2004) and Mullally et al. (2005). Castanheira et al. (2006c) find variability for two stars reported as nonvariables in the aforementioned searches, and Kepler et al. (2006) find the uncertainties in the SDSS parameters are a substantial fraction of the instability strip. Mukadam et al. (2006) suggest we can use the observed pulsation periods to determine Teff , as there is a strong correlation between period and Teff . Even with the small number of pulsations detected in the DAVs, seismology indicates hydrogen layer masses MH 10−4 to 10−8 M∗ , an important limit in the study of chemical evolution of the surface composition of white dwarf stars due to diffusion, radiative levitation, and convection. The rotation periods derived from pulsation splittings are around 1 d, consistent with those observed by line broadening. Velocity fields in line profiles start to be detected with time resolved spectra taken at the Keck 10 m telescopes. 224 Observational white dwarf seismology Pulsations in DAs in Cataclysmic Variables Ten pulsators were discovered recently in low mass accretion systems (van Zyl et al. 2004; Nilsson et al. 2006), indicating the mass transfer does not strongly disturb the subsurface partial ionization zone that causes convection and/or pulsation. 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M., Hansen C. J., 1981, ApJ, 245, L33 Winget D. E., Robinson E. L., Nather R. E., Fontaine G., 1982a, ApJ, 262, L11 Winget D. E., van Horn H. M., Tassoul M., et al., 1982b, ApJ, 252, L65 Winget D. E., Robinson E. L., Nather R. E., Kepler S. O., O’Donoghue D., 1985, ApJ, 292, 606 Winget D. E., Sullivan D. J., Metcalfe T. S., Kawaler S. D., Montgomery M. H., 2004, ApJ, 602, L109 Wu Y., 2001, MNRAS, 323, 248 DISCUSSION Hatzes: I was really amazed how dramatic the power spectrum of GD 358 changed. Do you worry that you are missing detail because of poor temporal sampling? Kepler: Since the modes came back at the same frequencies after the dramatic power change, we believe that there are no time scales shorter than a month involved. Since we need about 20 telescopes looking at the same star we can only do such a project every three or four years. Bedding: You need very large telescopes to measure mmag changes in a 22nd magnitude star. How much time do you need to do useful science? You can get, say, two or three nights on such telescopes, but not weeks. Kepler: It depends on what you want to do. If you really want to do seismology, you need lots of nights, but we can detect the pulsations in a couple of hours. You would need a couple of nights over two or three seasons to do seismology. Comm. in Asteroseismology Vol. 150, 2007 The Future of Computational Asteroseismology Travis S. Metcalfe High Altitude Observatory & Scientific Computing Division, National Center for Atmospheric Research, P.O. Box 3000, Boulder CO 80307 USA Abstract The history of stellar seismology suggests that observation and theory often take turns advancing our understanding. The recent tripling of the sample of pulsating white dwarfs generated by the Sloan Digital Sky Survey represents a giant leap on the observational side. The time is ripe for a comparable advance on the theoretical side. There are basically two ways we can improve our theoretical understanding of pulsating stars: we can improve the fundamental ingredients of the models, or we can explore the existing models in greater computational detail. For pulsating white dwarfs, much progress has recently been made on both fronts: models now exist that connect the interior structure to its complete evolutionary history, while a method of using parallel computers for global exploration of relatively simple models has also been developed. Future advances in theoretical white dwarf asteroseismology will emerge by combining these two approaches, yielding unprecedented insight into the physics of diffusion, nuclear burning, and mixing. Context In just the past few years, the Sloan Digital Sky Survey has tripled the sample of pulsating white dwarf stars (Mukadam et al. 2004; Mullally et al. 2005; Kepler et al. 2005; Castanheira et al. 2006). In the next few years we can expect similar increases to emerge for other types of pulsating stars, from space missions such as CoRoT and Kepler. The observations are quickly becoming too numerous for us to do traditional model-fitting by hand. We need to automate the procedure so we can spend more of our time thinking about the results. The great thing about computers is that they can work 24 hours a day, and they are so inexpensive that you can have many of them working for you at once (Metcalfe & Nather 2000). There are many exciting areas of pulsating star research where analytical work can contribute much to our understanding (e.g. studies of the mode selection mechanism, intrinsic amplitude variability, and non-sinusoidal light variations, to name just a few), but I won’t discuss them here. This will be a computer-centric view of the future. After a brief overview of white dwarf asteroseismology, I will outline two broad approaches that are currently being used to obtain physical insight from computational work. In the future, as our computing potential increases, we will eventually be able to combine these two approaches. White Dwarf Asteroseismology First let me remind you that there are several major spectroscopic classes of white dwarfs. With few exceptions, we expect all of them to have cores composed of a mixture of carbon and oxygen – the ashes of helium burning during the red giant phase (Metcalfe 2003). About 80% of white dwarfs are classified as type DA, with a mantle of helium above the core and beneath a thin surface layer of pure hydrogen. Most of the remaining 20% show no traces of hydrogen – exposing either a pure neutral (type DB) or ionized (type DO) helium surface. Each of these major spectral types produces its own class of variables in the H-R diagram, 228 The Future of Computational Asteroseismology spanning the temperature ranges for partial ionization of carbon and oxygen (DOV), helium (DBV), and hydrogen (DAV). The instability strips for these three classes are roughly equally spaced in log Teff (see Elsworth & Thompson 2004, their Fig. 1). Like other types of pulsating stars, the spherical symmetry allows us to model the variations with spherical harmonic functions, and because we do not have spatial resolution across the stellar surface only those modes with low spherical degree ( < ∼ 3) can be detected. In contrast to other types of pulsating stars, the field of white dwarf asteroseismology developed early along with helioseismology. This can be attributed to the fact that the pulsations in these stars are not subtle . The total light variations are typically ∼ 10% on convenient timescales of ∼ 10 minutes. The simultaneous presence of many closely-spaced frequencies leads to easily visible beating in their light curves. From a theoretical perspective, pulsation frequencies are basically determined by the sound speed (or Lamb frequency) and the buoyancy (or Brunt-Väisälä) frequency from the centre of a star to its surface. Pressure modes (p-modes) are excited at relatively high frequencies (larger than both of these natural frequencies) while gravity modes (g-modes) are excited at lower frequencies, smaller than both natural frequencies (Unno et al. 1989). The pulsations in white dwarf stars are excited in the range of frequencies characteristic of g-modes, and the models suggest that the periods are determined primarily by the buoyancy frequency. The strong gravity in white dwarf stars quickly stratifies the surface layers, and the resulting composition gradients cause perturbations to the buoyancy frequency that lead to deviations from the uniform period spacing predicted by asymptotic theory in homogeneous models. We can use these deviations to infer the interior structure through forward modelling. Beyond Local Fitting One way that we can obtain physical insight from computational work is to use relatively simple models, but to explore them more globally than we have in the past. What does this mean in practice? Most of you are probably familiar with Moore’s Law , which is really an empirical observation that “computing power per unit cost doubles approximately every 18 months.” This has been true for more than a century, spanning many different computing technologies. A somewhat less well known law (because I made it up) is the More is Better Law , which states: “If you spend more time writing the paper than running the models, you didn’t run enough models.” Of course, “writing the paper” is really just a euphemism for all aspects of a research project that do not involve either computing or interpreting the results. The point is that if you choose to take a computational approach to a problem, the actual computations should occupy a large fraction of the total time needed to complete the project. Thus, what we can accomplish is in some sense driven by Moore’s Law – but we can circumvent this limitation with parallel computing, and then concentrate on what More we can do. More Stars Although our models are often physically simplified, we can instill greater confidence in the computational results by fitting them to more stars. If this leads to a qualitatively consistent picture of what we theoretically expect to find, it could just be a coincidence – but as more and more stars support the same picture, it is easier to believe that even relatively simple models can provide important physical insights. Let me give you an example from my own work on white dwarf stars. The DB white dwarfs are thought to evolve from hydrogen-deficient post-asymptotic giant branch (post-AGB) stars, which are the result of a very late thermal pulse leading to the socalled born-again AGB scenario (Iben et al. 1983). The hot DO white dwarfs that emerge initially have envelopes containing a uniform mixture of helium, carbon, and oxygen. As the T. S. Metcalfe 229 Figure 1: Fourier spectra from multi-site observations of three DBV white dwarfs with different temperatures. The data are from Sullivan et al. (in prep.), Metcalfe et al. (2005), and Winget et al. (1994); temperatures are from Beauchamp et al. (1999). Note that the top panel shows amplitude, while the middle and bottom panels show power with different scales for the left and right side of the vertical dotted line. DO star cools over time, the helium floats to the surface – gradually growing thicker and transforming the star into a DB. This process continues within the DB instability strip, so we can test the theory by measuring the thickness of the pure helium surface layer in several DBV stars with different temperatures. Asteroseismic observations are now available for three DBV stars which exhibit many independent pulsation modes (see Fig. 1). Adopting the spectroscopic temperatures of Beauchamp et al. (1999), the hottest of the stars is EC 20058 (Sullivan et al., in prep.) at 28 400 K. Slightly cooler is CBS 114 (Metcalfe et al. 2005) at 26 200 K, and cooler still is GD 358 (Winget et al. 1994) at 24 900 K. The specific prediction of diffusion theory is that we should find progressively thicker surface helium layers for cooler DB white dwarfs. More Models To test this prediction, we have used a parallel genetic algorithm (Metcalfe & Charbonneau 2003) to globally minimize the root-mean-square (rms) difference between the observed and calculated pulsation periods in each of these three stars. We use relatively simple models with pure carbon cores since we are primarily interested in the envelope structure. The genetic algorithm searches a broad range for each of the four adjustable parameters, probing white dwarf masses (M∗ ) between 0.45 and 0.95 M , effective temperatures (Teff ) from 20 000 to 30 000 K, total envelope masses (Menv ) between 10−2 and 10−4 M∗ , and surface helium layer masses (MHe ) from 10−5 to 10−7 M∗ . For each model-fit, the genetic algorithm calculates more than 500 000 models – initially distributed over the full range of parameter values, but ultimately concentrated near the region of the global solution. 230 The Future of Computational Asteroseismology Table 1: Optimal model parameters for three DBV stars. Parameter Teff (K). . . . . . . . M∗ (M ) . . . . . . log(Menv /M∗ ) ... log(MHe /M∗ ) . . rms (s) . . . . . . . . EC 20058 28 100 0.550 −3.56 −6.42 1.89 CBS 114 25 800 0.630 −2.42 −5.96 2.33 GD 358 23 100 0.630 −2.92 −5.90 2.26 Uncertainty ±100 ±0.005 ±0.02 ±0.02 ··· The results of the three model-fits (see Table 1) are in qualitative agreement with the predictions of diffusion theory, with the inferred surface helium layer masses growing thicker for the progressively cooler stars. The inferred masses and temperatures for the three stars are in reasonable agreement with the spectroscopically determined values, and the total envelope masses are all within the range expected from stellar evolution theory (D’Antona & Mazzitelli 1979). The overall quality of each fit is quite good, especially considering that we have ignored any structure in the core. More Parameters Of course, we know that real white dwarfs do not have pure carbon cores. The actual interior chemical profiles consist of a uniform mixture of carbon and oxygen out to some fractional mass that depends on the size of the convective core in the red giant progenitor. Outside of this uniform region, the oxygen mass fraction decreases to zero in a manner that is determined by the conditions during helium shell burning. The most important feature of this chemical profile, from an asteroseismic standpoint, is the location of the initial break from a uniform mixture of carbon and oxygen. But the detailed shape of the oxygen mass fraction as it falls to zero also matters. We can investigate the relative importance of these effects by adding more parameters to our model. In the past, inferences of core structure in white dwarfs were made using a simple parametrization of the chemical profile that fixed the oxygen mass fraction to its central value (X0 ) out to some fractional mass (q) where it then decreased linearly to zero at the 0.95 fractional mass point (Metcalfe et al. 2001). Based on the calculations of Salaris et al. (1997), we have recently incorporated new chemical profiles into the models to specify the detailed shape of the oxygen mass fraction. We use the same two parameters, and simply scale the shape within each model. The initial application of these 6-parameter models to CBS 114 yields a globally optimal model that agrees with both the predictions of diffusion theory and the expected nuclear burning history of the progenitor (Metcalfe 2005). This example clearly demonstrates the potential of using simple models when combined with a more global fitting strategy. Beyond the Spherical Cow At some point, even a global exploration of simple models will run into limitations. A broad search is certainly useful for identifying the region of the global solution, but the final results may suffer from small systematic errors in the optimal parameter values. How else might we use our continually expanding computational potential? Another approach is to build the best possible models, but limit the exploration. The analysis is local, but for a variety of reasons the final results may be More reliable. T. S. Metcalfe 231 More Physics The most obvious thing we can do to improve the models is simply to use the most accurate physical ingredients that are currently available. A recent example of this approach for white dwarf models can be found in Córsico et al. (2004). This study was designed to probe the asteroseismic differences between partially crystallized models of DAV stars with different core compositions. This is motivated by the fact that only relatively massive DA stars are expected to crystallize while still within the instability strip, and the transition from carbon and oxygen dominated cores to those containing primarily oxygen and neon takes place in this same mass range (Iben et al. 1997). The authors include a time-dependent treatment of diffusion to describe the chemical profiles of the hydrogen and helium layers – making the calculations much more computationally demanding. They adopt initial profiles for the distribution of oxygen and neon in the cores of one set of models from detailed evolutionary calculations that follow the repeated carbonburning shell flashes in the progenitor. For the other set of models with carbon and oxygen cores, they include a self-consistent treatment of phase separation during the crystallization process. Although they make no attempt to fit these models to the available observations of BPM 37093 (Kanaan et al. 2005), they do find significant differences in the pulsation properties of the two sets of models which will ultimately make observational tests possible. More History We can also improve the white dwarf models by connecting them directly to the prior stages of their evolution. An impressive example of this approach was recently published by Althaus et al. (2005), who examine the possible evolutionary connection between DO, DB, and DQ stars. As outlined briefly in section 3.1, the surface chemical composition of DO stars suggests that as they cool, diffusion will gradually transform them into DB white dwarfs. Since the surface convection zone grows deeper as the DB star cools further, it may eventually reach the underlying carbon-rich layer and dredge up enough carbon to transform the star again, this time into a DQ. Although there is no known class of DQ pulsators, asteroseismic tests of these evolutionary calculations are possible within both the DOV and DBV instability strips. The study follows the complete evolution of a 2.7 M star from the zero age main sequence, through mass loss on the AGB, and into the white dwarf regime. The authors employ a coupled treatment of nuclear burning and mixing, including five chemical time steps for each evolution step, which is especially important to follow the fast evolutionary phases like the born-again episode. They also adopt the double-diffusive mixing-length theory of Grossman & Taam (1996) to allow non-instantaneous mixing for a fluid with composition gradients. While the paper does not include a pulsation analysis of any models, the asteroseismic results shown in Table 1 suggest that such work could be fruitful. More Dimensions All of the models we have been discussing so far are 1-D, so they assume spherical symmetry. While this is generally a very good assumption for white dwarf stars, we know that the effects of rotation and magnetic fields can break the spherical symmetry. It has recently become computationally feasible to perform star-in-a-box calculations (Turcotte et al. 2002), and some of the most important 3-D applications focus on core-collapse supernovae (Fryer et al. 2006), which are really just a type of white dwarf star hidden in the cocoon of its progenitor. So this is another way we might improve the models in the future. One caveat that I should mention comes from my thesis adviser, Ed Nather. When asked about the difference between 1-D models and 3-D models, he replied: “3-D models are wrong in three dimensions.” 232 The Future of Computational Asteroseismology The Future We have discussed two broad approaches to improving our understanding of pulsating stars using presently available computational resources. One option is to perform a global search by generating millions of simple models for comparison with the observations. Or, with similar resources, we can calculate a few complete evolutionary tracks using relatively sophisticated physical models. My prediction for the future should be uncontroversial: as computers get faster, they will eventually allow us to combine these two approaches and generate millions of complete evolutionary models, opening the door to new tests of fundamental physics in pulsating stars. Acknowledgments. I would like to thank the meeting organizers for inviting me to give this review, and for permitting me to write it for a broader audience. 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Metcalfe 233 DISCUSSION Christensen-Dalsgaard: I think I have to disagree with you. If you spend more time computing models than writing papers, you are probably not using enough time to interpret and present the results of the computations. Metcalfe: You can do parallel processing, that is, you should be running the models for your next paper while writing the present one. Christensen-Dalsgaard: I would like to discuss the excitation of oscillations in white dwarfs. Previously it was believed that the DAVs were excited by the opacity mechanism in the hydrogen-ionization zone. But later it was found that they were actually excited by convective driving, shown by the work of Brickhill. Metcalfe: It’s actually a cause-and-effect question. But I would like to refer that question to Mike Montgomery for a detailed answer. Montgomery: The DAs have a significant convection zone that dominates energy transfer. Brickhill did discover that this contributes to the driving, but only by doing numerical simulations, not hydrodynamical, and this was the discovery as you put it. Yanqin Wu and Peter Goldreich have given that an analytical basis. I hesitate to use the words that this is ”accepted” now, but it is the most promising explanation we have for driving in these objects. There may be some isolated cases where convection is not that important (such as a white dwarf which is accreting solar composition material), but for the majority of the objects this is probably the correct mechanism, for both DAVs and DBVs. I point out that the current generation of equilibrium models shows that convection should be important all across the instability strip, even at the blue edge. Gough: Apropos of Joergen’s first comment, permit me to mention a theorem which is so obvious that almost all funding agencies are oblivious to it: if more time is spent making observations with expensive equipment and reducing the data to palatable form than is devoted to analysing the results, then insufficient effort has been expended in extracting useful science from the valuable observations. Bedding: Is it a coincidence or is it an odd that the instability strip of the DAs lies on the extension of the classical instability strip in the HR diagram? Winget: Partial ionization and convection are coincident, i.e. partial ionization causes convection. Quirion: We understand the blue edge well, but if you go towards the red edge, there is more and more convection, so we have something like a ”generalized” κ-mechanism at work here. Kepler: I think we are going into semantics. At the blue edge of the DAV instability strip there is no convection. Later, the convection zone is very thin and pulsations cannot be excited by convection. In the middle of the instability strip, where convection is important, it adds to the driving. At the blue edge, driving comes only from partial ionization, and therefore the amplitudes are smaller and the light curves are linear and sinusoidal. In the middle of the strip the amplitudes are higher, the light curves become nonlinear and we have many modes. Christensen-Dalsgaard: I’m not a specialist on white dwarfs, but the physics is different depending on whether the heating is caused by opacity variations or by convective effects. You are right that hydrogen is the cause of all of these, and these mechanisms are both heat engines, but the physical mechanism is different. Quirion: You have the DA and DB stars, and then there’s the DO and PG 1159 stars. These are spectroscopic designations. The so called DOVs are all variable PG 1159 stars, and not DO variables. This is easily confused and I don’t know why people are keeping these designations. Metcalfe: So you are suggesting to drop the DOV designation? Kawaler: Spectroscopically, the PG 1159 stars are DOZQ stars! Comm. in Asteroseismology Vol. 150, 2007 Pulsating Hot Subdwarfs – An Observational Review D. Kilkenny South African Astronomical Observatory, PO Box 9, Observatory, South Africa Abstract In the decade since rapidly-pulsating sdB stars were discovered, slowly-pulsating sdBs have been found and multi-site campaigns have been carried out on both types. In addition, the first examples of pulsating He-sdB and sdO stars have been discovered and await detailed investigation. This paper briefly reviews the field and indicates some current trends and future possibilities. A suggestion is made for a new nomenclature. Rapidly-pulsating (p-mode) sdB stars The first rapidly-pulsating sdB stars were found accidentally in the mid-1990s (Kilkenny et al. 1997 and following papers in the same volume). Simultaneously – and independently – the Montreal group was showing that these stars should pulsate (see the review by Charpinet et al. 2001). Nearly 40 such stars are now known; they are p-mode pulsators with periods ∼ 2 − 5 minutes, though periods as long as 9 minutes are known. They can exhibit anywhere from 1 to over 40 pulsation modes (e.g. Kilkenny 2002) and occur amongst the hotter sdB stars with 28000 < Teff < 35000 and 5.2 < log g < 6.1. Figure 1: Part of a light curve for the rapidly-pulsating sdB star, EC 09582-1137. Figure 1 shows part of a light curve for the recently discovered pulsator, EC 09582-1137 (Kilkenny et al. 2006). The observations indicate a classical beating oscillator and Fourier amplitude spectra from data obtained in 2005 show two pulsations at 6612 and 7353 μHz (periods of 151 and 136 s), both with amplitudes near 0.008 mag, and with little evidence for any other frequency. Fourier spectra from three nights in 2006 are displayed in Fig. 2 where it can be seen (upper panel) that the 136 s mode has disappeared; in the middle panel it re-appears; and in the lower, a third period appears near 143 s. Spectra from other nights show similar behaviour – one, two or all three modes become so weak as to be undetectable. Also, in 2005, the amplitudes were ∼ 0.008 mag; in 2006, they never exceed 0.005 mag. There is thus evidence for amplitude variation on a range of time scales. EC 09582-1137 is an apparently simple case; PG 1605+072 is anything but. A multi-site campaign in 1997 found over 40 independent frequencies and ten sum frequencies (Kilkenny et al. 1999). In 2004, a two-week single-site campaign was carried out at the SAAO and the results are compared on a weekly basis with the 1997 data in Fig. 3. It is clear that in D. Kilkenny 235 1997 there was little difference between the two weeks of the campaign; in 2004, not only are the amplitude spectra quite different from 1997, but the two weeks show clear evidence for change far above the noise level. Again, amplitude changes are occurring on different time scales. Figure 2: Fourier amplitude spectra for EC 09582-1137. The two examples shown here are not isolated; many of the rapid pulsators show similar amplitude changes (see, for example, Kilkenny 2002, Reed et al. 2006, amongst others). Slowly-pulsating (g-mode) sdB stars The slowly-pulsating sdB stars were also discovered serendipitously during a search for eclipses, ellipsoidal and reflection effects in sdB binaries (Green et al. 2003). Over 30 slow pulsators are now known, though it is possible that a large fraction of the cooler sdB stars might pulsate. They are g-mode pulsators and typically have periods ∼ 1 – 2 hours. Like the rapid pulsators, they are multi-periodic but occur amongst sdB stars with Teff < 27000 and log g ∼ 5.4, and there appears to be a good separation between the rapidly- and slowly-pulsating sdBs in a Teff /log g diagram (see, e.g., Fig. 3 in Schuh et al. 2006). Observationally, the slow pulsators are a tougher prospect than the rapid ones because they have comparably small amplitudes and complexity of pulsation modes but ∼ 20 times longer periods. Nonetheless, a start has been made on multi-site campaigns: Reed et al. (2004) report a short campaign on the class prototype, PG 1716+426, whilst Randall et al. (2006a, 2006b) present results from a very successful campaign on PG 1627+017 (23 frequencies resolved) and describe campaigns on two other stars, PG 1338+481 and PG 0101+039, including the use of satellite data from MOST (Walker et al. 2003). 236 Pulsating Hot Subdwarfs – An Observational Review Figure 3: Fourier amplitude spectra for PG 1605+072 from 1997 and 2004. The 1997 multi-site data show a much simpler spectral window than the 2004 single-site data. As an example of a slowly-pulsating sdB star, Fig. 4 shows data from a single-site (SAAO) campaign on EC 21324-1346. This campaign lasted two weeks and resulted in good runs (> 5 hours) on 12 nights. From the full data set it was possible to extract nine oscillations with periods between about 3000 and 8000 seconds. But Fig. 5 shows the Fourier amplitude spectra for the EC 21324-1346 observations divided into two halves; it is clear that there is amplitude variation between the two weeks. As with the rapidly-pulsating sdBs, amplitude variation may be a rather common phenomenon. sdB stars with p and g modes Two exciting discoveries have been HS 0702+6043 and Balloon 090100001 (Schuh et al. 2006; Oreiro et al. 2004). These sdB stars show both p and g modes. HS 0702+6043 has at least two oscillations near 6 minutes (2606 and 2754 μHz) with a long-period variation at about an hour (283 μHz). Balloon 090100001 exhibits many modes; Baran et al. (2006) recently found 22 p modes in the range 2800 – 5500 μHz, 15 g modes in the range 100 – 800 μHz, and 13 sum/difference frequencies. Both stars are on the temperature boundary between rapidly- and slowly- pulsating stars (see, for example, Fig. 3 in Schuh et al. 2006). Importantly, stars which exhibit both p and g modes give us the potential to investigate different regions within sdB stars, because the acoustic and gravity waves sample the surface layers and the deeper interior, respectively. D. Kilkenny 237 Figure 4: Part of a single-site campaign on EC 21324-1346 in 2005 July. Numbers down the right-hand side are JD – 245 3500. The top panels show greater scatter because of shorter integration times. Figure 5: EC 21324-1346: Fourier amplitude spectra for nights 2005 July 5 – 11 (upper) and 12 – 18 July (lower). Corresponding spectral windows are at the right. 238 Pulsating Hot Subdwarfs – An Observational Review The first pulsating He-sdB star The first variable helium-rich sdB star, LSIV–14◦ 116, was recently found in a systematic search by Ahmad & Jeffery (2005). From the discovery observations (5 nights), these authors find two periods – 1950s and 2900s (amplitudes ∼ 0.004 mag) – and suggest that they are g modes. This is in accord with the long periods, but the star has Teff = 32500 K which puts it in the rapidly-pulsating zone (for normal sdB stars). Current models indicate that g modes should be stable at this temperature. Clearly, this He-sdB is rather different from the other sdB pulsators and merits further investigation. The first pulsating sdO star Just before this meeting, the discovery was announced of the first pulsating sdO star, SDSS J160043.6+074802.9 (Woudt et al. 2006). Variability was discovered fortuitously during a search for new AM CVn stars amongst Sloan Digital Sky Survey stars of appropriate colour. This star showed a very strong 2 minute oscillation (amplitude ∼ 0.04 mag) with a clear first harmonic near 1 minute. From 6 nights in 2006, Woudt et al. (2006) find at least another 8 frequencies between the main oscillation and its harmonic (see Fig. 6). Spectroscopically, the star appears to be a classical sdO star. Figure 6: J160043.6+074802.9: (a) Fourier amplitude spectrum from 6 nights in 2005; (b) The same, prewhitened by the strong frequency near 8380 μHz (119.3s) and (c) with ten frequencies removed. Analysing the observations in pairs of nights shows that some of the frequencies detected have variable amplitude, though the effect is not strong and so far we have a sample of only one star. D. Kilkenny 239 Current and future... The study of pulsating hot subdwarfs is a relatively young but rapidly expanding field. Observationally, there seem to be several avenues of investigation which are being pursued currently and planned for the near future: • Survey work certainly needs to continue. We have only one example of pulsation in each of the He-sdB and sdO classes, and a sample of one is weak – even astronomically. Additionally, the range of variability seen amongst the rapid sdB pulsators suggests that there might well be new species (sub-species?) to be found. • Multi-site campaigns have already been very successful; a few of these have been mentioned above. They are still important for resolving “all” frequencies/modes – particularly so that these can be matched theoretically – and for characterizing amplitude changes. • Spectroscopic campaigns are difficult; the very short periods mean that large telescopes are needed. An obvious candidate for such study is PG1605+072; it has large amplitudes and the longest periods (∼ 6 – 8 minutes). A campaign on this star by O’Toole et al. (2005) resolved some 20 frequencies. Such campaigns are difficult to organize and the faster pulsators are much harder to do, but Jeffery & Pollacco (2000) have had success with PB 8783 and KPD 2109+4401, for example. The slowly-pulsating sdB stars remain to be exploited (but see For et al. 2006) though they should be easier because of the longer periods. • Multi-colour observations give the possibility of determining the modes ( values, at least) via amplitude ratios and were first examined by Koen (1998). Simultaneous observations in several colours are required because pulsation amplitudes can vary with time. Jeffery et al. (2004), for example, have used ULTRACAM to obtain such measurements, and there seems to be substantial promise in this approach. • Line profile variations. Studying these is difficult because of the rapid variability and the high signal/noise required. Recent work on obtaining and modelling such variations has been described by Schoenaers & Lynas-Gray (2006), for example. A note on nomenclature Table 1 summarizes the nomenclature problem. Using “prototype” names would, in some cases, be ghastly; formal variable star names do not yet exist for most types and are likely to be unmemorable in any case; and the informal names (EC 14026, “Betsy” stars) – which have been a pleasant way of recognizing the discoverers of such objects – should, perhaps, now be replaced by a more systematic nomenclature. By analogy with the white dwarf stars, the simplest expedient is to add “V” to the spectral designation. The problem is that we have two (three ?) different types of pulsators within the sdB class. I have suggested that we add the subscripts “p”, “g” or “gp” to the V to indicate the modes present (or, alternatively, “r”,“s” or “rs” – for rapid and slow pulsators). The subscripts need not be added to the He-sdBV or sdOV designations unless new discoveries are made. Another option might be to use letters in parentheses instead of subscripts (parentheses would be required as some letters (p and s) are already used in spectral classification). Acknowledgments. I am very grateful to the conference organizers for inviting me to this excellent meeting and for providing a contribution towards my expenses. 240 Pulsating Hot Subdwarfs – An Observational Review Table 1: Summary of the nomenclature problem Type Prototype sdB (rapid) (p mode) sdB (slow) (g mode) sdB (both) (p and g ) He-sdB sdO EC 14026-2647 Variable Star Name V361 Hya PG 1716+426 Informal Suggested EC14026 sdBV PG1716 “Betsy” sdBVp HS 0702+6043 Balloon 0901000001 LSIV –14◦ 116 J160043.6+074802.9 sdBVg sdBVgp He-sdBV sdOV References Ahmad A., Jeffery C. S., 2005, A&A, 437, L51 Baran A., Oreiro R., Pigulski A., Pérez-Hernández F., Ulla A., 2006, Baltic Astr., 15, 227 Charpinet S., Fontaine G., Brassard P., 2001, PASP, 113, 775 For B.-Q., Green E. M., O’Donoghue D., et al., 2006, ApJ, 642, 1117 Green E. M., Fontaine G., Reed M. D., et al., 2003, ApJ, 583, L31 Jeffery C. S., Pollacco D., 2000, MNRAS, 318, 974 Jeffery C. S., Dhillon V. S., Marsh T. R., Ramachandran B., 2004, MNRAS, 352, 699 Kilkenny D., 2002, in Aerts C., Bedding T. R., Christensen-Dalsgaard J., eds, ASP Conf. Ser. Vol. 259, IAU Colloq. 185, Radial and Non-radial Pulsation as Probes of Stellar Physics. Astron. Soc. Pac., San Francisco, p. 356 Kilkenny D., Koen C., O’Donoghue D., Stobie R. S., 1997, MNRAS, 285, 640 Kilkenny D., Koen C., O’Donoghue D., et al., 1999, MNRAS, 303, 525 Kilkenny D., Stobie R. S., O’Donoghue D., et al., 2006, MNRAS, 367, 1603 Koen C., 1998, MNRAS, 300, 567 Oreiro R., Ulla A., Pérez Hernández F., et al., 2004, A&A, 418, 243 O’Toole S. J., Heber U., Jeffery C. S., et al., 2005, A&A, 440, 667 Reed M. D., Green E. M., Callerame K., et al., 2004, ApJ, 607, 445 Reed M. D., Eggen J. R., Zhou A.-Y., et al., 2006, MNRAS, 369, 1529 Randall S. K., Fontaine G., Green E. M., et al., 2006a, ApJ, 643, 1198 Randall S. K., Fontaine G., Green E. M., Brassard P., Terndrup D. M., 2006b, Baltic Astr., 15, 291 Schoenaers C., Lynas-Gray A. E., 2006, Baltic Astr., 15, 219 Schuh S., Huber J., Dreizler S., et al., 2006, A&A, 445, L31 Walker G. A. H., Matthews J., Kuschnig R., et al., 2003, PASP, 115, 1023 Woudt P. A., Kilkenny D., Zietsman E., et al., 2006, MNRAS, 371, 1497 DISCUSSION Charpinet: How far can you tell that the amplitude variations are not due to some beating? Kilkenny: I suppose in principle you can’t, but if your data base is long enough, you can expect all intrinsic modes to be resolved. As Kepler said earlier, we do need long time baselines, we need continuous observations and we need large glass. The problem is that these stars are all faint. Comm. in Asteroseismology Vol. 150, 2007 Ten years of asteroseismic modelling of pulsating B subdwarf stars: achievements, challenges, and prospects S. Charpinet,1 G. Fontaine,2 P. Brassard,2 P. Chayer,3 E. M. Green,4 S. K. Randall 5 2 1 Observatoire Midi-Pyrénées, 14 Avenue E. Belin, 31400 Toulouse, France Dépt. de Physique, Université de Montréal, Montréal, Québec, Canada, H3C 3J7 3 The Johns Hopkins University, Baltimore, Maryland 21218, USA 4 Steward Observatory, University of Arizona, Tucson Arizona 85721, USA 5 European Southern Observatory, Garching, Germany Abstract We present a short, non-exhaustive review of the major achievements and challenges resulting from a decade of modelling the pulsations in hot pulsating B subdwarf stars. We also briefly outline promising applications of sdB asteroseismology that will be explored in years to come, showing that this new domain of stellar astrophysics has many interesting ramifications and a strong potential for greatly improving our understanding of stellar structure and evolution. Introduction The year 2006 marks the tenth anniversary of the discovery of hot pulsating subdwarf B (sdB) stars. This discovery resulted from independent, but nearly simultaneous observational and theoretical efforts. The first pulsating sdB star, EC 14026-2647, was found by astronomers from the South African Astronomical Observatory (Kilkenny et al. 1997). In the meantime, Charpinet et al. (1996) had realized, after exploring the nonadiabatic pulsation properties of sdB stellar models, that physical conditions in the envelope of such stars were fulfilled to drive oscillation modes efficiently. This led, at that time, to the prediction that some sdB stars should be pulsating. Over the last decade, the joint development of theory and observation has led to significant breakthroughs in this field. We review some of them, as well as remaining difficulties, in the following sections. We also propose previews of what might be the future of sdB asteroseismology. Pulsations in Extreme Horizontal Branch Stars Hot B subdwarfs are believed to be the observed counterparts of the so-called Extreme Horizontal Branch (EHB) stars. In the HR diagram (or, equivalently, the log g −Teff diagram; see Fig. 1), the EHB forms an extension to the blue of the classical Horizontal Branch. Stars associated with this phase of stellar evolution are thus expected to be evolved objects burning helium in their core. EHB stars are peculiar in that they must have been stripped down of almost all their H-rich envelope during a previous evolutionary stage, leaving only a helium core with a mass usually expected in a narrow range centred around 0.48 M surrounded by an extremely thin residual envelope of mass lower than ∼ 0.02 M . This configuration produces stars, clearly associated with the B subdwarfs, that remain hot (Teff in the range 22 000 K – 40 000 K) and compact (log g in the range 5.2 – 6.2) during their entire lifetime on the EHB (∼ 108 years). In addition, such stars never ascend the AGB after core helium exhaustion and evolve instead as hot post-EHB stars – often identified to the observed subdwarf O stars – before fading out as low-mass white dwarfs. Only a small fraction of the white dwarf population (∼ 2%) is expected to have followed this path, however, as the vast majority 242 Ten years of asteroseismic modelling of pulsating B subdwarf stars Figure 1: Illustration of the EHB region in the log g − Teff plane. Representative EHB evolutionary tracks are shown (filled circles and dotted lines; from B. Dorman 1995, private comm.). Positions of EHB stars in this diagram are mainly determined by their total mass M∗ and the mass of their H-rich envelope (the log q(H) parameter). The trends are illustrated with a grid of ZAEHB models (for Z = 0.02) extending from the limit between the EHB and the Blue Horizontal Branch (BHB), at low Teff , to the ZAHeMS, at high Teff . A homogeneous sample of sdB stars with spectroscopic estimates of their atmospheric parameters is also shown (open circles). of them is produced from post-AGB evolution. Major questions concerning the EHB phase of stellar evolution are still pending. One of the most intriguing is the process that lead to the formation of such stars. How EHB stars manage to lose all but a tiny fraction of their H-rich envelope is, indeed, poorly understood. A number of competing scenarios have been proposed, from single star evolution to various binary evolution channels (e.g., mergers, common envelope evolution, stable and unstable Roche lobe overflow), but no clear solution has yet emerged. Following the discovery of nonradial pulsations in B subdwarfs, the interest in EHB stars has been revived with the promise of improving our knowledge of this phase of stellar evolution S. Charpinet et al. 243 Figure 2: The EC 14026 pulsators (open circles) and Betsy stars (filled circles) with their predicted instability strips in the log g − Teff plane. In the left panel, contours indicate the number of excited = 0 p modes (with a maximum near Teff ∼ 34 000 K and log g ∼ 5.7) in the nonadiabatic models. In the right panel, contours show the number of excited = 4 g modes. The highest contours corresponding to regions of highest efficiency for the driving mechanism are drawn as solid-lines. through the use of asteroseismology. Two classes of sdB pulsators are presently known (see also the review by Kilkenny 2007). The V361 Hya stars (or EC 14026 stars from the name of the prototype) – the first that were discovered in 1997 – form a group of rapid pulsators showing luminosity variations on a timescale of a few minutes (from 80 to 600 seconds, typically). They tend to cluster around values of Teff ∼ 33 000 K and log g ∼ 5.8 in the log g − Teff plane, but are found within a relatively wide range of parameters (Teff ∼ 33 000 – 36 000 K and log g ∼ 5.2 – 6.2; see Fig. 2). Comparisons with models immediately indicate that the involved pulsations are radial and nonradial, low-order and low-degree sound waves (or p modes). The second class of sdB pulsators, the PG 1716+426 stars (from the prototype, but often referred to as the ”Betsy stars”), was discovered in 2003 (Green et al. 2003). These stars show slow luminosity variations on a timescale of hours (from 2000 to 9000 seconds) which are associated with relatively high-order gravity modes (or g modes). They are cooler than the EC 14026 stars, having Teff and log g in the ranges 23 000 – 30 000 K and 5.2 – 5.6, respectively (see Fig. 2). Interestingly, two stars (HS 0702+6043 and BAL 090100001) are known to show both p- and g-mode pulsations, thus belonging to the two classes of pulsators. Hence, the blue edge of the Betsy star instability strip overlaps with the red-edge of the EC 14026 instability region. Understanding the pulsations in hot B subdwarf stars The nature of the driving mechanism for the EC 14026 stars was identified very early (Charpinet et al. 1996). It relies on two essential components. The first is the presence of heavy metals, especially from the iron-group, through their impact on the gas opacity. In EHB stellar models, heavy metals produce an opacity bump – the so-called Z -bump – that is ideally located in the envelope, thus producing an effective pulsation driving mechanism through a κ-effect. This driving, however, is not strong enough in standard EHB models assuming solar (Z ∼ 0.02) metallicity and needs to be enhanced to destabilize modes. This is where the second essential component, microscopic diffusion, comes into play. Subdwarf B stars are notorious for having 244 Ten years of asteroseismic modelling of pulsating B subdwarf stars chemically peculiar atmospheres. Helium is usually highly depleted by large amounts while other elements show complex, non-solar abundance patterns. These are commonly attributed to the competing action of radiative levitation, gravitational settling, and possibly weak stellar winds. Detailed calculations show that, indeed, the very stable radiative envelopes of sdB stars offer auspicious conditions for microscopic diffusion to modify their internal chemical composition. In particular, elements from the iron-group tend to accumulate in the envelope, thanks to radiative levitation. This results in a strong amplification of the Z -bump and of the associated κ-effect, leading to the excitation of pulsation modes. It was later shown by Fontaine et al. (2003) that this mechanism is also responsible for the pulsations seen in Betsy stars. Diffusion is therefore a fundamental ingredient that must be taken into account if one wants to understand and exploit the pulsations in sdB stars. Our current EHB models (referred to as the ”second generation” models) implement the nonuniform abundance profile of iron (the main contributor to the Z -bump) derived from detailed diffusion calculations assuming equilibrium between radiative levitation and gravitational settling. Comparisons between the theoretical and observed properties of sdB pulsators using these second generation models are numerous (see, e.g., Charpinet et al. 2006a). One of particular interest concerns the theoretical instability strips which are illustrated in Fig. 2. In this figure, the contours provide a view of the efficiency of the driving mechanism as a function of log g and Teff for both the rapid p-mode pulsators (left panel) and the g-mode pulsators (right panel). Clearly the correspondence between observations and models is excellent in the case of the EC 14026 pulsators, especially as the driven modes have periods identical to those actually seen in these stars. Nonetheless, difficulties remain considering that the theoretical p-mode instability strip is wider than observed and because pulsators and non-pulsators coexist (with a ratio ∼ 1 over 10) in the same region of the log g − Teff plane. Some of these issues, however, will likely be solved with further refinements in the modelling of the diffusion processes in sdB stars (see, e.g., Fontaine et al. 2006). The situation for the long-period Betsy stars has been more intriguing. In our second generation models, g-mode instabilities are indeed found for relatively high degree ( > 3), high-order g modes with periods in the range of those observed. The theoretical blue-edge of the g-mode instability region is, however, much too cool compared to the atmospheric parameters derived for the known Betsy stars from spectroscopy. This discrepancy (∼ 5000 K for = 3 − 4 modes, as the blue edge depends, in fact, on the index of the modes) has been a major puzzle over the last 3 years. A significant breakthrough toward a solution to this problem was made recently by Jeffery & Saio (2006; see also these proceedings). While exploring the effects of nickel abundance enhancements on the Z -bump and the driving mechanism, these authors found that adding Ni and using opacities from the Opacity Project (as opposed to OPAL) result in blue-shifting the g-mode instability strip by ∼ 5000 K. Hence, a reinvestigation of the driving mechanism with models including these new elements, and in particular nonuniform profiles of Ni predicted by diffusion calculations, is needed. Asteroseismology of subdwarf B stars The most recent activities on sdB pulsators have been attempts to model individual stars in detail. The aim is to fully and accurately reproduce the observed pulsation period spectra and to isolate the model that corresponds most closely to the star being studied, hence constraining the stellar structure of EHB stars from asteroseismology. Both the EC 14026 and Betsy stars present a high potential for asteroseismology, but the EC 14026 pulsators have received the highest attention in this area, so far (however, see Randall et al. 2006 for a first tentative of asteroseismic analysis of a Betsy star). In the recent years, we have set up a new global approach to the problem of asteroseismology of EC 14026 pulsators. Our technique – a global optimization procedure – allows us to exhaustively and efficiently explore the vast model parameter space in order to isolate the S. Charpinet et al. 245 Figure 3: The preliminary empirical mass distribution of sdB stars as derived from asteroseismology of nine EC 14026 stars (histogram). In comparison, two theoretical distributions are also shown (vertical lines: the single star evolution scenario. Dotted curve: the double star evolution scenario). model that can best-match the period spectrum of the EC 14026 pulsator under study. Developed mainly in the context of interpreting white light fast-photometric data for which no a priori information on the mode identification exists, our procedure is a ”double-optimization” scheme that simultaneously searches for the optimal combination of observed and computed periods (for a model with given parameters) and for the optimal set of model parameters. This method leads objectively to the best match of the observed periods, providing estimates of the structural parameters of the star and a complete mode identification (i.e., the and k indices) of the observed periods. Currently, six EC 14026 pulsators have been fully analysed with this method. These are PG 0014+067, PG 1047+003, PG 1219+534, Feige 48, EC 20117-4014, and PG 1325+101 (see Charpinet et al. 2006b and reference therein). In addition 3 other EC 14026 stars have been studied in a preliminary form. In all cases, a best-fit model solution completely consistent with the atmospheric parameters of the star estimated from spectroscopy has been found. In all cases, all the observed periods are matched to driven modes, according to nonadiabatic calculations. Typically, the observed and computed periods are matched with an average dispersion of < ΔP/P >∼ 0.5% or, on an absolute scale, < ΔP >∼ 0.5 s or < Δν >∼ 40 μHz (as a comparison, typical large spacings for acoustic modes are ∼ 1000−1600 μHz in these stars). Acoustic modes of degree = 0−4 are involved (and usually required by the observed mode density). Clearly, improvements at the level of the stellar models are needed, especially as the accuracy at which the frequencies (or periods) are determined with our current observations (0.5 − 3 μHz is the typical resolution achieved) is still one order of magnitude better than the mean dispersion of the best-fit models. This leaves significant room for future refinements in the description of EHB stellar structures. Note also that tests of the seismic models are possible with multicolour photometry leading to the independent identification of the index of some of the observed modes. These can then be compared with the mode identification derived from the asteroseismic analysis. 246 Ten years of asteroseismic modelling of pulsating B subdwarf stars Figure 4: Expected (solid curves) and observed (dots with error bars) correlations between the mass of the H envelope, the effective temperature, and the total mass of the nine EC 14026 pulsators analysed. This shows a nice test of stellar evolution theory and illustrates the strong internal consistency that exists between the derived parameters (thick horizontal bands indicate the mass derived from asteroseismology). The future of B subdwarf asteroseismology A preview of some of the most interesting prospects of sdB asteroseismology is given in Fig. 3 and Fig. 4 (see figure captions for details). Objectives are to help identify the evolutionary channels that lead to the formation of EHB stars, for instance by comparing mass distributions derived from asteroseismology to those expected from different formation scenarios (Fig. 3). Moreover, asteroseismology of sdB stars now shows a strong potential for accurately testing EHB structure and stellar evolution (Fig. 4). In both cases, the number of stars analysed so far is insufficient to draw firm conclusions on these topics, but it will become possible with improved statistics. References Charpinet S., Fontaine G., Brassard P., Dorman B., 1996, ApJ, 471, L103 Charpinet S., Fontaine G., Brassard P., Chayer P., Green E. M., 2006a, Baltic Astron., 15, 305 Charpinet S., Silvotti R., Bonanno A., et al., 2006b, A&A, 459, 565 Fontaine G., Brassard P., Charpinet S., et al., 2003, ApJ, 597, 518 Fontaine G., Green E. M., Chayer P., et al., 2006, Baltic Astron., 15, 211 Green E. M., Fontaine G., Reed M. D., et al. 2003, ApJ, 583, L31 Han Z., Podsiadlowski P., Maxted P. F. L., Marsh T. R., 2003, MNRAS, 341, 669 Jeffery C. S., Saio H., 2006, MNRAS, 372, L48 Kilkenny D., 2007, these proceedings Kilkenny D., Koen C., O’Donoghue D., Stobie R. S., 1997, MNRAS, 285, 640 Randall S. K., Green E. M., Fontaine G., et al., 2006, ApJ, 645, 1464 Comm. in Asteroseismology Vol. 150, 2007 The Red Edge of GW Virginis stars P.-O. Quirion,1 G. Fontaine,2 P. Brassard 2 2 1 Aarhus Universitet, Århus C, Denmark, DK-8000 Université de Montréal, Montréal, Québec, Canada H3C 3J7 We derive the theoretical red edge of the pulsating GW Vir stars by using full evolutionary calculations that involve mass loss and diffusion. The specific mass loss law used in the evolutionary computations determines the red edge’s position. By combining this specific property with the observed location of the red edge in the effective surface temperature gravity domain, we obtain interesting constraints on possible mass loss laws for PG 1159 stars. We used an improved version of the evolutionary code based on a finite element method to model the effects of diffusion and mass loss on the red edge’s position. Here are the mass loss laws used in the present calculation: WM1 = 1.14 × 10−11 L0.93 is a fit to the mass loss rates measured in five PG 1159 type stars, three of which are also GW Vir stars; WM2 = 1.82 × 10−13 L1.36 is a fit to the five previous stars plus nine nuclei of planetary nebulae of similar luminosity; for WM3 = 1.29 × 10−15 L1.86 we chose the theoretical model used for typical post-AGB calculations; finally, WM4 = 1.00 × 10−17 L2.38 is an empirical law derived in such a way that the theoretical red edge falls directly on the empirical red edge observed for the GW Vir class. The effects of the mass loss over the position of the red edge is pictured in Fig. ??. We have calculated the evolution of three different models having masses of 0.5, 0.55 and 0.6 M . These models were all allowed to evolve under the effects of the WM1, WM2, WM3, and WM4 wind models. We then used our nonadiabatic pulsation code to probe the stability of the models along each track. The red edges obtained in the figure are simply fits along the three tracks calculated with the different mass loss laws WM2, WM3 and WM4. The position of the WM1 red edge, around Teff = 30 000 K, is not shown here as it is off scale. As is well known, no PG 1159 stars exists at this low temperature. This temperature is clearly too cool and that particular mass loss law must be abandoned. The same conclusion could be drawn for WM2, but we prefer to set conservatively this law as a maximum value for the magnitude of the mass loss in GW Vir stars, Ṁ < WM2. By construction, and as indicated above, we have devised the WM4 model in order to match fairly closely the empirical red edge as defined by the position of the coolest known GW Vir star, PG 0122+200 at 80 000 K. However, it should be noted that the predicted surface composition according to the WM4 model at that effective temperature is highly deficient in carbon and oxygen as compared to the real atmospheric chemical composition of PG 0122+200 (X (He) = 0.43, X (C) = 0.39, and X (O) = 0.17). Hence, it would appear that the WM4 model underestimates the true average mass loss in the GW Vir stars. On the other end, the empirical red edge could also be actually somewhat cooler than the effective temperature of PG 0122+200. In any case, we can use the WM4 model to set a minimum value for the mass loss in GW Vir stars, Ṁ > WM4. On the other hand, the WM3 wind model, still permits relatively high abundances of carbon and oxygen close to the empirical red edge. Also, the red edge produced by this wind model is not far, in the log g − Teff diagram, from the coolest known GW Vir stars. This model with Ṁ = WM3, is therefore more likely to be representative of the actual red edge of GW Vir stars. 248 The Red Edge of GW Virginis stars Figure 1: Positions of the known GW Vir stars in the log g − Teff diagram. The four spectroscopic types and sub-types of GW Vir are shown along with a representative 0.604 M track from F. Herwig (personal communication) and with the calculated red edges for WM2, WM3 and WM4. Some more LOC announcements to come! Comm. in Asteroseismology Vol. 150, 2007 Doubling the number of DBVs and a closer look at their Instability Strip A. Nitta,1,2 S. J. Kleinman,2 J. Krzesinski,3 T. S. Metcalfe,4 A. Mukadam,5 F. Mullally,6 R. E. Nather,6 D. J. Sullivan,7 S. E. Thompson,8 D. E. Winget,6 M. A. Wood 9 1 Gemini Observatory, 670 N A’ohoku Pl., Hilo, HI 96720 USA Subaru Telescope, 650 N A’ohoku Pl., Hilo HI 96720 USA Mt. Suhora Observatory, Cracow Pedagogical University, ul. Podchorazych 2, 30-084 Cracow, Poland 4 High Altitude Obs., National Center for Atmospheric Research, P.O. Box 3000, Boulder CO 80307, USA 5 Dept. of Astronomy, Univ. of Washington, 3910 15th Ave NE, Seattle WA 98195 6 Astronomy Dept. & McDonald Observatory, University of Texas at Austin, Austin, TX 7 School of Chemical & Physical Sciences, Victoria University of Wellington, Wellington, NZ 8 Dept. of Physics, Colorado College, 14 E. Cache La Poudre, Colorado Springs, CO 80903 USA 9 Dept. of Physics & Space Science, SARA Obs., Florida Institute of Technology, Melbourne, FL, USA 2 3 Abstract Prior to the Sloan Digital Sky Survey (SDSS), there were only nine known DBVs compared to 35 DAVs. The latest SDSS DR4 White Dwarf Catalogue (Eisenstein et al. 2006) has quadrupled the number of known white dwarf stars. We have been searching for new DBVs from the SDSS catalogue. Increased numbers of DBVs will help us better understand the structure and evolution of DBs, the nature of their instability strip as well as plasmon neutrino processes (Winget et al. 2004). We searched for DBV candidates using effective temperatures and surface gravities determined by fitting SDSS spectra with Koester’s atmosphere models. We then obtained time-series photometric data on those with fit temperatures near those of the known pulsators. So far we have discovered 8 new DBVs, nearly doubling the number of previously known DBVs. With increased numbers of DBVs, we will be able to better characterize the instability strip, but, we also need more precise determinations of the temperatures and surface gravities via better signal to noise spectra and better lower limits for the observed non-variables. This effort is ongoing. Acknowledgments. Funding for the SDSS and SDSS-II has been provided by the Alfred P. Sloan Foundation, the Participating Institutions, the National Science Foundation, the U.S. Department of Energy, the National Aeronautics and Space Administration, the Japanese Monbukagakusho, the Max Planck Society, and the Higher Education Funding Council for England. The SDSS Web Site is http://www.sdss.org/. References Beauchamp A., Wesemael F., Bergeron P., et al., 1999, ApJ, 516, 887 Eisenstein D. J., Liebert J., Harris H. C., et al., 2006, ApJS, 167, 40 Winget D. E., Sullivan D. J., Metcalfe T. S., Kawaler S. D., Montgomery M. H., 2004, ApJ, 602, L109 250 Doubling the number of DBVs Figure 1: Effective temperatures and surface gravities of the SDSS DBs (Eisenstein et al. 2006) around the DBV instability strip, along with the previously known DBVs with their physical parameters taken from Beauchamp et al. (1999). Solid dots show the new DBVs and triangles the previously-known DBVs. Squares show the DBs which did not show any variability and hollow circles show the rest of the DBs in the SDSS DR4 WD catalogue. Most of the DBs which we did not see any variability so far have such high amplitude limits that we cannot tell if they are truly non-pulsators or not. To characterize the instability strip better, we need better determinations of the physical parameters (from better signal-to-noise spectra) and better variability amplitude limits (1 mma or better). We found no pulsator hotter than EC20058 and hence the best chance of determining the neutrino production rates still lies with this star. Table 1: Results of our work so far. The top section of the table shows the objects that showed variability during at least one observation. Separated by a double vertical line, the second half of the table shows the objects which did not yet show variability. In the status section, we noted the objects which showed variability by ”DBV”. For the objects we have not seen variability of, we put the amplitude limit in the status section. The objects we have only observed once are noted by (1). Beating of multiple modes and amplitude modulation can make a pulsator appear as a non-pulsator. Therefore, we aim to observe each object at least two separate times, including new pulsators to ensure we have found a real pulsator. Object (SDSS J) 034153.03-054905.8 094749.40+015501.8 140814.63+003838.9 125759.03-021313.3 104318.45+415412.5 122314.25+435009.1 130516.51+405640.8 130742.43+622956.8 001529.74+010521.3 085950.29-000339.6 090409.03+012740.9 090456.11+525029.8 092200.97+000834.3 095256.68+015407.6 095649.55+010812.4 101131.88+050729.3 101502.95+464835.3 105929.60+554039.2 122241.27-003614.4 133215.93+640656.2 135610.32-002230.6 141258.17+045602.2 231324.24-001636.9 235322.16+002653.8 g[mag] 18.113 20.034 18.981 19.050 19.041 18.838 17.389 18.710 18.711 20.022 17.850 18.665 18.450 17.292 20.361 18.841 18.433 18.458 17.947 18.285 19.230 17.191 19.632 19.594 Teff 24490 23819 25314 26114 26020 23312 23562 24926 35974 25289 22480 36708 22754 32600 17143 24767 23355 24877 23497 20176 17033 29822 22331 25000 σTeff 440 1362 1271 1191 846 1218 386 962 899 2588 521 615 729 295 915 937 552 553 624 751 265 318 3809 1649 logg 8.04 7.96 8.01 7.53 7.78 7.83 8.07 8.08 8.00 8.00 7.97 7.94 8.11 8.15 7.32 7.79 8.05 8.10 8.22 7.98 8.00 7.95 7.51 8.05 σlogg 0.060 0.192 0.129 0.137 0.133 0.131 0.054 0.104 0.129 0.289 0.060 0.087 0.070 0.038 0.240 0.106 0.068 0.099 0.061 0.076 0.155 0.040 0.309 0.186 Status DBV DBV(1) DBV(1) DBV DBV DBV(1) DBV DBV(1) 7.2(1) 11.8(1) 3.5 9.0(1) 6.8(1) 4.3(1) 11.5(1) 8.1(1) 6.2(1) 7.6(1) 4.1(1) 8.7(1) 11.1(1) 2.6 16.9(1) 11.2(1) Comm. in Asteroseismology Vol. 150, 2007 GD 99 - an unusual, rarely observed DAV white dwarf Zs. Bognár,1 M. Paparó,1 B. Steininger,2 G. Virághalmy 1 2 1 Konkoly Observatory, P.O.Box 67, H-1525 Budapest, Hungary Institute of Astronomy, University of Vienna, 1180 Vienna, Austria Abstract New observations of GD 99 are analysed. The unusual pulsation behaviour, showing both long and short periods, has been confirmed. All the available periods show a grouping of short and long period modes with roughly regular spacing. If we interpret the groups separately, a binary nature can be a possible explanation as in the similar cases of WD 2350-0054 and G 29-38. Observations and interpretation Amplitude [mmag] GD 99 was previously observed in 1975 (McGraw & Robinson 1976) and in 2003 (Chynoweth et al. 2004). On three consecutive nights we obtained 23 hours of observation in white light at Piszkéstető, the mountain station of Konkoly Observatory in February 2002, with a CCD attached to the 1m telescope. Data reduction and frequency analysis were carried out by using the standard IRAF packages and the MUFRAN package (Kolláth 1990). 15 10 5 0 0 200 400 600 800 1000 1200 Period [s] Figure 1: All the excited periods of GD 99 at different epochs. Four periods (1058.1, 228.7, 1026.1 and 223.9 s) were identified with amplitudes of 7.0, 5.8, 4.0 and 2.4 mmag, respectively, in 2002. Three of them (1058.0/8.3, 228.9/4.5 and 223.6/2.9, P(s)/A(mma)) are confirmations of modes given by Mukadam et al. (2006) (hereafter M06). The fourth period is a newly identified mode. Their other modes and three short period modes (frequencies given by Bradley (2000); amplitudes given by Clemens (1993)) are presented in Fig 1. The last three modes are not included in M06 because of uncertainty. The unusual behaviour of GD 99 (Teff = 11820 K, log g ∼ 8.08) is obvious: despite the well-established trend of decreasing pulsation period with increasing effective temperature, GD 99 (situated on the blue edge of the DAV instability strip) shows both short and long periods. Some kind of grouping can be seen both among the long and short period modes. The spacing in the short period group is about twice as large as than the spacing in the long period group. 252 GD 99 - an unusual, rarely observed DAV white dwarf Recently a new classification criterion was published (M06). Based on the weighted mean period hot, intermediate and cool subclasses were introduced. According to the spectroscopic temperature GD 99 belongs to the hot subclass. The weighted mean period puts it into the intermediate class. GD 99 could be situated in the cool subclass if we regard only the modes given by M06. It is quite improbable that a single star belongs to both subclasses. If we interpret the groups of long and short period modes separately, a plausible explanation could be a binary nature. One component is situated at the hot and the other at the cool border of the instability strip. The effective temperature and pulsation periods of WD 2350-0054 (Mukadam et al. 2004) and G29-38 (Kleinman 1995) also do not fit the general trend of DAV stars. According to the binary concept, one component of WD 2350-0054 would pulsate, and the other should pass the red edge of the DAV instability strip. In the hypothetic binary concept of G29-38, one component pulsates with a long period, while the other has not passed over the blue edge of the DAV instability strip. GD 99 definitely needs a more complex investigation (DARC/WET run). References Bradley P. A., 2000, Baltic Astron., 9, 485 Clemens J. C., 1993, Baltic Astron., 2, 407 Chynoweth K. M., Thompson S., Mullally F., Yeates C. 2004, BAAS, 36, 1514 Kleinman S. J., 1995, Ph.D. Thesis, Univ. of Texas at Austin Kolláth Z., 1990, Occ. Techn. Notes Konkoly Obs., No. 1 McGraw J. T., Robinson, E. L., 1976, ApJ, 205, L155 Mukadam A. S., Winget D. E., von Hippel T., et al., 2004, ApJ, 612, 1052 Mukadam A. S., Montgomery M. H., Winget D. E., Kepler S. O., Clemens J. C., 2006, ApJ, 640, 956 Comm. in Asteroseismology Vol. 150, 2007 Mapping Convection using Pulsating White Dwarf Stars M. H. Montgomery 1,2 2 1 Department of Astronomy, University of Texas, Austin, TX 78712, USA Delaware Asteroseismic Research Center, Mt. Cuba Obs., Newark, DE, USA Parametrization of Convection Zone As shown by Montgomery (2005), the non-sinusoidal shape of the light curves of pulsating white dwarf stars can be used to constrain models of convection in these objects. In particular, τ , the timescale on which the convection zone responds to a change in input flux at its base, can be parametrized as „ « Teff −N τ = τ0 , Teff0 where τ0 and Teff0 are the equilibrium values of τ and the effective temperature, respectively, Teff is the instantaneous effective temperature, and N is an exponent which determines how rapidly the depth of the convection zone changes with Teff . Figure 1: τ0 versus Teff assuming the pure He (no H) Teff values from Table 1. Table 1: Derived convective parameters for two DBVs star θi (deg) τ0 (sec) N Teff (no H) Teff (with H) GD 358 PG1351+489 62 58 450 87 25 21 24 900 K 26 100 K 24 700 K 22 600 K 254 Mapping Convection using Pulsating White Dwarf Stars Mapping the DBV Instability Strip We currently have examined two stars in the DBV instability strip: PG 1351+489 and GD 358. In Table 1, we list the convective parameters of the fits to these stars, as well as the derived inclination angles, θi . In addition, we list the effective temperatures determined from spectroscopic fits (Beauchamp et al. 1999), both for the case of pure He atmospheres and for the case of H contamination. In Fig. 1, we show the location and slopes of these stars in the log τ0 − Teff plane, and we show the predictions of the Böhm & Cassinelli (1971) mixing length theory (ML2) for various values of α (dashed curves). ML2/α = 1.1 provides a reasonable fit to the τ0 of these stars. We note that if the effective temperatures assuming H contamination are used, we obtain the nonsensical result that the cooler star has the thinner convection zone (i.e., smaller value of τ0 ), something which is not possible based on very general arguments. Acknowledgments. This research was supported in part through National Science Foundation grant AST-0507639. References Beauchamp A., Wesemael F., Bergeron P., et al., 1999, ApJ, 516, 887 Böhm K.-H., Cassinelli J., 1971, A&A, 12, 21 Montgomery M. H., 2005, ApJ, 633, 1142 Orlagh Creevey, Travis Metcalfe (partly obscured), Dennis Stello and Mike Montgomery. Comm. in Asteroseismology Vol. 150, 2007 Towards Asteroseismology of Long-Period Variable Subdwarf B Stars S. K. Randall,1 G. Fontaine,2 P. Brassard,2 E. M. Green3 1 European Southern Observatory, Garching bei München, Germany 2 Université de Montréal, Montréal, Québec, Canada 3 Steward Observatory, University of Arizona, Tucson, Arizona, USA Abstract Given the recent successes in the asteroseismological study of short-period variable subdwarf B stars, we investigate the asteroseismic potential of their long-period pulsating counterparts on the basis of both ground- and space-based photometry. We find the interpretation of the slow oscillators to be more challenging than that of the fast pulsators for a variety of reasons, however the first results obtained are encouraging and should pave the way for future observational efforts. Introduction During the last few years, we carried out an extensive observational campaign aimed at quantifying and interpreting the period spectra exhibited by members of the recently discovered class of slowly pulsating subdwarf B stars (Green et al. 2003). Generally cooler than their rapidly oscillating counterparts, these are thought to excite high radial order gravity modes with periods of the order of an hour through the action of a classical kappa mechanism associated with a local overabundance of heavy elements (Fontaine et al. 2003). We obtained an average 300+ hours of time-series photometry for each of three representative targets - PG 1627+017, PG 1338+481, PG 0101+039 - in the course of two dedicated multi-site campaigns on 1 to 2 m-class telescopes as well as an exploratory run on the 15 cm MOST space telescope. In what follows, we present a brief overview of the period spectra extracted for all three stars and their potential for asteroseismology; for more details please see Randall et al. (2006). Campaign Results From the periodicities extracted from the Fourier transforms of the combined light curves for the three long-period variables monitored we notice that 1. The periods and amplitudes of the pulsations seem to decrease the hotter and more compact the target. While the first effect is in line with current non-adiabatic theory, the second cannot be explained by linear pulsation calculations. 2. The distribution of the period spectra is non-uniform, with a central agglomeration of dominant peaks apparently separated from higher and lower frequency clusters of lower excess power, and closely spaced periodicities occurring within the clusters. One possible explanation is the preferential channelling of energy into certain frequency bands by an unknown mode selection mechanism, as has also been suggested for other types of variable stars. 256 Towards Asteroseismology of Long-Period Variable Subdwarf B Stars 3. In the case of PG 1338+481, we see a relatively uniform period spacing of around 275 s between six of the high-amplitude oscillations. This corresponds to the near-asymptotic behaviour predicted for = 1 modes with consecutive radial orders from appropriate stellar models, an interpretation which is also supported by the exploitation of multicolour photometry. Assuming this mode identification as well as the values of log g and Teff inferred from spectroscopy, we were able to narrow down the other fundamental parameters for this target, but failed to find a unique and well-constrained family of optimal models. Conclusions 1. Asteroseismology of long-period variables is more challenging than that of their shortperiod counterparts due to difficulties in extracting the much slower pulsations observationally, probable deficiencies in the models, and the weak dependence on the internal stellar parameters of the high-order g modes themselves. 2. In order for asteroseismology to be viable, assumptions regarding the mode identification and the spectroscopic parameters have to be made from the outset. This requires knowledge of the degree indices using an independent means (such as multi-colour photometry, line profile variations or rotational splitting) as well as tightly constrained values of log g and Teff . 3. The future of these stars’ study clearly lies in space-based observations with satellites such as MOST or COROT, which can monitor targets for several weeks without significant gaps and enable the extraction of more periodicities. References Fontaine G., Brassard P., Charpinet S., et al., 2003, ApJ, 597, 518 Green E. M., Fontaine G., Reed M. D., et al., 2003, ApJ, 583, L31 Randall S. K., Green E. M., Fontaine G., et al., 2006, ApJ, 645, 1464 Comm. in Asteroseismology Vol. 150, 2007 An old puzzle in a new light: PG 1336−018 M. Vučković,1 C. Aerts,1,2 R. Østensen,1 G. Nelemans,2 H. Hu,1,2 V. S. Dhillon,3 T. R. Marsh,4 and C. S. Jeffery 5 2 1 Instituut voor Sterrenkunde, K. U. Leuven, Belgium Department of Astrophysics, Radboud University Nijmegen, The Netherlands 3 Department of Physics and Astronomy, University of Sheffield, UK 4 Department of Physics, University of Warwick, UK 5 Armagh Observatory, Northern Ireland Abstract We present the first preliminary results from VLT photometric and spectroscopic observations of PG 1336−018, a rapidly pulsating eclipsing sdB binary. Observations High–speed multicolour photometric observations of PG 1336−018 were acquired on May 19, 2005 with the 3-channel ULTRACAM camera (Dhillon & Marsh 2001) attached to the ESO VLT at Paranal Observatory in Chile. We gathered about 5 h of data simultaneously in three bands u’, g ’ and r ’ of the SDSS system (Fukugita et al. 1996). The data were reduced using the standard ULTRACAM reduction pipeline software. Three differential light curves of PG 1336−018 were obtained, one for each filter. The g ’ light curve is presented in Fig. 1 (top panel). We have also obtained high–resolution time series spectroscopy of this unique star. A total of 399 high–resolution spectra was gathered with the UVES spectrograph attached to the ESO VLT at Paranal Observatory, Chile, on 28 April 2005, covering about 4 full orbits. Results We measured radial velocities by fitting two Gaussians to the highest S/N Balmer lines in the spectrum. A sinusoidal fit to the radial velocity curve gives an amplitude K1 = 79.6 ± 0.6 km/s, in agreement with Kilkenny et al. (1998). The best simultaneous fit for Teff , log g and helium abundance yields: Teff = 31300 ± 250, log g = 5.60 ± 0.05 and log y = −2.93 ± 0.05. Numerical orbit solutions have been investigated using PHOEBE (Prša & Zwitter 2005). Even though a unique solution is impossible to select, given the large number of free parameters and the strong correlations between orbital parameters, theoretical considerations give a most favourable solution with a mass of the sdB primary of 0.484 ± 0.006 M and a mass ratio 0.262 ± 0.002 for the system. The best orbit solution is presented in Fig.1, together with the residuals before and after prewhitening with the four highest amplitude oscillation frequencies found in our data set. A detailed presentation of this work can be found in Vučković et al. (2007). References Dhillon V., Marsh, T., 2001, New Astr. Rev., 45, 91 Fukugita M., Ichikawa T., Gunn J. E., et al., 1996, AJ, 111, 1748 Kilkenny D., O’Donoghue D., Koen C., Lynas-Gray A. E., van Wyk F., 1998, MNRAS, 296, 329 Prša A., Zwitter T., 2005, ApJ, 628, 426 Vučković M., Aerts C., Østensen R., et al., 2007, A&A, submitted 258 An old puzzle in a new light: PG 1336−018 12.0 11.0 Flux ratio 10.0 9.0 8.0 7.0 6.0 Residuals Residuals 5.0 4.0 0.4 0.2 0.0 -0.2 -0.4 0.4 0.2 0.0 -0.2 -0.4 0.46 0.48 0.50 0.52 0.54 0.56 0.58 0.60 0.62 0.64 0.66 0.68 0.70 HJD - 2453509.0 Figure 1: The ULTRACAM/VLT g ’ phase binned light curve together with the synthetic light-curve solution (PHOEBE). The middle panel shows the residuals. The bottom panel shows the residuals after prewhitening. Dave Kilkenny enjoys Karen Pollard’s and Maja Vučković’s company. Comm. in Asteroseismology Vol. 150, 2007 Time resolved spectroscopy of the multiperiodic pulsating subdwarf B star PG 1605+072 A. Tillich,1 U. Heber,1 S. J. O’Toole 2 1 Dr.Remeis-Sternwarte Bamberg, Universität Erlangen-Nürnberg, D-96049 Bamberg, Germany 2 Anglo-Australian Observatory, P.O. Box 296 Epping, NSW 1710, Australia We present results for the 2m spectroscopic part of the MultiSite Spectroscopic Telescope campaign, which took place in May/June 2002. In order to perform an asteroseismological analysis on the multiperiodic pulsating subdwarf B star PG 1605+072 we used over 150 hours of time resolved spectroscopy to search for and analyse line profile variations by using phase binning. This pilot analysis using the BRUCE and KYLIE programs and assuming strong rotation and low inclination favours models with = 1 or = 2 with m ≤ 0. The MSST data and phase binning Four observatories (Steward Observatory, ESO, Siding Spring Observatory, NOT) produced 10892 time resolved spectra. O’Toole et al. (2005) detected the 20 strongest modes in radial velocity. Here we treat the data sets of each telescope separately. After reducing the spectra using IRAF we coadded them according to their phase for the four dominant modes. Then we fitted LTE-model spectra using the FITPROF program (Napiwotzki, 1999) in order to determine simultaneously the three atmospheric parameters for every bin. The results derived from the Steward Observatory data are shown in Fig. 1. Figure 1: Top: variations of the atmospheric values with errors and sine fit for the strongest mode f1 (481.74 s). Bottom: temperature variations for the four strongest modes with errors and sine fit. 260 Time resolved spectroscopy of the multiperiodic pulsating subdwarf B star PG 1605+072 Modelling of line profile variations and mode identification In order to identify the modes, we used the BRUCE and KYLIE routines (Townsend 1997), to model various pulsation modes by perturbing our static models. We then determined the atmospheric parameters of the perturbed models using FITPROF. The required parameters eq (vrot = 130 kms−1 , i = 17◦ ) were taken from previous analyses (Heber et al. 1999; Kawaler 1999). The results are shown in Fig. 2. Figure 2: Variation of Teff and log g with errors and sine fit. Top: models for = 1, m = ±1. Bottom: observations of the dominant period and model = 1, m = 0. For the the dominant period (481.74 s) the mode with = 1, m = 0 is the best fit. But also for the other three modes, this pilot analysis assuming strong rotation and low inclination favours models with = 1 or = 2 with m ≤ 0. Nevertheless the parameter range has to be further exploited to derive a consistent model. References Heber U., Reid I. N., Werner K., 1999, A&A, 348, L25 Kawaler S. D., 1999, in Solheim J.-E., ASP Conf. Ser. Vol. 169, 11th European Workshop on White Dwarfs. Astron. Soc. Pac., San Francisco, p. 158 Napiwotzki R., 1999, A&A, 350, 101 O’Toole S. J., Heber U., Jeffery C. S., et al., 2005, A&A, 440, 667 Townsend R. H. D., 1997, PhD Thesis, University College London, UK Comm. in Asteroseismology Vol. 150, 2007 Change of splittings in Balloon 090100001 Baran,1,2 A. R. Oreiro,3,4 A. Pigulski,5 F. Pérez,3,4 A. Ulla,6 R. Garrido,7 C. Rodrı́guez,6,7 T. Monserrat,3 L. Fox Machado,3 J. M. Gonzáles,3 M. Reed,8 A.-Y. Zhou,8 S. Harms,8 J. R. Eggen,8 S-L. Kim,9 R. Crowe,10 K-J. Choo,9 W-P. Chen,11 H-T. Lee,11 F-Y. Huan,11 M. Siwak,1 D. Koziel,1 S. Zola 1 1 Mt. Suhora Observatory, Poland Toruń Centre for Astronomy, Poland 3 Instituto de Astrofisica de Canarias, Spain 4 Universidad de La Laguna, Spain 5 Uniwersytet Wroclawski, Poland 6 Universidade de Vigo, Spain 7 Instituto de Astrofı́sı́ca de Andalucı́a – CSIC, Spain 8 Missouri State University, USA 9 Korea Astronomy & Space Science Institute, Korea 10 University of Hawaii at Hilo, USA 11 National Central University, Taiwan 2 Abstract We present the first results obtained during the multi-site campaign on the brightest pulsating sdB star Balloon 090100001. Our campaign was carried out in August and September 2005 spanning over 7 weeks. From the frequency analysis we confirm most of frequencies discovered during the 2004 campaign including an equidistant triplet and a quintuplet. The triplet and quintuplet have nearly the same separations, clearly indicating that rotational splitting might be involved. However, the splitting of multiplets increased by about 15% between 2004 and 2005. As far as we are aware, this is the first example of such a large change of frequency splitting in a pulsating star. The data and results The 2005 campaign involved eight optical telescopes. The frequency resolution was around 0.5μHz, similar to that in 2004 data (Baran et al. 2005), but the noise level and aliases were considerably lowered (Baran et al., in preparation). It appeared from the preliminary analysis of the 2005 data that the amplitudes of some modes change on a time scale of days or weeks. We therefore allowed linear amplitude changes in the analysis. The data were analysed by means of the Fourier transform with consecutive prewhitening of detected frequencies. There were nine modes in the 2.8 mHz region detected: the main mode, the triplet and the quintuplet. Their frequencies derived from the 2004 and 2005 data are schematically shown in Fig. 1. The frequencies of the main mode and the central peak of the triplet did not change between 2004 and 2005. On the other hand, the three frequencies of the quintuplet detected both in 2004 and 2005, presumably with m = +2, +1 and −1, changed their frequencies. However, the multiplets remained almost symmetrical. The average splitting for the triplet increased by about 14%, while for the quintuplet by about 12% for the |m| = 1 and by 21% for the |m| = 2 components. What can cause this to happen? If we assume that this splitting is caused only by rotation we have to explain how the star increased its rotational frequency by 15%, on average, during a year. Magnetic fields measured 262 Change of splittings in Balloon 090100001 2004 2005 2.81 2.82 2.83 2.84 Frequency [mHz] 2.85 2.86 Figure 1: Schematic Fourier spectrum of Balloon 090100001 in the region of the dominant mode. in a few sdB stars, about 1.5 kG (O’Toole et al. 2005), are too weak to cause this effect. A combination of the rotational splitting modulated by a magnetic field can be a plausible explanation. It seems that this star is really an unusual object among all pulsating sdB stars and monitoring of its pulsational properties is undoubtedly worth doing. Acknowledgments. This work was supported by the grant 1 P03D 013 29. References Baran A., Pigulski A., Koziel D., et al., 2005, MNRAS, 360, 737 O’Toole S. J., Jordan S., Friedrich S., Heber U., 2005, A&A, 437, 227 Hans Bruntt has something interesting to show to Tanya Ryabchikova and Luca Fossati. Comm. in Asteroseismology Vol. 150, 2007 Mode identification in the pulsating subdwarf Balloon 090100001 by means of the spectrophotometric method A. Baran,1,2 A. Pigulski,3 S. J. O’Toole4 1 Mt. Suhora Observatory, Poland Toruń Centre for Astronomy, Poland 3 Astronomical Institute, University of Wroclaw, Poland 4 University of Sydney, Australia 2 Abstract We present the first successful application of the spectrophotometric method of mode identification to a pulsating subdwarf B star, Balloon 090100001. We confirm that the dominant mode is radial and that the observed triplet can be interpreted in terms of a rotationally split dipole mode. The data and results Balloon 090100001 (hereafter Bal09), a recently discovered pulsating subdwarf, appeared to be extremely interesting because both p and g modes were revealed in its frequency spectrum. In addition, two rotationally split multiplets, a triplet and a quintuplet, were detected. The star was observed during two photometric campaigns in 2004 (Baran et al. 2005, Oreiro et al. 2005) and 2005. Multicolour BVRI photometry was obtained. Simultaneously with the photometric observations, spectroscopic observations were carried out by Telting & Østensen (2006). Six modes with the largest amplitudes were detected in the radial velocities. Using the photometric and spectroscopic observations, we applied the method elaborated by Daszyńska-Daszkiewicz et al. (2003) to Bal09. A grid of model atmospheres (Heber et al. 2000) for sdB stars was calculated for this purpose. Since six modes were detected in radial velocities, only these modes could be identified by means of the full version of the method. The results of the application of the spectrophotometric method to Bal09 are shown in Fig. 1. From the data available to us, we were not able to unambiguously identify the values of any of the detected modes on the basis of the photometry alone. Including spectroscopy, we get unambiguous discrimination of for the two modes with the largest amplitudes, f1 and f2 , while for the others, two or three values of are equally possible. From the frequency pattern, we have already suggested (Baran et al. 2005) that the dominant mode in Bal09 is radial and the triplet represents the rotationally split = 1 mode. This is now confirmed by this work, as the strongest triplet component, f2 , has a convincingly identified value of equal to 1, and for the other two, f3 and f4 , = 1 is one of the possibilities. Acknowledgments. This work was supported by the grant 1 P03D 013 29. References Baran A., Pigulski A., Koziel D., et al., 2005, MNRAS, 360, 737 Daszyńska-Daszkiewicz J., Dziembowski W. A., Pamyatnykh A. A., 2003, A&A, 407, 999 Heber U., Reid I. N., Werner K., 2000, A&A, 363, 198 Oreiro R., Pérez Hernández F., Ulla A., et al., 2005, A&A, 438, 257 Telting J. H., Østensen R., 2006, A&A, 450, 1149 264 Mode identification in the pulsating subdwarf Balloon 090100001 PHOTOMETRY + SPECTROSCOPY MODE PHOTOMETRY r2 10 1 5 r2 0 6 4 0 1 2 2 3 4 0 1 3 4 0 1 2 3 4 0 1 2 3 4 0 1 2 3 4 2 2 r2 0 6 0 1 2 3 4 4 3 2 r2 0 6 0 1 2 3 4 4 4 2 r2 0 6 0 1 2 3 4 4 8 2 r2 0 6 4 0 1 2 3 4 4 0 1 2 3 0 1 2 3 Spherical degree l B 2 0 0 1 2 3 Spherical degree l 4 4 Figure 1: Discrimination of the spherical degree for the six strongest modes in Bal09 by means of the spectrophotometric method. The panels show reduced χ2 for five different spherical degrees , ranging from 0 to 4, for six modes detected in spectroscopy. Open circles indicate the result of the discrimination, i.e., the possible values of . Comm. in Asteroseismology Vol. 150, 2007 Time resolved spectroscopy of Balloon 090100001 R. Østensen,1 J. Telting,2 U. Heber 3 1 Instituut voor Sterrenkunde, Leuven, Belgium Nordic Optical Telescope, La Palma, Spain Dr. Remeis-Sternwarte, Bamberg, Germany 2 3 Abstract We obtained 2552 good low-resolution spectra of the bright sdBV star Balloon 090100001 with the Nordic Optical Telescope in August/September 2004. Results of the frequency analysis of this dataset have already been published (Telting & Østensen 2006; TØ06). Eight independent frequencies were recovered in radial velocity and equivalent width, all in agreement with established photometric pulsation frequencies (Baran et al. 2006). The radial velocity amplitude of the main mode was found to be 18.9 km/s which is the largest radialvelocity amplitude found in a pulsating sdB star. Here we report our preliminary results from phase folding and fitting the spectroscopic data to synthetic model grids. Results and analysis Our spectra cover the wavelength range 3500 – 5050 Å with a spectral resolution of ∼ 3 Å at a dispersion of 0.77 Å/px. Each exposure was 30 s. In order to derive physical parameters, we fit the spectroscopic data to an LTE hydrogen + helium model grid suitable for sdB stars in this temperature range (Heber et al. 2000). The normalized and detrended spectra were folded into 20 phase bins on the main pulsation period, with the first bin centered on the phase given in Table 7 of TØ06. The physical parameters derived from this procedure is shown in Fig. 1. A sinusoidal fit (dotted line) to the points gives: Teff = 28883 ± 1186 ± 23 K, log g = 5.416 ± 0.084 ± 0.002 and log y = −2.730 ± 0.003. The values quoted for Teff and log g are the mean, amplitude and fitting error of the sinusoidal fit, and for log y just the rms error when fitting a constant. The amplitude of the radius variation due to the 18.9 km/s velocity amplitude of the main mode is Ar = Av P/2 = 1072 km; the corresponding acceleration is Aa = Av 2/P = 333 m/s2 . At the observed mean gravity this corresponds to log g = 0.056 dex. The change in gravity due to the change in radius is only log g = 0.006 dex. Together these come close to the observed gravity variation of log g = 0.084 dex, but the discrepancy is significant. Due to the high amplitude of the main mode and the complex shape of the window function of our observations (see Fig. 3 in TØ06), the second, third and fourth highest peak in the radial velocity spectrum are all strongly contaminated by the main mode, and are only recovered in the Fourier transform after prewhitening. Phase folding of the spectra on the secondary pulsation frequencies can therefore not produce anything useful, unless we first prewhiten the main mode from the spectra. We have implemented a procedure that generates a synthetic spectrum of the main pulsation mode for each spectroscopic observation, and subtracts the difference between the model for the time of observation and a model for the mean parameters, before folding the spectra on the secondary frequencies. This procedure gives useful results for the second highest peak in the velocity spectrum (see Fig. 1). The fourth peak is also recovered using this procedure, but we still have problems with the third peak. 266 Time resolved spectroscopy of Balloon 090100001 Figure 1: Upper panel: Spectroscopic model fit to the 20 spectra binned on the main pulsation period. The upper curve is the gravity, the middle shows effective temperature and the lower curve the Helium abundance. Note that the temperature and gravity were refitted, after fixing the Helium abundance to the mean value. Lower panel: Same, but for the spectra folded on the second highest pulsation frequency, and after spectral prewhitening of the main mode. References Baran A., Oreiro R., Pigulski A., Pérez Hernández F., Ulla A., 2006, Baltic Astron., 15, 227 Telting J. H., Østensen R., 2006, A&A, 450, 1149 Heber U., Reid I. N., Werner K., 2000, A&A, 363, 198 Comm. in Asteroseismology Vol. 150, 2007 The frequency distribution of PG 1657+416, a rapidly pulsating sdB star R. Oreiro,1,2 F. Pérez Hernández,1,2 R. Østensen,3 J.-E. Solheim,4 J. MacDonald,5 A. Ulla 6 1 Instituto de Astrofı́sica de Canarias, 38200, La Laguna, Spain 2 Universidad de La Laguna, 3820, La Laguna, Spain 3 Instituut voor Sterrenkunde, 3001, Leuven, Belgium 4 Institude of Tehoretical Astrophysics, University of Oslo, Norway 5 Department of Physics and Astronomy, University of Delaware, DE 19716 6 Dpto. Fı́sica Aplicada, Universidade de Vigo, 36310, Spain Abstract We analyse the frequencies shown by the recently discovered pulsating sdB star PG 1657+416. It has at least four frequencies in the range 6.8–7.8 mHz, which are used to constrain the log g value of the star. Moreover, we derive an estimate of the radial order of the modes on the basis of the observed frequency distribution. Introduction PG 1657+416 was discovered to show periodic light variations during a program to search for pulsating sdBs of the V361 Hya type (see Kilkenny 2007). Additional photometric data were acquired in order to undertake a theoretical analysis based on the observed frequencies of the star. The observations, as well as the data analysis and some theoretical results, are described by Oreiro et al. (2006). The frequency spectrum, whose schematic version is displayed in Fig. 1, reveals at least four frequencies showing variable amplitudes, always below 2.7 mma. Figure 1: Schematic amplitude spectrum of PG 1657+416. The frequency separations (μHz) between the peaks are also indicated. Physical parameters from spectrocopic fit 2MASS photometry (J = 15.8, H = 15.64, KS = 15.13) clearly identifies PG 1657+416 as a system containing a hot subdwarf plus a main sequence star (Stark & Wade 2003). Thus, a line profile fit to the SDSS spectrum was performed only after the companion star contribution was removed (see Oreiro et al. 2006). The spectroscopic fit gives Teff = 32 200 ± 500 K, log g = 5.73 ± 0.10 dex. 268 The frequency distribution of PG 1657+416, a rapidly pulsating sdB star Physical parameters from seismology The frequency distribution (Fig. 1), consisting of four peaks in a narrow frequency range (< 1 mHz), allows the possibility of all of them having different value (considering modes with ≤ 3. Also, two peaks could have the same degree with consecutive radial order n. In this case, only three possible cases exist, giving a frequency separation for modes with consecutive n in the range Δν = 0.676 − 0.940 mHz. Theoretical Δν separations were computed for acustic modes of a grid of structural models. Δν is known to be a linear function of the square root of the mean density of a model (< ρ >1/2 ), which is fulfilled by our sdB models, as can be seen in the left panel of Fig. 2. The linear dependence can be fitted to: < Δν(mHz) >= −0.0298 + 0.961 < ρ(cgs) >1/2 . Figure 2: Left: Mean value of the frequency separation between p-modes with the same degree and consecutive n as function of the < ρ >1/2 of the model. Right: frequency of the fundamental mode as function of the log g value of the model. The observed frequencies of PG 1657+416 would correspond to a mean density in the range < ρ >= 54.4 − 102.7 gcm−3 that, assuming a total mass of 0.47 M , leads to a possible range in log g = 5.38 − 5.57 dex, relatively lower than the spectroscopic derivation, which would imply either that the four peaks have different value, or that the errors in the spectroscopic fit are larger than those previously considered. On the other hand, the frequency of the fundamental mode ( = 0, n = 1) of a given model follows the behaviour shown in the right panel of Fig. 2. Using a second order polynomial, this dependence can be expressed as: νfund = 85.70 − 35.6 log g + 3.74 log g 2 , which would place the fundamental mode of PG 1657+416 in the interval 2.27 − 3.32 mHz, given the possible log g range. In this case, the observed frequencies would have radial orders: 4 − 7 ≤ nobs ≤ 6 − 9, where the lower (upper) range corresponds to the possibility with the higher (lower) log g value. References Kilkenny D., 2007, these proceedings Oreiro, R., Pérez Hernández, F., Østensen, R., Solheim, J.-E., MacDonald, J. & Ulla, A., 2006, A&A, accepted Stark, M. & Wade, R., 2003, AJ, 126, 1455 Comm. in Asteroseismology Vol. 150, 2007 Observations of 23 EC 14026-type pulsating subdwarf B stars M. D. Reed,1 D. M. Terndrup,2 J. R. Eggen,1 and C. T. Unterborn 2 1 Department of Physics, Astronomy and Material Sciences, Missouri State Univ., Springfield, MO, USA 2 Department of Astronomy, The Ohio State University, Columbus, OH 43210 USA Abstract Since the discovery of pulsating subdwarf (sdB) stars in 1997 (the EC 14026 class), nearly 40 members have been discovered. After nearly a decade, many of these have had significant follow-up observations to resolve their pulsation spectra and to discern their pulsation properties. In this work we compare and contrast the frequency content in terms of richness and range and the amplitudes and phases for 23 sdB pulsators. We draw no conclusions but merely show the incredible variety of pulsations emanating from seemingly similar stars. Pulsation properties Figure 1 shows some of the tests we have applied to the resolved pulsators. Panel A compares the ratio of high-amplitude (with A≥Amax /5) to total frequencies for individual pulsators with gravity. Note that this ratio is lowest for stars with lower gravity (i.e. less even-amplitudes) while all of the H/T=1 values (roughly equal amplitude pulsations) occur for higher gravity, though there are exceptions. Panel B compares the summed pulsation amplitudes (solid lines with the top line representing the lowest-amplitude 90% of frequencies, and subsequent lines indicating the fractional amplitudes of the lowest 70%, 50%, and 10%, respectively) while the dashed line indicates the fractional amplitude of the highest-amplitude frequency. The stars are ordered by, but not scaled with gravity. Like panel A, this indicates a general trend for lower gravity stars to have relatively few pulsation frequencies that contain nearly all of the pulsation power. But it also indicates the large variety observed as stars near log g ∼ 5.7 have a complete range of values. Panel C shows the frequency density compared to gravity with the dotted line indicating the limit for ≤ 2, m = 0 and the dashed line indicating the limit for ≤ 2, all possible m values. For several stars, ≥ 3 values are required to explain the observed density. Panel D shows the amplitude deviations divided by the average amplitude as a measure of pulsation stability. The open circles indicate frequencies known to be phasestable over time, filled triangles indicate non-phase-stable frequencies, and squares indicate frequencies for which the stability of phases is unknown. The dashed line is σA /A = 0.52, a value indicative of stochastic oscillations and the horizontal bar is the average error. For the full comparison, see our paper in MNRAS, which is coming soon. Acknowledgments. Support for DMT came in part from funds provided by the Ohio State University Department of Astronomy. Support for MDR is from the National Science Foundation under Grant Number AST007480, the American Astronomical Society and Missouri State University. Travel for JRE was supported by the Missouri Space Grant Consortium. 270 Observations of 23 EC 14026-type pulsating subdwarf B stars Figure 1: Group properties of sdBV pulsators. Mike Reed and Dave Kilkenny finding some time to relax. Comm. in Asteroseismology Vol. 150, 2007 Time-Series Spectroscopy of the subdwarf B Star PG 1219+534 J. R. Eggen,1 M. D. Reed,1 S. J. O’Toole,2 J. H. Telting,3 R. Østensen,4 D. M. Terndrup,5 S. L. Harms,1 A.-Y. Zhou,1 R. L. VanWey 1 1 Missouri State University, Missouri, USA Anglo-Australian Observatory, PO Box 296, Epping NSW 1710, Australia 3 Nordic Optical Telescope, Apartado 474, 38700 Santa Cruz de La Palma, Spain Instituut voor Sterrenkunde, Katholieke Univ. Leuven, Celestijnenlaan 200 D, B-3001 Leuven, Belgium 5 Department of Astronomy, The Ohio State University, 140 W. 18th Avenue, Columbus, Ohio, USA 2 4 Abstract We report on the progress of the analysis of our time-series spectroscopy of the pulsating sdB star PG 1219+534. PG 1219+534 has four stable pulsation frequencies (6721, 6961, 7490, and 7807 μHz) with nearly constant photometric amplitudes. The pulsation spectrum is simple enough to be resolved within a couple of hours, yet complex enough that multiple -degrees must be present. Our data set consists of 5072 spectra obtained in April 2004 from the Mayall 4m at Kitt Peak National Observatory (KPNO), at 1.4Å/pixel resolution, and the Nordic Optical Telescope (NOT), with 0.8Å/pixel resolution. Though still under analysis, we have already measured line-centroid variations to discern pulsation velocities using Balmer and He I lines between 3750 and 5000 Å. Preliminary Results We have detected significant radial velocity variations from the NOT data with marginal detections in the KPNO data. The left panels of Fig. 1 show the Fourier transforms of the KPNO, NOT, and total data sets. Insets are the data windows, solid lines indicate the 4σ detection limit and dashed lines indicate the positions of the photometric pulsations. We have noticed substantial differences in velocity amplitudes between the KPNO and NOT data, which are temporally separated by one week. Photometric amplitudes, obtained simultaneous to the spectroscopic data are stable. Night-to-night velocity variations are also marginally detected in the NOT data. We suspect these may be a systematic effect, but have not yet found the culprit. The NOT data were also phase-binned (Fig. 1, right panels) by the four known pulsation frequencies. While the scatter of the individual points is relatively large, average values (fit with a solid line) clearly show the velocity variations. We have also completed a preliminary search for equivalent width variations in the Balmer lines, but no variations were detected. We are now completing a more thorough analysis of pulsation velocities, searching again for equivalent width variations, and fitting phase-binned spectra to atmospheric models to measure temperature, gravity, and changes in the helium ionization fraction caused by pulsation. Along with a velocity/photometry comparison, we anticipate that our results will constrain the modes of pulsation. Acknowledgments. Support for MDR is from the National Science Foundation under Grant Number AST007480, the American Astronomical Society and Missouri State University. Travel for JRE was supported by the Missouri Space Grant Consortium. 272 Time-Series Spectroscopy of the subdwarf B Star PG 1219+534 Figure 1: Left: Fourier transforms of radial velocity data. Right: Pulsation phase-binned velocities of the NOT data. The pulsation frequencies (in μHz) are provided in each panel along with a best-fit line. Comm. in Asteroseismology Vol. 150, 2007 Stability analysis of sdO equilibrium models C. Rodrı́guez-López,1,2 R. Garrido,1 A. Moya,1 J. MacDonald,3 A. Ulla 2 1 Instituto de Astrofı́sica de Andalucı́a-CSIC, E 18008 Granada, España 2 Universidad de Vigo, E 36200 Vigo, España 3 University of Delaware, DE 19176 Newark, USA Abstract We present fully nonadiabatic calculations describing the driving of pulsations in equilibrium models of sdO stars. The first pulsating sdO, SDSS J160043.6+074802.9 has been recently discovered showing short period oscillations suggesting p modes. Stability analysis Hot subdwarf O stars (sdOs) are blue subluminous objects in a stage immediately prior to the white dwarf phase. With the final aim of using the tools of asteroseismology to unravel the sdO’s evolutionary state, we undertook a theoretical stability analysis to explore their feasibility as pulsators. The evolution code JMSTAR (Lawlor & MacDonald 2006) was used to calculate a total of 16 sdO equilibrium models corresponding to different full evolutionary sequences. We used the nonadiabatic code of oscillations GRACO (GRAnada COde, Moya et al. 2004) to perform the nonadiabatic analysis (Rodrı́guez-López 2007). Out of the 16 models, one (Teff = 45 000K, log g = 4.2, Z = 0.14) was found to drive unstable modes. We plot below the normalized growth rate, η, vs. frequency as an indicator of the stability (η < 0) or instability (η > 0) of the mode; and the derivative of the work integral and opacity vs. log q (= 1 − Mr /M). A negative (positive) value of dW /dlog q at a given location in the model indicates that this region contributes locally to driving (damping) of the mode. We found excited modes, for = 2, within the frequency ranges: 0.29 ≤ ν ≤ 0.32 and 0.38 ≤ ν ≤ 0.42 mHz. The excited modes fall within a wider range favoured for instability 0.2 ≤ ν ≤ 1.5 mHz. Meanwhile, modes with frequencies ν ≥ 2 mHz were found highly stable with values of η = −1. Figure 1 (bottom left) plots the g190 mode with ν = 0.31 mHz and η = 0.17 as representative of the two zones of instability. There is a wide driving zone at the location of the Z -bump. Hence, the instability is explained by the classical κ-mechanism associated with partial ionization of heavy elements in the envelope of the star, the same mechanism that drives oscillations in sdB pulsators. In this case, the excited modes correspond to high radial order g modes. Figure 1 (bottom right) plots the g177 mode with ν = 0.33 mHz and η = −0.95 representative of the stability zones. The stability is due to the near extinction of the previous driving region and all the significant energy contributing to damp the modes. The development and extinction of a region contributing to driving (with its maximum taking place at the location of the Z -bump) at the expense of a damping region is responsible for the oscillatory profile of the growth rate. This model does not excite p modes which are the only ones found to date in the discovered sdO pulsator (Woudt et al. 2006). Some of our models, however, present a tendency to drive low radial order p modes (Rodrı́guez-López et al. 2006, Rodrı́guez-López 2007). 274 Stability analysis of sdO equilibrium models Figure 1: Top: Growth rate parameter vs. frequency in the region of interest. The dashed-dotted lines represent the two regions of unstable modes and the diamonds mark the modes plotted beside. Bottom: Energy and opacity for the g190 and g177 modes, respectively. The vertical dashed-dotted line depicts the convection zone. Both plots have been scaled to arbitrary units. Acknowledgments. This work was supported by the Spanish Ministerio de Ciencie y Tecnologı́a under project ESP2004-03855-c03-01. References Lawlor T. M., MacDonald J., 2006, MNRAS, 371, 263 Moya A., Garrido R., Dupret M.-A., 2004, A&A 404, 1081 Rodrı́guez-López C.. 2007, Ph.D. Thesis, Universidad de Vigo Rodrı́guez-López C., Moya A., Garrido R., et al., 2006, Baltic Astronomy 15, 313 Woudt P. A., Kilkenny D., Zietsman E., et al., 2006, MNRAS, 371, 1497 Comm. in Asteroseismology Vol. 150, 2007 Discussion on pulsating white dwarf and sdB stars led by Don E. Winget Department of Astronomy, University of Texas, Austin, TX 78712, USA Winget: Before we start this discussion I would like to make a short comment to Michel because this is obviously in his honour. In my official capacity, on behalf of the University of Texas, I want to thank Michel for his pedagogical scientific legacy and his legacy of instruments used to do science (other than he intended to do originally). His pedagogical legacy is the classes he created, the effect he had: the observational astronomy class shaped the University of Texas as a training ground for observers and instrumentalists. There is also a human side that all present are familiar with. There are former and current students who are excellent scientists due to Michel’s training. I’ve had the good fortune to work with two of these: Don Kurtz and Gerald Handler. They speak for Michel’s qualities as a mentor. I’m honoured to be here. On a personal side now, I want to say that I often visited Michel to seek his wisdom. Many times Michel went far outside the box, listening even for my crazy ideas. We’ve talked about networks, mode identification and selection mechanisms, and nonlinear processes. When the ideas went too far, Michel’s energy and enthusiasm always pulled me back, bringing things sharply into focus. With his input, the idea would evolve into something useful and productive. So thank you Michel, for many years of science! I’m going to make a couple quick comments before we start the discussion. The first thing I want to say is that if you look at asteroseismology just like at any field of science, not just astronomy, you have a sort of trade-off between doing interesting work as compared to doing anything just long enough until it becomes interesting and important work. But you can carry that too far. That’s one thing. The other thing is that work you find interesting often produces very exciting and unexpected results because that’s the nature of basic research. You cannot put a panel together and decide where important discoveries will be made in the next ten years. That said, I want to look briefly at the astrophysical context for the white dwarf and the sdB pulsators in particular. We don’t really know what their evolutionary state actually is. Asteroseismology offers great promise of illuminating that. Also, in the case of the white dwarf stars, we learnt a great deal about the structure of their progenitors, as Travis has talked about. We learnt about extreme physics: crystallization and neutrinos. Interestingly, we can connect with dark matter, we learnt about axions. It is not possible, to the great frustration of many particle physicists, to hide axions completely. If they exist, they carry energy, and so one can use the energy loss of the white dwarf stars to measure some pulsators to constrain astrophysically interesting candidates for dark matter in the form of axions. You can also, as Mike Montgomery showed, look at time dependent convection; you can look at how the convection changes during the pulsation cycle and actually learn something about it in real time. Also, you can use these really accurate clocks, the pulsating white dwarf stars, as the most stable clocks we know of. If you have these stable clocks, you can use them for many things, for instance to search for extrasolar planets. These searches using white dwarf stars are unique in the sense that they can show us other solar systems dynamically similar to our own. So there is a wide range of things that one can do asteroseismically looking at sdB stars and white dwarf stars and it’s that context that we always have to keep in mind when we ask where we should go in the future. So that said, I am opening up to the questions 276 Discussion on pulsating white dwarf and sdB stars that have come up and I hope for some disagreements and hopefully get perspectives for the future. Mukadam: I would like to hear the theorist’s view on amplitude modulation. Breger: The question of the amplitude modulation from the observational side seems to be simple, namely you make a Fourier analysis and look at the peaks. If you have two peaks, you have two frequencies; if you have three peaks, you have three frequencies, or you have one frequency with a sinusoidal amplitude modulation. Now this simple scheme does not work well. The Fourier analysis does not tell you what happens, and you need specific models to test. One of the models is beating by two close frequencies. When you have beating, you have specific predictions, as shown by Dutch astronomers already half a century ago. One of the tests is that the amplitude variation has to be accompanied by specific phase or period variations. It is a small effect: particularly, at minimum amplitude you need to have the largest phase change. To see this you require a large amount of data and the data set should be longer than the beat cycle. A few large data sets for sdB stars do exist. Fossat: From my experience with solar data, I believe you seem to ignore the interplay between signal and noise. The noise, by definition, is noisy. When it’s noisy, it’s changing its amplitude rapidly. For instance, when you have a S/N ratio in the amplitude spectrum of four, the noise can sometimes be two. Then you can have four plus two and four minus two. But four minus two means no signal, because it’s lost in the noise. Therefore, you can have either a lot or nothing with actually zero amplitude modulation. Winget: Absolutely. In addition, you don’t only have noise that’s random, but you also have pattern noise, which is the influence of other frequencies that are known to be present, and those may modify your detection as well. Breger: What do you do when you have a mode that disappears and comes back with a phase shift of almost half a cycle (e.g., 0.48 ± 0.02 in 4 CVn)? This suggests beating between two modes with the same amplitude. An alternative explanation of a disappearing mode with re-excitation would have a random phase shift. Of course, you need relatively small error bars for the phase shift to make this test. So I agree with Eric’s comment that the data may not be too noisy. Kawaler: Kepler has talked about GD 358 that is a relatively cool DB that shows amplitude modulation that’s larger than anything explained by noise. Dave Kilkenny showed PG 1605, a cool short-period sdB, which also shows apparent changes of amplitude that are much larger than the noise. So there’s some physics there, it’s not just signal analysis. In the case of the white dwarfs, also in the cool DAs, not only the DBs, we have turbulence, the convection zone, ”weather”. It’s a mess of its own. We don’t have that in PG 1605; it does not have a convective envelope. So if you want to blame the period and amplitude modulation on turbulence or convection, what do you do about PG 1605? Bedding: A probably related question concerning excitation. In the instability strips, do you always see the pulsating stars where they should be, or is it like in other instability strips, where some are constant and some are not? Kilkenny: The instability strips for both the slow and fast sdB pulsators are certainly covered with stars that are constant, but the question really is, to what limits can you make detections? Winget: Concerning the DAVs, some recent work by Anjum Mukadam has shown that there may be non-variables within the strip. Kepler, Barbara Castanheira and others are working on the DBVs to find out whether this is just an observational detection limit problem or an error in temperature measurements. This is an important question because you really want to know if there possibly needs to be an additional parameter in the models, maybe some magnetic fields or something else, perhaps metallicity. Reed: A short question for the theorists that goes along with that. I was interested in these stochastic parameters that Jørgen did some years ago. Some pulsating sdB stars have strong amplitude variability, but are in fact phase stable, whereas others have fairly weak D. E. Winget 277 amplitude variability, but are not phase stable. It’s not beating because it does not switch on and off. What information is hidden in that? And is there any way to get to that information? Breger: The problem with beating is that at high amplitudes the phases are nearly constant. The phase variations become large when the amplitudes are small. It is therefore possible that you may be misled in seeing stable phases because you undertake your study when the amplitude is large. Bedding: I have a suggestion on the name conventions. Rather than p and g subscripts, rapid and slow is used both for pulsating stars and in neutron capture. So I want to stress rapid and slow. Reed: Stephane had an idea that was nice in the beginning, sP and lP; SPsdBV and lPsdBV. Quirion: Coming back to the fact that the instability strip is not always pure. The atmospheric composition of sdBs is not homogeneous. If the driving is due to the κ mechanism, you can have pulsating and non-pulsating stars in the instability strip because the chemical composition varies from star to star. Winget: Many years ago, Hideyuki looked at the question: are r modes excited in pulsating white dwarf stars? His theoretical calculations showed they should be driven. The question is: do we know observationally whether there are r modes or not? Saio: At that time, we didn’t understand the effect of convection and we used simple models. I think that my calculations would be affected by the treatment of convection in white dwarfs. If p modes and g modes are excited in white dwarfs, and the same energy laws apply to r modes, the r modes should be excited as the g modes are. Kepler: The change of amplitude with wavelength is different for g modes than for r modes. I looked at that back in 1984 for two stars. For those two stars the amplitudes excluded r modes. Kepler [to Charpinet]: There are more = 4 modes in the models than = 3 and so on. When you calculate a fit, do you normalize by the value of ? Charpinet: That’s true for g modes, but if you look at p modes, you have the same number of modes for each (excluding rotational splitting). Kawaler: In the observed period range, how many modes do your models have and how many are observed? Are there modes excited in your models that you do not see in the star? Charpinet: For instance, for PG 1325, there were twelve observed frequencies and the number of theoretical modes was 4 or 5 times higher. Winget: We’ve reached our time limit now, so we should stop here now, answer any further questions informally, and thank the speakers again. 278 Discussion on pulsating white dwarf and sdB stars Danish astronomers use different strategies to protect their ears during a fire alarm... ...whereas Belgian astronomers seem to have some training for such situations. Comm. in Asteroseismology Vol. 150, 2007 Asteroseismology: Lessons From the Past and Prospects for the Future Steven D. Kawaler Dept. of Physics and Astronomy, Iowa State University, Ames, IA 50014 USA Abstract Ground-based, and now space-based, studies of a range of stellar families (all represented at this workshop) have, in large part, moved from study of pulsations for their own sake on to information of real value for stellar physics and its applications. This required a combination of improved observations, and open-minded stellar modelling, that continues today. Pulsating compact stars provide a good example of this progress. A flurry of activity from the mid 1980s to the mid 1990s, both observational and theoretical, began to realize this potential. A new generation of stellar models, coupled with reanalysis of seismological data and discovery of many new faint pulsators, have recently revitalized this field and may soon provide firm answers to some of the outstanding problems of post-AGB evolution. The discovery and analysis of pulsating sdB stars has followed an accelerated trajectory, enjoying mature theoretical model framework largely in place at the same time as the developing observational base. Compact pulsators: asteroseismology in action The story of stellar seismology spans nearly a century if one acknowledges that classical variable stars have revealed fundamental stellar properties such as the mean density of radial pulsators. However, it was the discovery of multimode pulsating stars that precipitated exploration of the details of stellar interior physics and structure. One of the earliest milestones was the 1965 discovery of pulsations in white dwarfs by Arlo Landolt (Landolt 1968). Following this discovery, astronomy soon recognized the importance of these multiperiodic stars. Theoretical exploration led to the discovery of the pulsating DB white dwarfs. Around that time, we were faced with the serendipitous discovery of the pulsating DOZQ1 white dwarfs (pulsating PG 1159-035 stars, or GW Vir stars for the purists). Despite a few fits and starts, we eventually learnt how to analyse them, and now routinely probe interesting features of their interiors: compositional stratification, crystallization, and rotation. Rather than a comprehensive overview of the voluminous scientific results, I will try to use a few sample results to illustrate how the promise of asteroseismology has been realized, and how our more optimistic views have needed to respond to reality. Twenty years after the discovery of pulsating white dwarfs, Don Winget reviewed the state of play of the seismology of compact objects at IAU Symp. 123 in Aarhus (Winget 1988). Today, twenty years later, that review serves as an interesting touchstone to judge our progress. Here I’ll discuss a few examples of the organic growth process in white dwarf seismology. Nonadiabatic studies and the “thick vs. thin” debate One of the early achievements of white dwarf seismology was the determination that the ZZ Ceti stars were pulsating in nonradial modes, with partial ionization of hydrogen providing the driving energy and (to some degree) a mode selection mechanism. The history of this discovery is recounted in Winget (1988) and will not be repeated here. This was a very successful theory, whose success can be judged in part by its application to the prediction (and later observational verification) of pulsating DB white dwarf stars by Winget et al. (1982). 280 Asteroseismology: Lessons From the Past and Prospects for the Future However, consider the following example of the subtleties of nonadiabatic calculations that were not fully appreciated at the time. Stability calculations by Winget and others (e.g. Winget et al. 1982) suggested that only DA white dwarfs with thin H envelopes (< 10−8 M ) showed unstable g modes at temperatures corresponding to ZZ Ceti stars. This argument for “thin” envelopes ran counter to evolutionary calculations (e.g. Iben 1984) that showed that hydrogen burning in pre-DA white dwarfs would leave a “thick” layer of 10−4 M . Models by Art Cox and colleagues (e.g. Cox et al. 1987) did not have the same thermal structure in the envelope, and showed instabilities with thick envelopes. After much argument, the “thick” vs. “thin” issue clarified when updated opacities were included in the DA models (i.e. Bradley & Winget 1994), showing that pulsations could be driven, at the proper temperatures, with “thick” envelopes. We are now in an era of renewed progress in understanding driving in white dwarfs. This includes the vexing convection-pulsation interaction (e.g. Wu & Goldreich 2001). Another area of recent, rapid progress is in understanding the driving of pulsations in GW Vir stars. The general picture of driving by C and O ionization by Starrfield et al. (1983) has been updated recently by several, including Cox (2003), Quirion et al. (2004) and Gautschy et al. (2005). Mode trapping by composition transition zones Through the early 1980s, model studies of the pulsations of white dwarfs concentrated on the driving mechanism of the ZZ Ceti stars. Progress in that area spawned active discussions concerning the thickness of the surface hydrogen layer. Winget et al. (1981) were able to show that certain modes can be concentrated in the surface layers via resonant mode trapping – placing a node in the perturbation eigenfunction near the (steep) composition transition zone separating the hydrogen surface layers from the subsurface helium layer can choke the amplitude of the eigenfunction in the interior. Such modes should therefore be easier to excite (since only the non-degenerate outer parts of the star participate in oscillatory motion). This idea was used in an effort to understand mode selection in white dwarfs – the observed number of frequencies is usually much smaller than the number of modes available to the star. Mode trapping as a selection mechanism was one way that early work in this field informed the debate about the internal structure of white dwarfs. It is largely an adiabatic property of the modes, and so is at first blush a robust tool. Nonadiabatic studies generally conformed, finding faster linear growth rates in trapped modes. But translation between linear growth rates and observed amplitudes is a difficult process. Without a more complete mode spectrum, or other constraints on global stellar parameters, mode trapping alone is insufficient for providing conclusive inferences about white dwarf structure. Exploitation of mode trapping to determine subsurface compositional structure had to wait for a different diagnostic – one that relied on the asymptotic modes not generally seen in the ZZ Ceti stars, but familiar to helioseismology. It was the prototype GW Vir star PG 1159-035 that showed the first evidence of a pulsation spectrum that could be analysed with similar asteroseismological tools as were being used on the Sun. An early multi-site observing run on this star enabled Winget et al. (1985) to produce a list of eight frequencies for PG 1159-035 that was free of diurnal aliases and sufficiently resolved. Kawaler (1986, 1988) showed that these frequencies formed a partial sequence of modes roughly equally spaced in period (with some missing members), with a common period spacing of about 21 seconds – as expected for an asymptotic g-mode pulsator. For = 1 modes, a period spacing of 21 seconds was found to be perfectly consistent with models of PG 1159-035 if it had a mass of close to 0.60M . This conclusion was based on a statistical treatment of the mode list (see Fig. 1) that showed the pattern was unlikely to be caused by chance. Figure 1 shows the results of a Kolmogorov-Smirnov test (Kawaler 1988). The K-S statistic reaches a minimum at 21 seconds. While this looks like a convincing result (and was 281 S. D. Kawaler 0 -1 -2 Original 8 -3 -4 10 20 30 40 50 Figure 1: PG 1159-035 period spacing K-S diagnostic using the original eight periods. taken as such by the author at the time it was first seen) it is difficult to assign an absolute significance level from the K-S statistic Q. Formally, a value of −3 corresponds to a 1-in-1000 chance of random occurrence, but as can be seen in Fig. 1 two other peaks sit at close to the same significance as the 21 s signal. A more appropriate and modern approach is to simulate the problem via Monte Carlo techniques, running a large number of trials each with eight random periods selected from the overall range of periods seen in PG 1159-035. Doing a K-S test on each trial, and looking at the relative frequency of the Q statistic for the best spacing for each trial gives a better feel for how significant the result is for PG 1159-035 with the original eight modes. Figure 2 shows a sample of this kind of Monte Carlo analysis for eight random periods. The significance of the original PG 1159-035 result is at about the 90% confidence interval. Another test, the inverse variance test (O’Donoghue 1994), shows similar results. In isolation, the significance of the original period spacing determination seems far from certain. However, coupled with the theoretical expectation of equal spacing in period for high–order g modes, the spacing allowed derivation of an asteroseismic mass for the star. Furthermore, this led to the expectation that if more modes were found, they should fit the pattern. Within a few years, conclusive observational evidence followed from a global, coordinated observing effort - the Whole Earth Telescope (Nather et al. 1990). The WET observations of PG 1159-035 (Winget et al. 1991) were of much higher quality and density than any single-site efforts. They fully resolved the multiplets in PG 1159-035 and uncovered a nearly complete sequence of = 1 overtones along with several = 2 modes. With those new modes added, the K-S statistic (log Q) for the best-fit spacing of 21 seconds fell to −31.0, with a confidence interval of much better than 99.99%. The complete set of modes provides a deeper seismic inference for PG 1159-035. As shown by Winget et al. (1991) and Kawaler & Bradley (1994) for GW Vir stars (and for DB stars by Bradley et al. 1993), departures from uniform spacing in period are characteristic of trapped modes. They were able to compare the observed departures with models to make an asteroseismological determination of the thickness of the surface He+C/O layer in PG 1159-035. Application of this adiabatic mode-trapping determination to DA models soon followed with the work of Brassard et al. (1992) and Kawaler and Weiss (1991), following up on analytic work by C. Hansen (unpublished). These basic tools remain central ideas in white dwarf seismology today, and have led to determinations of white dwarf masses and other 282 Asteroseismology: Lessons From the Past and Prospects for the Future 0 -5 -10 -15 10 20 30 40 50 Figure 2: Monte Carlo simulation of 10 000 trials of eight randomly chosen periods. Each point shows log Q for the best period spacing. The original PG 1159-035 spacing (circle) shows a constant period spacing at about the 90% confidence level. Table 1: Rotational splitting deviations in pulsating white dwarfs Star NGC 1501 PG 2131 RX J2117 GD 358 PG 1159 = 1 HL Tau 76 GD 165 δν/ν [%] 1.51 1.07 0.504 0.340 0.222 0.173 0.057 variation (%) within multiplets between multiplets 2.0 6.0 13.2 3.1 (3.4) 20.0 14.5 3.9 4.9 1.3 10.2 3.5 7.0 9.0 properties for a growing number of stars... including a probable detection of a crystalline core in the massive ZZ Ceti star BPM 37093 (Montgomery & Winget 1999, Metcalfe et al. 2004, Corsico et al. 2005, Kanaan et al. 2005). Faith and rotational splitting Studies of rotational splittings in pulsating stars rely on several fundamental “truths.” First is that rotational splitting produces multiplets with equal splittings. When all m modes are present, 2 + 1 peaks appear, equally spaced in frequency by a multiple of the rotation frequency. For uniform rotation with depth in a star, all multiplets show the same splitting. In practice, though, we find that all of these assumed truths are not fully realized. Table 1 illustrates this with published results for a number of white dwarf pulsators. In most cases, the departures from uniformity are small but still much larger than the observational uncertainty, ranging from a few percent up to 20 percent variation from the mean spacing. There is no clear trend for fractional asymmetry to increase as the ratio of rotation rate to pulsation frequency increases (as one might expect from basic theory). Other physics can play a role. Magnetic field effects which can shift the m = 0 peak within a multiplet and produce non-uniform spacing (Jones et al. 1989, Winget et al. 1991). Some members of multiplets may not be visible (or even excited). Uniform rotation with depth does not necessarily produce equally spaced multiplets across several overtones because of mode S. D. Kawaler 283 trapping effects (Kawaler et al. 1999, Goupil et al. 2000). And differential rotation within stars could produce quite varied spacings (i.e. Goupil et al. 1996, Kawaler and Hostler 2005). Also, as rotationally split multiplets are nearly in 1:1 resonance, nonlinear effects can play a role in perturbing the observed frequencies. Given all of the above, we should not be surprised that the observed frequency spacings in multiplets in white dwarfs show significant departures from the expected truths. Interpretation of these asymmetries, however, needs to be approached with some caution. Initially, the changing splittings in GD 358 were interpreted as direct evidence for differential rotation (i.e. Winget et al. 1994), but further analysis by Kawaler et al. (1999) revealed the influence of mode trapping on the splittings. And in some sdB stars, relatively large, equally split multiplets appear (i.e. PG 1605, Kawaler 1999 and PG 0014, Vuckovic et al. 2006) that are not easily reconciled with limits on surface rotation velocities. The pulsating sdB stars The 40 year history of pulsating white dwarf studies has been repeated, on a much compressed time scale and with some interesting complications, in the development of sdB seismology. This field, ably reviewed by Stephane Charpinet at this workshop, was enabled in part by the experience gained by asteroseismologists in developing white dwarf seismology. In the case of the sdB stars, as in the white dwarfs, the discovery of the pulsator, EC 14026, was through a sequence of serendipitous events. The account of their 1995 discovery by Kilkenny et al. (1997) ranks, in my opinion, as one of the most engaging tales to appear in the refereed astronomical literature. It should be required reading for all graduate students embarking on a research career, as Kilkenny et al. (1997) stress that one must always keep an open mind when dealing with astronomical data. Their ultimate words bear quoting here as it has turned out to apply at so many stages in asteroseismology: “Despite a programme of careful observation, serendipity appears to have a major role to play in research and we are forcibly reminded that if we only look for what we expect to find, we might well miss exciting new discoveries.” Simultaneously, and without knowing that the South African group had found these stars, the Montreal group had done some exploratory calculation of the pulsational instability of sdB stars, and predicted that some should indeed pulsate (Charpinet et al. 1996). When the discovery of the EC 14026 stars was announced, it took only minor modification of their models to match the basic parameters - stellar and pulsational - of the new variable stars (Charpinet et al. 1997). For further details, see Stephane’s review in these proceedings. Only 10 short years later, models of these stars correspond even more closely to the observations - and demonstrate the potential of asteroseismology to probe important interior processes such as radiative levitation and winds. It took nearly twice as long to reach a similar level of detail with the white dwarfs. Conclusions In conclusion, we live in a very special time – for most of us of the “Breger-and-students” generation, the field of asteroseismology was born, went through a stormy adolescence, and is reaching maturity. The big brother (in terms of age) of the asteroseismology family, the pulsating white dwarfs, have already left the nest and become a mature area of detailed study, joined by the δ Scuti stars. In Don Winget’s review (Winget 1988) many of the expectations were met, other promises still await fulfilment, and entirely unexpected developments have, as expected, been made. Other younger siblings, such as the sdB stars, and SPB stars and solar-like pulsators, are still in the growth phase, and it will be a lot of fun to watch those stars, and other kinds yet to be discovered, teach us about stellar evolution from the inside out in the coming decades. 284 Asteroseismology: Lessons From the Past and Prospects for the Future Acknowledgments. The author thanks Gerald Handler and the other organizers of this celebration for their invitation, and for some travel support. Additional support came from NASA Grant NNG05-GG20G. References Bradley P. A., Winget D. E., Wood M. A., 1993, ApJ, 406, 661 Bradley P. A., Winget D. E., 1994, ApJ, 421, 236 Brassard P., Fontaine G., Wesemael F., Hansen C. J., 1992, ApJS, 80, 369 Charpinet S., Fontaine G., Brassard P., Dorman B., 1996, ApJL, 471, L103 Charpinet S., Fontaine G., Brassard P., et al., 1997, ApJL, 483, L123 Corsico A. H., Althaus L. G., Montgomery M. H., Garcia-Berro E., Isern J., 2005, A&A, 429, 227 Cox A. 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Lecture Notes in Physics, Vol. 367, Springer Verlag, Heidelberg, p. 431 Kawaler S. D., Bradley P. A., 1994, ApJ, 427, 415 Kawaler S. D., 1999, in Solheim J.-E., Meistas E., eds, ASP Conf. Ser. Vol. 169, 11th European Workshop on White Dwarfs. Astron. Soc. Pac., San Francisco, p. 158 Kawaler S. D., Sekii T., Gough D. O., 1999, ApJ, 516, 349 Kawaler S. D., Hostler S. R., 2005, ApJ, 621, 432 Landolt A. U., 1968, ApJ, 153, 151 Kilkenny D., Koen C., O’Donoghue D., Stobie R., 1997, MNRAS, 285, 640 Metcalfe T. S., Montgomery M. H., Kanaan A., 2004, ApJL, 605, L133 Montgomery M. H., Winget D. E., 1999, ApJ, 526, 976 O’Donoghue D., 1994, MNRAS, 270, 222 Quirion P.-O., Fontaine G., Brassard P., 2004, ApJ, 610, 436 Vučković M., Kawaler S. D., O’Toole S., et al., 2006, ApJ, 646, 1230 Winget D. E., Van Horn H. M., Tassoul M., et al., 1982, ApJL, 252, L65 Winget D. E., Van Horn H. M., Hansen C. J., 1981, ApJL, 245, L33 Winget D. E. 1988, in Christensen-Dalsgaard J., Frandsen S., eds, IAU Symp. 123: Advances in Helioand Asteroseismology, Reidel, Dordrecht, p. 305 Winget D. E., Nather R. E., Clemens J. C., et al., 1991, ApJ, 378, 326 Winget D. E., Nather R. E., Clemens J. C., et al., 1994, ApJ, 430, 839 Wu Y., Goldreich P. 2001, ApJ, 546, 469 S. D. Kawaler 285 DISCUSSION Roxburgh: You started off by asking what are the big questions and then stated your own interests. I am sitting on a committee that is dominated by cosmologists and astrobiologists. What part of what you do is of interest to these two factions? Kawaler: What is immediately obvious is white dwarf chronology by finding the ask of the disk of our Galaxy. A rather unexpected outcome would be models of planet formation using stellar evolution codes but also watching the planets grow. Montgomery: I would just like to state that in the past we haven’t used the combination frequencies very much but I am just in the process of doing that, generating nonlinear models of light curves. There is a lot of promise in that, such as constraining models of convection in white dwarf envelopes. I am just plugging my poster here. Dziembowski: What is the magic about 1.52? Kawaler: There were some stars whose names I don’t remember now, that had frequencies at multiples of 1.52, 2.52 etc. or 1.48, 2.48 etc. of the dominating mode frequency. So it was about half way in between harmonics, offset by some constant . Dziembowski: And what was the explanation of this? Kawaler: There were peaks, but they just turned out to be modes that happened to be close. It turned out that 2/100 of that frequency interval was just not that close. Moskalik and Handler: These stars were PG 1351+489 and GD 154. Runa Briguglio, Ennio Poretti, Michel Breger and Jean-Claude Valtier. Ground-based asteroseismology Two ground-based astronomers: Joanna Molenda-Żakowicz and Jørgen Christensen-Dalsgaard. Comm. in Asteroseismology Vol. 150, 2007 The Network Activities in HELAS M. Roth Max-Planck-Institut für Sonnensystemforschung, Katlenburg-Lindau, Germany Abstract The Helio- and Asteroseismology Network (HELAS) is a Coordinated Action funded by the FP6-Infrastructure-Programme of the European Commission. The objective of HELAS is to co-ordinate European activities in helio- and asteroseismology. In order to achieve this objective HELAS runs six network activities. I describe these in this short contribution, with a special focus on the asteroseismology network activity. HELAS The European Helio- and Asteroseismology Network (HELAS) has its major objective in bringing together the widely dispersed European research groups active in helio- and asteroseismology. HELAS will combine the core expertise of the individual research groups through six network activities in order to ensure European competence and competitiveness in this research area by spreading expertise, enhancing the synergy between helio- and asteroseismology, and improving the public understanding and interest in solar and stellar physics. These objectives will be achieved by organizing workshops of smaller groups within the individual network activities, by organizing annual conferences for the international audience, and by providing a common platform for the exchange of data and software among the participants. The transfer of knowledge and data analysis techniques through HELAS will lead to a structuring of this field of research, as needed to prepare the European research community for important missions in the near future: the NASA space missions Solar Dynamics Observatory (SDO) and Kepler, the CNES missions CoRoT and PICARD, the ESA mission Solar Orbiter, the French/Spanish mission GOLF-NG, as well as ongoing and planned ground-based initiatives. The funding of HELAS started on April 1, 2006 under the Sixth Framework Programme of the European Union and will last until March 31, 2010. HELAS receives a grant of 2.265.000 EURO. Currently HELAS consists of ten members. Moreover HELAS will embed many of the activities of the European Network of Excellence in Asteroseismology (ENEAS). HELAS Members HELAS will become an important contact point for the European groups active in helio- and asteroseismology. It is an integrative activity. Consequently, it is expected that the activities are not limited to the institutions directly taking part in the network. The contact addresses of the ten HELAS members are listed in Table 1. Network Activities HELAS itself is not able to fund research and development. The major activity of HELAS is to contribute to the coordination of research and development on the European level by supporting the interaction of scientists. This coordination action is split into six network activities: 288 The Network Activities in HELAS Kiepenheuer-Institut für Sonnenphysik Schöneckstr. 6 79104 Freiburg, Germany http://www.kis.uni-freiburg.de Contact: Prof. Oskar von der Lühe Tel.: +49 (0)761 3198 0 Fax: +49 (0)761 3198 111 E-mail: [email protected] Instituto de Astrofı́sica de Canarias C/ Vı́a Láctea, s/n E38200 - La Laguna (Tenerife), España http://www.iac.es Contact: Pere L. Pallé Tel.: +34 / 922 605 200 Fax: +34 / 922 605 210 E-mail: [email protected] Department of Applied Mathematics University of Sheffield Hicks Building Hounsfield Road Sheffield S3 7RH, U.K. http://www.shef.ac.uk Contact: Prof. Michael J. Thompson Tel.: +44 (0)114 222 3733 Fax: +44 (0)114 222 3739 E-mail: Michael.Thompson@sheffield.ac.uk Institut for Fysik og Astronomi Aarhus Universitet Ny Munkegade, Bygn. 1520 DK-8000 Århus C, Denmark http://astro.phys.au.dk Contact: Jørgen Christensen-Dalsgaard Tel.: +45 8942 3614 Fax: +45 8612 0740 E-mail: [email protected] Centro de Astrofisica Universidade do Porto Rua das Estrelas P-4150-762 Porto, Portugal http://www.astro.up.pt Contact: Mario Joao P. F. G. Monteiro Tel.: +351 - 226 089 830/857 Fax: +351 - 226 089 831 E-mail: [email protected] Max-Planck-Institut für Sonnensystemforschung Max-Planck-Strasse 2 37191 Katlenburg-Lindau, Germany http://www.mps.mpg.de/en/index.html Contact: Laurent Gizon Tel.: +49 (0)5556 979-439 Fax: +49 (0)5556 979-240 E-mail: [email protected] Table 1: The ten HELAS member institutions. Addresses and contact details are given. To be continued Management – The first activity handles the overall coordination and management of the consortium, the setting of the strategies, the financial management, and the interaction with the European Commission. Coordinator: Oskar von der Lühe, Kiepenheuer-Institut für Sonnenphysik, Project Scientist: Markus Roth, Max-Planck-Institut für Sonnensystemforschung. HELAS Forum – The HELAS Forum serves as platform for discussing all network activities of HELAS and for developing the plans of mutual interest. Once a year an international conference is organized. The plan for these annual events is laid out in table 2. Moreover the HELAS Forum will generate and exploit synergies between the network activities. An internet portal will allow the exchange and distribution of software and data. The internet portal will be accessible at: http://www.helas-eu.org Chair: Pere Pallé, Instituto de Astrofı́sica de Canarias. Public Outreach – The major objectives of public outreach in HELAS is the coordination of actions to raise awareness and interest in helio- and asteroseismology in the general public and at all levels of the educational system throughout Europe. This includes the preparation of state-of-the-art university lectures and other material for further outreach. Chair: Jørgen Christensen-Dalsgaard, Institut for Fysik og Astronomi. 289 M. Roth INAF National Institute for Astrophysics Viale del Parco Mellini 84 I-00136 Roma, Italy http://www.iasf-roma.inaf.it Contact: Maria Pia Di Mauro Tel.: +39 06 4993 ext 4087 Fax:+39 0620660188 E-mail: [email protected] Instituut voor Sterrenkunde Katholieke Universiteit Leuven Celestijnenlaan 200 D B - 3001 Leuven, Belgium http://www.ster.kuleuven.be Contact: Conny Aerts Tel.: +32/16/32 70 28 Fax: +32/16/32 79 99 E-mail: [email protected] Instytut Astronomiczny Uniwersytet Wroclawski ul. Kopernika 11 Pl-51-622 Wroclaw, Poland http://www.astro.uni.wroc.pl Contact: Jadwiga Daszyńska-Daszkiewicz Tel.: +48 71 37 29 373 Fax: +48 71 37 29 378 E-mail: [email protected] Observatoire de la Côte d’Azur Bd. de l’Observatoire B.P. 4229 F-06304 Nice Cedex 04 France http://www.obs-nice.fr Contact: Thierry Corbard Tel.: +33 (0)492003011 Fax: +33 (0)492003033 E-mail: [email protected] Table 1: Continued. Global Helioseismology – This network activity coordinates methods and software developments for global helioseismology. Furthermore data analysis tools and solar models will be distributed in the HELAS community. Additionally, expertise and techniques will be shared with asteroseismology. To coordinate the activities in global helioseismology three workshops will be held on the topics • Low frequency spectral range, Canary Islands, Summer 2007 • Solar-cycle variations and magnetic effects on stellar oscillations, Sheffield, 2008 • New insights into the Sun, Porto, 2009. Chair: Michael Thompson, University of Sheffield. Local Helioseismology – This network activity concentrates on local helioseismology. There it is necessary to identify the needs and to develop actions for structuring research in the field of local helioseismology. The development and distribution of specific software is meant to provide Europe with the means to participate in the analysis and interpretation of HMI-SDO data. The first workshop “Roadmap for local helioseismology” was held September 25–27, 2006 in Nice. The next two workshops are • Local helioseismology and solar MHD processes, Freiburg, 2008 • Local helioseismology with SDO data, Katlenburg-Lindau, 2009. Chair: Laurent Gizon, Max-Planck-Institut für Sonnensystemforschung. 290 The Network Activities in HELAS Conference Title Location Date (1) SOHO-18 / GONG 2006 / HELAS-I Beyond the Spherical Sun Sheffield, Great Britain August 7 –11, 2006 (2) HELAS-II Helioseismic, Asteroseismology and MHD Connections Göttingen, Germany August 20 – 24, 2007 (3) HELAS-III CoRoT-Conference Paris-Meudon, France Summer 2008 (4) HELAS-IV Four Years of HELAS Tenerife, Spain Summer 2009 Table 2: Plan for the annual international HELAS symposia. Titles, locations and dates are given. These are still preliminary for the years 2008 and 2009. Asteroseismology – This scientific network activity develops programmes to ensure European competitiveness in the field of asteroseismology. This comprises comparisons of model and frequency calculations in order to improve their reliability. Furthermore the developments of stellar modelling software will be coordinated and its results distributed within the HELAS community. The following section gives more details on the objectives of this network activity and the topics of the four organized workshops. Chair: Conny Aerts, Instituut voor Sterrenkunde. Specific Objectives of the Asteroseismology Network Activity The major objective of the asteroseismology activity in HELAS is to promote a vital exchange between groups acting on the field of stellar physics. Collaborations will be initiated between the scientists that work on the theoretical description of the physical properties of stars and on the interpretation of stellar oscillation data. In particular, for stellar modelling different codes are circulating. HELAS aims at rationalizing the work on further code developments. For this a comparison of all different stellar evolution codes is necessary. It is a key work package of HELAS to compare the stellar models produced by these codes. The idea is then to update the codes coherently as soon as the physical details in the stars become understood. This work was initiated by the asteroseismology community to become prepared for the advent of CoRoT. HELAS will support these efforts. HELAS will also coordinate activities that concentrate on analysing and interpreting stellar oscillation data. This comprises the development, testing and application of techniques for interpretation of asteroseismic data, including inversion techniques, as well as the improvement of stellar model and oscillation frequency calculations. Especially, in stellar modelling the need for nonstandard models that include effects of rotation, diffusion and magnetic fields is identified. The aim is also to rationalize methods of pulsation mode identification from time series photometry and spectroscopy, by combining both types of data sets. A major task of HELAS is to make software tools for data analysis, data management and stellar modelling available to the whole helio- and asteroseismology community in generally accessible and documented form. Furthermore some exemplary asteroseismic data sets and M. Roth 291 basic reference models will be available. The spread of the available tools over Europe will result in a larger community that makes use of these tools. This will promote the development of new data analysis tools, as new ideas for new techniques will come up faster. HELAS will offer a platform for discussing this development of the next generation tools. Asteroseismology needs long time series. Large observing proposals need to be coordinated to make observations with unprecedented extent in time coverage and precision possible. HELAS will provide support for proposals for multi-site campaigns using existing and future facilities. Considering the setup of new facilities, HELAS will be the platform to exchange ideas and to formulate the needs of the asteroseismic community. Besides the “Future of Asteroseismology Workshop” in Vienna, one workshop was held on “Comparison and tests of stellar evolution codes” November 20–23, 2006 in Porto. Two more workshops will be organized by HELAS on the topics: • Interpretation of asteroseismic data, Wroclaw, 2008 • Synergies between solar and stellar modelling, Rome, 2009. Contacts The European Helio- and Asteroseismology Network can be contacted at: HELAS Project Office Kiepenheuer-Institut für Sonnenphysik Schöneckstr. 6 79104 Freiburg / Germany Tel.: +49 761 3198 182 FAX: +49 761 3198 111 e-Mail: [email protected] WWW: http://www.helas-eu.org Acknowledgments. HELAS is funded by the European Union’s Sixth Framework Programme. This funding allowed to support the “Future of Asteroseismology” workshop in Vienna. References HELAS website 2006, http://www.helas-eu.org/ DISCUSSION Kupka: Considering the issue of updating the microphysics, it is simply not clear what is better. For instance, yesterday I heard for the first time for a long time that OP opacities are better than OPAL ones for some applications. There are some potential surprises that people are aware of that make them reluctant to change anything they are using. Roth: What we are trying to do is to help in thinking about what happens if one changes things in one or the other code and then compare the results. The idea of HELAS is not to do the science but to bring scientists together to do it. Hatzes: You said you’ll support multisite observing campaigns. Does that include funding of travel to observatories if you get the time? Roth: No. 292 The Network Activities in HELAS Aerts: Don and I have made some efforts last year, for instance, to write to OPTICON to make available a number of the European telescopes across the world for an asteroseismic run. This has been difficult, but as of 2008, OPTICON does foresee such applications. In that case you can ask for travel support from them. So, the answer is ”no, not really in general”, but in practice we are moving along and we have to wait about one more year before they implement that possibility. So we can get a serious amount of OPTICON funding if we write the best proposals. Roxburgh: Most of what you’re saying happens anyway. These are activities that have been organized in the community and that HELAS has gotten attached to rather than the other way around. So I don’t quite see what one gets out of it, except for a bit of money to support outreach. It’s an enormous bureaucracy for a bit of money. Roth: Yes, it is a bit of bureaucracy to deal with the European Union. The EU gives us the money to use e.g. in workshops, which not only deal with outreach. We might have then own funds free to use for other things, e.g. to use them for science. HELAS is a coordination action. We are not here to bring big scientific ideas out of the ten that are currently organizing HELAS, we are here to bring together all the scientists. Then they bring out the new ideas as we give them the chance to think about new ideas. Kaye: What are your plans to decrease the bureaucracy levels to interact with the AAS or the NSF? Roth: We haven’t thought about that yet, but we would like to also have links to the American science community. HELAS is currently restricted to doing networking in Europe, nevertheless we are certainly interested on the efforts of the American scientific society. We cannot do research in the US. We will spend all the EU money within Europe but we can invite scientists from the US to come to the workshops. Comm. in Asteroseismology Vol. 150, 2007 The Delaware Asteroseismic Research Center: Convection in Pulsating White Dwarfs J. L. Provencal,1 H. L. Shipman,1 The WET TEAM 2 1 Mt. Cuba Observatory and the University of Delaware, Dept. of Physics and Astronomy, Newark, DE 19716, USA 2 www.physics.udel.edu/darc/wet/ Abstract We introduce the Delaware Asteroseismic Research Center (DARC), a new initiative sponsored by Mt. Cuba Observatory and supported by the Department of Physics and Astronomy at the University of Delaware. DARC’s mission is to promote and facilitate international collaboration in the field of stellar seismology. We present preliminary results from XCOV25, the first observing run sponsored by DARC. XCOV25’s primary target was GD358, the prototype DB pulsating white dwarf. The scientific goals focus on expanding our understanding of stellar convection. Introducing DARC The light from stellar sources, be it detected using a 0.6 m or a 10 m telescope, originates from their surfaces. Stellar interiors cannot be directly observed. Asteroseismology offers the best method to indirectly peer below stellar surfaces, using pulsations to determine internal structure. Multisite photometric and spectroscopic campaigns are the primary observational tool, providing the uninterrupted observations and lengthy timebase necessary to resolve complicated pulsation spectra of many variable stars. The Whole Earth Telescope (WET), founded in the 1980s by R. E. Nather and D. E. Winget (Nather et al. 1990), took multisite campaigns to the next level. WET’s purpose is to obtain continuous coverage of a primary target, and to maximize the use of telescope time to cover additional targets by providing real-time data reduction and an interactive headquarters. In 2004, WET’s governing council gave permission to one of us (HLS) to explore the possibility of private funding to support WET. The result was the formation of the Delaware Asteroseismic Research Center (DARC) in 2005. WET moved from Iowa to Delaware and completed the first WET run supported by DARC (XCOV25) in May of 2006. Preliminary results from this run are reported below. DARC is sponsored by Mt. Cuba Observatory in collaboration with the Department of Physics and Astronomy at the University of Delaware. Our purpose is to support and promote international collaboration in the field of stellar seismology. The DARC director is supported by an Advisory board. We encourage development of instrumentation and software, observing techniques, and science goals. To this end, we are in the process of expanding our theoretical and technical support. Targets for WET runs or campaign support should not be limited to white dwarfs and can be submitted at any time through the DARC website (www.physics.udel.edu/darc/proposal.html). Submit approximately one page describing the proposed target and scientific justification. If the target and science goals require a full WET run with headquarters, please justify your reasoning. WET runs require about a year of organization, so submit targets early. The Director and the Advisory Board will debate/discuss the proposal, and respond with any additional questions. We are also in the progress of creating an on-line data archive. Many older PMT runs are already 294 The Delaware Asteroseismic Research Center available at www.physics.udel.edu/darc/archives.html. We are extremely interested in feedback from the community. If you have suggestions, please send them along via the feedback form on the website, or mail DARC at [email protected]. A detailed discussion of available opportunities can be found in Provencal et al. (2007) or at our website at www.physics.udel.edu/darc. Looking at Convection in Pulsating White Dwarfs Convection is an important means of energy transfer for virtually all stars, yet convection remains one of the largest uncertainties in stellar modelling. Montgomery (2005) presents a method by which precise observations of light curves of certain types of variable stars can be used to determine parameters characterizing the convection zone of a particular star. In general, stellar pulsations are described in terms of spherical harmonics, and are assigned 3 indices (k, , and m) that describe the pulsation. The quantities and m describe the angular geometry of a given nonradial pulsation. The radial component is defined by k. Montgomery (2005) and Montgomery (2007) outline the theoretical details of this technique to investigate white dwarf convection zones. Observationally, it requires 1) a nonlinear pulsator 2) knowledge of the k, and m values of the pulsations, and 3) a very high signalto-noise light curve (4–5 hours minimum for white dwarfs). We chose GD358 as a good target for this technique. It is a well studied, large amplitude nonlinear pulsator with known k, and m values (Winget et al. 1994). We organized a WET campaign in May 2006 with two goals: 1) to acquire a high signal to noise light curve, 2) to obtain contemporary frequency, phase, and amplitude information. The Observations Twenty-two telescopes participated in the run, from May 12 to June 14 (a complete list of participants can be found at www.physics.udel.edu/darc). We obtained over 282 hours of observations, achieving 73% coverage during the main portion of the run. The observations were acquired with a mixture of CCD and PMT photometers and were optimized to use identical comparison stars where possible. The majority of sites used a BG40 filter to normalize spectral response. The data were reduced using the techniques described in Nather et al. (1990) and Kepler et al. (2003). Figure 1 presents a portion of the complete light curve. Figure 2 presents the Fourier Transform (FT) of the entire data set. Multi-frequency analysis was carried out using the Period04 software package described by Lenz & Breger (2005). We find power at the = 1 modes of k = 21, 19, 18, 15, 14, 12, 9 and 8, albeit with different amplitudes than in previous years. In addition, we detect ≈ 100 combination frequencies, a few of which are labelled in Fig. 2. The Fourier Transform Table 1 lists a preliminary sampling of frequency identifications. The dominant mode is k = 18 (1234.124 μHz, 810.291 s) with an average amplitude of 24.04 mma. The mode k = 18 was detected in previous observations but not as the dominant frequency. Kepler et al. (2003) detected significant power at 1255.4 μHz, but speculated that this represents an = 2 mode. We do not detect power at 1255 μHz. The mode k = 12 has the second largest amplitude at over 16 mma. This mode was detected in 1990, 1994, 1996, and 2000 but never with amplitudes significantly above 1 mma. Both k = 18 and k = 12 exhibit complex multiplet structure which is undergoing further analysis. The modes k = 9 and k = 8 are both present with frequencies and amplitudes similar to previous measurements. The multiplet splitting is 3.8 μHz. 295 J. L. Provencal, H. L. Shipman & The WET TEAM Fract. Amplitude .2 .1 0 ï.1 1350000 1360000 1370000 1380000 Time (s) Figure 1: Portion of the XCOV25 light curve of GD 358 k=18 .025 .02 Amp (mma) k=12 .015 k=9 k=19 .01 k=8 k=15? 2x12 k=21? 18+12 195+Hz .005 0 0 500 1000 1500 2000 2500 3000 3500 4000 Frequency (+Hz) Figure 2: Fourier Transform of GD358 (XCOV25) 4500 5000 296 The Delaware Asteroseismic Research Center Table 1: Preliminary frequency solution for GD 358 from XCOV25. The third column gives k values, identifies harmonics, or identifies sum/difference frequencies. The 1223 and 1245-μHz “components” of the k = 18 mode may be combination frequencies or be due to amplitude modulation. Frequency (μHz) ±0.001 Amplitude (mma) ±0.07 Note 195.0685 617.4310 1039.0758 2.73 2.04 7.94 1173.0152 1222.9457 1228.7918 1234.1243 1239.5107 1245.2199 1429.2096 7.24 4.30 5.06 24.03 4.93 4.90 5.63 1512.1414 1736.3016 1741.6663 1746.9094 1749.0833 2150.3934 2154.2235 2158.0740 2273.6910 2359.0525 2363.0582 2366.5243 2468.2817 2663.3676 2975.8137 1.80 16.35 11.01 1.85 11.84 4.09 5.51 7.18 4.23 5.95 1.64 6.60 5.19 2.95 3.47 (k = 18) − (k = 21)? (k = 18)/2 k = 21? (k = 18) − 195μHz k = 19 k = 18 k = 18 k = 18, m = 0 k = 18 k = 18 k = 15? (k = 18) + 195μHz k = 14 k = 12 k = 12 k = 12 k = 12 k =9 k = 9, m = 0 k =9 2 × (k = 18) − 195μHz k =8 k = 8, m = 0 k =8 2 × (k = 18), m = 0 2 × (k = 18) + 195μHz (k = 18) + (k = 12) We find numerous combination frequencies, in particular a complex area near 3000 μHz. The largest peak is 2975 μHz, corresponding to a combination of the dominant frequencies of k = 18 and k = 12. Additional peaks in this region correspond to combinations of other multiplets of these two modes. The Role of Amplitude Modulation Comparison of our results with those from previous years naturally results in the conclusion that amplitude modulation plays a role in GD358. Montgomery’s nonlinear fitting technique requires knowledge of the frequencies present in the light curve. We are interested in identifying actual modes and excluding artifacts due to amplitude modulation. Drawing an analogy with radio, the general idea supposes a constant carrier wave modulated by an amplitude modulation frequency which may or not be variable itself. In the simplest case, the FT of such a signal will contain the carrier frequency, two sidebands (± the modulation frequency) and the modulation frequency itself. Armed with this simplistic model, we looked for this signature in the FT. If we assume that the carrier frequency is k = 18, then we find two peaks, at 1429.210 and 1039.076 that are separated from k = 18 by 195 μHz. Interestingly, we also find a significant peak at 195.685 μHz. We tentatively identified the power at 1429.210 μHz as k = 15, but this frequency is shifted by ≈ 2μHz from previous J. L. Provencal, H. L. Shipman & The WET TEAM 297 measurements. Amplitude modulation would naturally explain this shift. In addition, we are exploring similar signatures surrounding k = 18’s first harmonic and combination frequencies near 3000 μHz (k=18 + k=12). We have also looked at the FTs of subdivisions of the light curve to establish timescales of modulation. The FT is stable over timescales of about one week, but starts to exhibit amplitude variation on shorter timescales (a few days). The mode k = 18 varies in amplitude from 28 to 20 mma, while k = 12 varies from 10 to 28 mma. The beat time between k = 12 and k = 18 is of order half an hour, so this cannot account for the variations we observe. Work is ongoing on the implications. Light Curve Fitting and Convection Montgomery (2007) outlines the technique of light curve fitting. Our preliminary fits use 15 independent modes. The best linear fit solution, including just the 15 frequencies and excluding combination frequencies, has residuals of σ2 = 3.4 × 10−4 . The best linear fit including combination frequencies, introducing 112 additional parameters, has residuals of σ2 = 1.3 × 10−4 . Figure 3 shows the best nonlinear fit, which includes the 15 independent frequencies and 3 additional convection parameters. The residuals for this fit are σ2 = 1.3 × 10−4 . Figure 3: Best fit, nonlinear solution (3 additional parameters) Conclusions This data set has given us new insight into GD358, stellar convection and pulsation/convection interaction, but raised new questions as well. The role of the convection zone in nonlinear pulsators seems clear. For example, convection does not play a role in the DOV pulsators, and no combination frequencies are detected in these stars. Going back to basic physics demonstrations, water in a tank will reflect off the tank walls. In a star, the bottom of the convection zone plays the role of the wall. Yet, because the star is pulsating, the convection 298 The Delaware Asteroseismic Research Center zone is constantly changing. For an m=0 mode, the poles appear to recede, but the equator does not. In other words, the convection zone does not always form a spherical reflective surface. Could this explain the difference in behaviour of the various modes in GD358? Can this explain the apparent changes in mode trapping we observe? What is the role of amplitude modulation? What physical process could modulate one mode and not others? The nonlinear light curve fitting technique allows us to probe the convection zone of stars other than our sun. We now have two DBVs spanning the helium instability strip and one DAV probing the DA instability strip. Our future work includes searching for additional targets to map both instability strips completely, and expanding this technique to apply to other types of variable stars. Acknowledgments. DARC acknowledges the support of the Crystal Trust Foundation and Mt. Cuba Observatory. We would also like to thank everyone involved in the network for their time and support. References Kepler S. O., Nather R. E., Winget D. E., et al., 2003, A&A, 401, 639 Lenz P., Breger M., 2005, Comm. Asteroseis., 146, 53 Nather R. E., Winget D. E., Clemens J. C., Hansen C. J., Hine B. P., 1990, ApJ, 361, 309 Montgomery M. H., 2005, ApJ, 633, 1142 Montgomery M. H., 2007, these proceedings Provencal J. L., Shipman H. L., Montgomery M. H., et al., 2007, in Napiwotzki R., Burleigh M., eds, ASP Conf. Ser., 15th European Workshop on White Dwarfs. Astron. Soc. Pac., San Francisco, in press Winget D. E., Nather R. E., Clemens J. C., et al., 1994, ApJ, 430, 839 DISCUSSION Dziembowski: I am curious whether in your feeling the randomness we observe in the mode spectra rather reflects the stochastic nature of convection or rather mode interaction? Montgomery: I would rather say mode interaction. The motions in the convection zone occur on such a small scale that they are well averaged out over the disk and over the modes that we observe, but I don’t know for sure. Mukadam: The hot PG 1159 stars exhibit nonlinear pulse shapes, similar to those shown by the 25 000K DB white dwarf pulsators. Kepler informed us yesterday that the convection zones in the hot PG 1159 stars are extremely thin. How can we understand the nonlinearities in the hot white dwarf pulsators? Montgomery: Actually, while there may be significant beating between the excited modes in these objects, their pulse shapes are quite linear. This fits in nicely with the idea (from models) that these stars do not have surface convection zones. Kiss: We know of many high-amplitude pulsating stars, like RV Tauris or Miras, which show strong nonlinear interactions and a relatively small number of modes. Do you see any restrictions which would prevent the use of your method in those cases? Montgomery: The crucial assumption that makes this easier than other time-dependent convection formalisms, is that in our treatment the convection zone responds instantaneously to the flux perturbations. This is due to the fact that the convective turnover time is of order one second, while the pulsation modes have periods which are much longer, of order hundreds of seconds. I suspect that in the stars which you mention that this might not be the case. In other words, the mode period may be of the same order of magnitude as the J. L. Provencal, H. L. Shipman & The WET TEAM 299 convective turnover time and that’s outside the range of this approximation. However, for some parameter ranges we might still be in the regime where we can learn something, so we might be able to go further than we think with this approximation. Kepler: Did Brickhill or Goldreich & Wu calculate a nonlinear energy contribution for the convectional driving of the pulsations? Montgomery: They both did. This convective response is what drives things. I should mention to Wojtek and the other theorists that what I did is sort of an adiabatic version of what they did. I assumed that all the flux that goes into the convection zone eventually comes out of the top. It doesn’t go into mechanical driving. In other words, the amplitudes have saturated. This is actually a slightly simpler version of their theory, but it gives support to what they did. Bedding: You mentioned the differences between the models and the light curves. Wouldn’t it be better to use your model to predict the combination frequencies and compare them to the combination frequencies of the observations? Montgomery: I’m not sure that I would agree that this would be better, but yes, I think it is something we should also do. Michel Breger and Katrien Kolenberg. Comm. in Asteroseismology Vol. 150, 2007 Stellar Oscillations Network Group F. Grundahl, H. Kjeldsen, J. Christensen-Dalsgaard, T. Arentoft, S. Frandsen Danish AsteroSeismology Centre (DASC), Department of Physics and Astronomy, University of Aarhus, Ny Munkegade, 8000 Aarhus C, Denmark Abstract Stellar Oscillations Network Group (SONG) is an initiative aimed at designing and building a network of 1m-class telescopes dedicated to asteroseismology and planet hunting. SONG will have 8 identical telescope nodes each equipped with a high-resolution spectrograph and an iodine cell for obtaining precision radial velocities and a CCD camera for guiding and imaging purposes. The main asteroseismology targets for the network are the brightest (V < 6) stars. In order to improve performance and reduce maintenance costs the instrumentation will only have very few modes of operation. In this contribution we describe the motivations for establishing a network, the basic outline of SONG and the expected performance. Background and network motivation After the discovery of the global solar oscillations in the 1970’s it was quickly realized that long continuous observations were needed in order to obtain the best possible oscillation spectra. This ultimately led to the construction of several networks, such as BiSON (Chaplin et al. 1996), IRIS (Fossat 1991) and GONG (Harvey et al. 1996) dedicated to the observation of the solar p-mode oscillations. In the study of oscillations in stars other than the Sun, the limitations of short observing periods are well known, leading to aliasing problems in the observed power spectra resulting from a poor window function, and low frequency precision caused by short observing runs. As was the case for the solar oscillations the best way to overcome this problem is to obtain long observing runs with high duty-cycle, and this demands either a ground-based telescope network or a space-based observatory such as CoRoT or Kepler. During the past ∼5 years several teams have demonstrated the successful detection of solar-like p-mode oscillations in other stars (Bedding et al. 2001, Bouchy et al. 2002) from time-series spectroscopy. The development of methods to measure high-precision velocities by groups hunting for extrasolar planets has made the direct detection of solar-like oscillations in other stars possible. It is well known that the solar oscillations can be detected by measuring intensity variations or surface radial-velocity changes. In Fig. 1 we show the solar amplitude spectrum as measured in velocity (GOLF; Gabriel et al. 1995) and intensity (VIRGO; Fröhlich et al. 1995) by the SoHO satellite. We note that the background is dramatically lower for the velocity signal compared with the intensity signal, as already noted by Harvey (1988); this demonstrates that velocity observations will be most efficient in detecting oscillations in other stars. A further advantage of observing solar-like oscillations in radial velocity is that modes with = 3 can be detected which is not possible for intensity observations. The need for a network As has been extensively discussed at this meeting, asteroseismology has a great potential for increasing our understanding of stellar physics and evolution. The current instrumentation F. Grundahl et al. 301 Figure 1: Comparison of data from VIRGO (green channel) and GOLF. The power is normalized such that the p-mode amplitude for = 1 at peak power (near 3.1 mHz) is one for both VIRGO and GOLF. The background is dominated by granulation and activity. A simple Harvey model is used to describe the background (the different components shown as dashed curves). The diagram also contains the smoothed power for both VIRGO and GOLF. At high and low frequencies the p-mode signal-to-noise ratio (SNR) is almost the same for GOLF and VIRGO. One should also note that the intensity background at frequencies above 3–4 mHz is decreasing with frequency to the fourth power (which is not included in the Harvey model). does not allow easy access to the facilities needed to provide long, uninterrupted velocity time series. At the same time with the remarkable precision reached at the best instruments, such as HARPS (Mayor et al. 2003), UVES (Dekker et al. 2000), UCLES (Walker & Diego 1985) and HiRES (Vogt et al. 1994) it is also clear that the access and availability of dedicated instrumentation is now the main limiting factor in the field. It is worth noting that the success of HARPS, UVES, UCLES and HiRES is due to the excellent quality of the instruments, more than a reflection of the primary mirror size. Thus a network dedicated to observing bright (V < 6) stars will need high-quality instrumentation, more than aperture size – this is a huge advantage in terms of cost, since aperture is one of the main cost-drivers for large-aperture telescopes. A dedicated spectroscopic network will allow many different asteroseismic projects to be carried out, including both long-term projects for a few stars and short-term campaigns on several stars. Our simulations show that it will be possible to determine reliably the large and small frequency separations for solar-like stars in about one week of observations, which for example could be used to determine the ages of known planet-hosting stars and of a significant fraction of the DARWIN mission targets, typically FGK-type main-sequence stars. On the other hand, observations over several months of a given star will allow very detailed investigations of stellar internal properties, utilizing also the expected reasonable SNR for even relatively low-order p modes whose frequency can be determined with very high accuracy. For many of the SONG targets it will also be possible to determine radii from interferometric observations which is a great help in the asteroseismic analysis. 302 Stellar Oscillations Network Group Network baseline To investigate whether a network such as SONG is realistic, a conceptual design study has been carried out during 2006 at the University of Aarhus. Here we briefly describe the current (autumn 2006) baseline for SONG. One of the main risks associated with the construction of a network is the running costs and up-time of the instruments, and thus it is necessary to pay close attention to these issues. As a consequence of this we aim to limit the number of components in the dome to avoid exposure to ambient conditions and have as few moving parts a possible which implies a limited number of operation modes. The network will have 8 identical telescope nodes, four in each hemisphere, located at existing sites in order to avoid building significant new infrastructure. An illustration showing possible locations of sites is given in Fig. 2. Each instrument will be remotely controlled; for the long-term use of the network robotic observations are envisaged. It is, however, an extremely complex task to robotize a telescope and hence full automatization may not be achieved during the initial phases of operation. Figure 2: A possible distribution of SONG sites, with horizontal bars indicating the observability of an object which can be observed to ±4.5 hours on either side of the meridian. For equatorial objects, which can be observed from both hemispheres, it would be possible to obtain ∼60 hours of observation per 24 hours if all eight nodes were observing the same object. Note that there will always be at least two sites which can observe the same (equatorial) target, thus ensuring a high duty-cycle and valuable cross-checks on the measured velocities which will help to eliminate long-term drifts in the velocity zero points. The conceptual design assumes telescopes with a diameter of 80cm and an alt-az mount with a Coudé focus, housed in a dome with a diameter of 4m. For the building we aim to use a standard 20 foot shipping container in which the two main instruments (spectrograph and imaging camera) will be located at the Coudé focus. The dome/building configuration is similar in concept to that adopted by the Bradford Robotic Telescope on Tenerife (http://www.telescope.org). Our main motivation for choosing a Coudé focus is that this allows the dome to be completely empty, apart from the telescope, and to keep the instrumen- F. Grundahl et al. 303 tation in a thermally controlled environment where all main components will be stationary – this will be beneficial for reducing maintenance. Located at the focal station will be an optical table on which the instruments are mounted. The main instrument will be a high-resolution spectrograph optimized for precision radialvelocity work. As velocity reference we will use an iodine cell in an arrangement similar to that developed by Butler et al. (1996). The spectrograph will be thermally isolated and will employ a UVES-like white-pupil design with a spectral resolution of 105 . An R4 echelle grating and a beam diameter of 75 mm will result in a slit width of 1.5 arcsecond on the sky which will ensure a high throughput for most observing conditions. A 2K×2K detector with low readout noise and coatings optimized for the 500 nm to 600 nm region will be used to record the spectrum. This will possibly be a frame-transfer CCD which would allow a very high duty-cycle. The spectral coverage will be from 480 nm to 670 nm in order to cover the primary region of interest when using iodine and to also include the Hα line. A preliminary optical design of the spectrograph carried out at the Anglo Australian Observatory shows that essentially diffraction-limited image quality across the detector can be achieved with very little variation of the line-spread function. It is planned to include also tip-tilt correction of the spectrograph feed in order to ensure maximum throughput and reduce the effects of guiding and tracking errors. The spectrograph will have a fixed setup, although we may include a few slits of fixed width to be able to change the spectral resolution. Figure 3 shows the basic outline of the telescope and focal plane. In front of the slit an atmospheric dispersion corrector (ADC) will be implemented, as well as calibration lamps and the temperature controlled iodine cell. Data are stored on-site for several weeks before being transported to a central institution; pipeline-reduced data will, however, be transmitted via the internet as soon as they have been processed by the data reduction pipeline. Performance We have made a detailed assessment of the spectrograph performance based on the AAO preliminary study and realistic numbers for seeing, slit width, mirror reflectivities and detector efficiency. The results are shown in Fig. 4 for a 75 mm beam diameter spectrograph and a 1.25 arcsecond slit in 2 arcsecond seeing at an airmass of two. This performance compares well with that of UVES on VLT as reported by Butler et al. (2004). The main reason that SONG performs almost equally well as UVES on bright targets is the low duty-cycle for UVES due to the long detector readout time, compared with the integration time and to the narrow slit (0.3 arcsecond) needed to obtain the high resolution. With this performance we have carried out simulations for solar-like stars to see what would be required to estimate their ages based on the values for their large and small frequency separations. The simulations show that for stars brighter than V ≈ 5 these can be accurately determined from a one week observing campaign. Status and schedule Currently (autumn 2006) SONG is nearly through its conceptual design phase. This is to be followed by detailed specifications and design of all components for a prototype during 2007. We plan to have an extended prototype phase (2008–2009) in order to eliminate all problems before going to full-scale operations, which is planned for around 2011–12. At http://astro.phys.au.dk/SONG further information and contact addresses for SONG can be found. 304 Stellar Oscillations Network Group Figure 3: Schematic layout of a SONG telescope and enclosure. The telescope focus is shown as a cross near (x, y) = (−3, 1) and the thick black bar is the optical table for the spectrograph and imager. The spectrograph and optical table will be thermally and mechanically isolated from the surroundings. Note that this design only uses 4 mirrors. The configuration shown here is essentially a German equatorial mount with the polar axis in a vertical position – this makes the design independent of the geographical latitude of the sites. The housing for the spectrograph is a standard 20 foot shipping container. Such containers are very rugged and easily available. Acknowledgments. The Carlsberg Foundation, the Villum Kann-Rasmussen foundation and the Danish Natural Science Research Council (FNU) are thanked for generous financial support to the conceptual design phase of this project. References Bedding T. R., Butler R. P., Kjeldsen H., et al., 2001, ApJ, 549, L105 Bouchy F., Carrier F., 2002, A&A, 390, 205 Butler R. P., Marcy G. W., Williams E., et al., 1996, PASP, 108, 500 Butler R. P., Bedding T. R., Kjeldsen H., et al., 2004, ApJ, 600, L75 Chaplin W. J., Elsworth Y., Howe R., et al., 1996, Solar Physics, 168, 1 F. Grundahl et al. 305 Figure 4: The predicted velocity precision for a single SONG node for a one minute observation versus the V magnitude of the observed star. A spectral type similar to α Centauri A and a slow rotation has been assumed. The echelle grating measures 75×300mm, and the spectrograph has a collimated beam diameter of 75 mm. The resolution with a 1.25 arcsecond slit is around 120 000. Dekker H., D’Odorico S., Kaufer A., Delabre B., Kotzlowski H., 2000, in Iye M., Moorwood A. F., eds, Proc. SPIE Vol. 4008, Optical and IR Telescope Instrumentation and Detectors. The International Society for Optical Engineering, Washington, p. 534 Fossat E., 1991, Solar Physics, 133, 1 Fröhlich C., Romero J., Roth H., et al., 1995, Solar Physics, 162, 101 Gabriel A. H., Grec G., Charra J., et al., 1995, Solar Physics, 162, 61 Harvey J. W. 1988, in Christensen-Dalsgaard J., Frandsen S., eds, Advances in Helio- and Asteroseismology, Proc. IAU Symposium No. 123. Reidel, Dordrecht, p. 497 Harvey J. W., Hill F., Hubbard R., et al., 1996, Sci, 272, 1284 Mayor M., Pepe F., Queloz D., et al., 2003, The Messenger, 114, 20 Vogt S. S., Allen S. L., Bigelow B. C., et al., 1994, in Crawford D. L., Craine E. R., eds, Proc. SPIE Vol. 2198, Instrumentation in Astronomy VIII. The International Soc. for Optical Engineering, Washington, p. 362 Walker D. D., Diego F., 1985, MNRAS, 217, 355 306 Stellar Oscillations Network Group DISCUSSION Telting: Can your spectrographs also be used for other types of stars? Grundahl: Yes. At the outset we had solar-like oscillations, but this has to be a sciencedriven project. We can imagine many different operation modes, depending on the science, like long-term projects where you only need two observations per night. I think the number of possibilities is endless in some sense. Telting: The other question is wavelength range. Why do you put a limit there? Grundahl: Wavelength range is both a cost and performance driver. I think we can cover many, many things, but not everything. Baglin: What would be the duration and duty cycle of a typical run? Grundahl: For the solar-like oscillators, we expect to dedicate the full network to one target, so you have all the possibilities to test for stability and so on. From the GONG experience, we expect to get in excess of, say, 85% duty cycle for equatorial targets, and correspondingly less, if you go North or South. There will be seasonal dependencies of course. Aerts: How long will the runs be? Grundahl: Months. Aerts: That means very few targets? Grundahl: Yes, but you see, e.g. also from Günter’s plots, that you need really good data, and I think this kind of data are needed to make real progress, and to get theorists to scratch their heads. Christensen-Dalsgaard [to Aerts]: It will be few targets per year, but for many years. We hope to be running for decades. Comm. in Asteroseismology Vol. 150, 2007 Asteroseismology at Dome C in Antarctica Eric Fossat LUAN, Universite de Nice, Parc Valrose, F-06108 Nice cedex 2, France Abstract The Antarctica plateau, at altitudes between 3 and 4 kilometres, offers the best possible sky for many astronomical purposes. Among these are the need for an excellent sky transparency, a heavily reduced level of scintillation and the possibility of very long times of integration only interrupted by rare clouds. So, asteroseismology observations using both photometry and spectroscopy are among the first scientific targets for the next few years at the ItaloFrench Concordia station, that is now open for winter-over activity since February, 2005. I briefly described the site testing activity and what we already know of the sky quality, and then the asteroseismic programmes that are likely to start within the next 5 years or so. DISCUSSION Hatzes: You are building a telescope in a rather extreme environment. Is there an estimate of how much more it would cost to build and operate it compared to a telescope of the same size at a ”normal” site? Fossat: We have only built telescopes of 25 − 35 cm diameter so far. The cost of making them work in this region is only about 10% larger. If you are building a large telescope, it may be different. We are not taking into account the logistical costs. Philippe Mathias, Janine Provost and Er*c Fossat. 308 Asteroseismology at Dome C in Antarctica Oleg Kochukhov seems happy with his coffee. Behind: Mikhail Sachkov. Comm. in Asteroseismology Vol. 150, 2007 A Fourier Tachometer at Dome C in Antarctica B. Mosser 1 and the SIAMOIS team 2 1 LESIA, Obs. Paris, CNRS/UMR 8109, 5 pl J. Janssen, 92195 Meudon, France 2 LESIA, IAS, UNSA/LUAN, OMP/LATT, IAP, OCA, SESO Abstract Dome C appears to be the ideal place for ground-based asteroseismic observations. The unequalled weather conditions yield a duty cycle as high as 88% over 3 months. We intend to install there the Fourier Tachometer SIAMOIS. Spectrometric observations with SIAMOIS and a dedicated small collector will be able to detect the = 3 oscillation modes that cannot be observed in photometry, in bright low-mass stars. Future ground-based asteroseismic observations It is well known that asteroseismic observations require long duration time series with the highest duty cycle. In parallel to the CoRoT mission, the next spectrometric ground-based observations will have to reach a high duty cycle. Then, they will give access to complementary information ( = 3 modes, hence the small separation between = 1 and 3 modes). SIAMOIS, a Fourier Tachometer to be installed at Dome C, will observe bright low-mass targets that will not be observed by CoRoT. Fourier Tachometry (FT) appears to give excellent performance (Mosser et al. 2003) for a much lower investment than échelle spectrographs; FT was chosen for the GONG helioseismic network after a long study of competing measurement strategies. The multiplex advantage of FT makes possible to observe simultaneously different targets with different telescopes fibrelinked with the same instrument. With SIAMOIS, we intend to observe with two dedicated 40-cm telescopes. Observations at Dome C Dome C appears to be an exceptional site for astronomy (Agabi et al. 2006). Monitoring of the clear sky fraction has shown that the duty cycle during the 100-day long polar night reaches 86%. An asteroseismic network such as the proposed SONG project (http://astro.phys.au.dk/SONG/) with nodes typically at the same place as the 6 GONG units cannot provide such a high duty cycle (Fig. 1, from Mosser & Aristidi 2007). As a consequence, Dome C is certainly the best ground-based site for continuous long-duration observations. The scientific programme at Dome C includes main targets, to be observed for 90 days with a duty cycle better than 88%, and secondary targets to be observed for 1 month, just before and after the polar night, with a duty cycle better than 60%. Hence, SIAMOIS offers a specific scientific program after CoRoT, for more than 6 winters. SIAMOIS is currently in phase A; first observations at Dome C are projected for 2011. References Agabi K., Aristidi E., Azouit M., et al., 2006, PASP, 118, 344 Mosser B., Aristidi E., 2007, PASP, 119, 127 Mosser B., Maillard J.-P., Bouchy F., 2003, PASP, 115, 990 310 A Fourier Tachometer at Dome C in Antarctica Figure 1: Comparison of the daily duty cycle distributions, at Dome C (full light line) or for a multi-site network (dashed light line: 6 sites; dot-dashed line: 5 sites; dot-dot-dashed line: 4 sites), and corresponding integrated duty cycle (heavy lines). Simulations for the network have been considered in the favourable case of an equatorial target, and for mean weather conditions. Comm. in Asteroseismology Vol. 150, 2007 Use of NIR spectroscopy for the study of pulsating stars P. J. Amado,1,2 J. C. Suárez,1 R. Garrido,1 A. Moya,1 S. Martı́n-Ruiz 1 1 Instituto de Astrofı́sica de Andalucı́a (CSIC), Granada, Spain 2 Universidad de Granada, Granada, Spain Asteroseismology relies on the identification of some of the oscillation modes in pulsating stars, which is a difficult and critical task requiring specific theoretical calculations and precise data. This situation can be greatly improved by extending the wavelength range used both in photometry and in spectroscopy. In a new era opened up by the advent of high-resolution infrared spectrographs at large telescopes, the present work might open up new possibilities for mode identification. It will also allow us to assess the real possibilities of low-medium resolution and the need for high-resolution, NIR spectroscopy for the study of these stars. As a first step in this study, V703 Sco was selected because of its high amplitude, its visibility and the number of periodicities already detected in its light curve. The main goal was to detect the pulsations by obtaining its radial velocity (RV) curve or in the measurements of the equivalent width (EW) of the hydrogen lines in the low-resolution data provided by the instrument SofI on the 3.6m telescope at La Silla. The star is a HADS star with periods of P0 = 0.14996, P1 = 0.11522 and P3 = 0.09354 days and a ratio between the fundamental and first overtone periods of 0.768. The rotational velocity is v sin i = 16 km s−1 and the spectral type is F0. A time series of 8 spectra was obtained in two nights with SofI, which provides a resolution of ∼ 1500. The data were reduced with IRAF and synthetic spectra computed from Kurucz grids, degraded to the resolution of the data and compared with the overall mean of the whole set of spectra. The data seem to indicate that the star is metal deficient as suggested by Strömgren photometry with −1.0 < [Fe/H] < −0.5. The best fit to the data is obtained with a model with [Fe/H] = −0.5, 6250 < Teff < 6750 K and log g = 4.5. V703 Sco probably is an SX Phe star. The Petersen diagram suggests that the star could be either a 1.90 M star of solar metallicity or a lower mass star of lower metallicity. The high gravity derived from the synthetic spectra contradicts what would be expected from the periods of this star which imply an evolved status. However, LTE modelling of the NIR hydrogen lines might fail to reproduce the strength of the lines (Przybilla & Butler 2004). The dispersion in the RV and EW measurements was too high to detect the pulsations in these data. Discussion and conclusions The results from the data obtained on V703 Sco show that the low resolution provided by instruments like SofI (R ∼ 1500) is not sufficient to produce RV curves of adequate precision. This resolution is clearly too low to study the line profiles. Perhaps, with better data, a study of the time series using the EW of the hydrogen lines could result in sufficiently precise curves from which to extract the amplitudes and phases in the optical (Dall et al. 2003 and references therein). High-resolution time series of a sample of pulsating stars are needed to check what lines are variable in this region of the spectrum. Spectroscopic techniques already used in the optical (moment method, line profile fitting, Doppler imaging) could be applied to the NIR, and, therefore, information of the modes extracted from this spectral region could constrain and help in the identification of the modes. The diagnostic potential of these lines comes from their different sensitivity to changes in Teff and log g with respect to the optical and the interplay between the pulsation and the limb-darkening effects. Also, knowing that the 312 Use of NIR spectroscopy for the study of pulsating stars sensitivity of the H i lines in this region to Stark broadening is higher than for the optical lines, the effects of a radial pulsation in these lines as the star goes through its expansioncompression cycle should be more easily observable. This should be tested by trying to detect periodic changes in the shape or equivalent width of the lines, which should become highly broadened as the star shrinks and, therefore, the density increases. These same tests could be used to try to observe non-radial pulsations and for the identification of the modes. Finally the spectra taken in this region can be used for spectral typing of the objects. For future work, proposals to observe pulsating stars of various amplitudes have been sent to both Science Verification and P79 for CRIRES. Simultaneous high-resolution spectroscopy in the optical and the NIR should be acquired to study pulsating stars. Acknowledgments. PJA acknowledges the staff of La Silla observatory for their helpfulness and specially Michael Sterzik and Maarten Baes for preparing and taking the observations. References Dall T. H., Handler G., Moalusi M. B., Frandsen S., 2003, A&A, 410, 983 Przybilla N., Butler K., 2004, ApJ, 609, 1181 Comm. in Asteroseismology Vol. 150, 2007 Jovian seismology: preliminary results of the SYMPA instrument P. Gaulme,1 F. X. Schmider,1 J. Gay,2 C. Jacob,1 F. Jeanneaux,1 E. Fossat,1 J. C. Valtier,2 M. Alvarez,3 M. Reyes 3 2 1 LUAN/Universite de Nice, Parc Valrose, 06108 Nice Cedex 02, France Observatoire de la Cote d’Azur, Bd de l’Observatoire, BP. 4229 Nice cedex 4, France 3 Instituto de Astronomı́a, UNAM, México D.F., México Abstract Jupiter’s internal structure is poorly known (Guillot et al. 1997). Seismology is a powerful tool to investigate the internal structure of planets and stars, by analysing how acoustic waves propagate. Mosser (1997) and Gudkova & Zarkhov (1999) showed that the detection and the identification of non-radial modes up to degree = 25 can constrain strongly the internal structure. SYMPA is a ground-based network project dedicated to the Jovian oscillations (Schmider et al. 2002). The instrument is composed of a Mach-Zehnder interferometer which produces four interferograms of the planetary spectrum. The combination of the four images in phase quadrature allows the reconstruction of the incident light phase, which is related to the Doppler shift generated by the oscillations. Two SYMPA instruments were built at the Nice university and were used simultaneously during two observation campaigns, in 2004 and 2005, at the San Pedro Martir Observatory (Mexico) and the Izana Observatory (Las Canarias). We present for the first time the data processing and the preliminary results of the experiment. References Gudkova T. V., Zharkov V. N., 1999, Planet. Space Sci., 47, 1211 Guillot T., Gautier D., Hubbard W. B., 1997, Icarus, 130, 534 Mosser B., 1997, in Provost J., Schmider F. X., eds, Proc. IAU Symp. 181, Sounding solar and stellar interiors. Kluwer, Dordrecht, p. 251 Schmider F. X., Gay J., Jacob C., 2002, in Combes F., Barret D., eds, Semaine de l’Astrophysique Francaise, EdP-Sciences Conference Series, Les Ulis, p. 611 314 Jovian seismology: preliminary results of the SYMPA instrument Werner Weiss presents Gerald Handler’s deserved remuneration for running the meeting. Comm. in Asteroseismology Vol. 150, 2007 Small IRAIT Telescope: photometry and asteroseismology at Dome C G. Tosti,1 G. Nucciarelli,1 M. Bagaglia,1 A. Mancini,1 S. Castellini,1 O. Straniero,2 R. Briguglio,3 K. G. Strassmeier,4 (for the IRAIT Collaboration) D. Stello 5 1 Dipartimento di Fisica, Universitá di Perugia, Via A. Pascoli, I-06100 Perugia, Italy 2 INAF- Osservatorio di Teramo, Via Maggini, I-64100 Teramo, Italy 3 Dipartimento di Fisica, Univ. La Sapienza, P. le Aldo Moro 2, I-00185, Roma, Italy 4 Astrophysical Institute Potsdam, Potsdam, Germany 5 School of Physics, University of Sydney, NSW 2006, Australia Abstract Small IRAIT is a 25 cm telescope planned to be installed at Dome C during February 2007. It will be equipped with a CCD, a filter wheel, two photomultipliers and a liquid crystal tunable filter. Small IRAIT is intended to: test astronomical measurements from Dome C; provide site qualification and suitability for asteroseismology by taking advantage of the low scintillation level and the possibility for long uninterrupted observations. Small IRAIT will be the forerunner of the IRAIT telescope that will be installed during the Antarctic Summer 2007−2008. Astronomy from Antarctica In the last years attention has been focused towards Antarctica as a possible astronomical site. Extremely low temperatures (-30 C during summer, -80 C during winter), small scintillation and good seeing (at least a factor of two better than at La Silla, Agabi et al. 2006) and the long duration of the polar night are promising ingredients for photometry. Antarctica seems to be an alternative to expensive space missions, with the great advantage of the possibility for logistics and personnel to work on the experiments on the base. Concordia Base, a joint Italian-French cooperation, has been fully operational also in the winter period since 2005. Small IRAIT Telescope Small IRAIT is the little brother of the IRAIT infrared telescope. The task of the small telescope is to perform astronomical experiments before the arrival of IRAIT itself. Small IRAIT is an optical telescope, 25 cm of diameter and with 3 m focal length. The acquisition unit set up on the focal plane is inside a heated, insulated box. It is equipped with an automated temperature controller and is decoupled from the outside by an optical window. The experimental setup has been assembled following two guidelines: redundancy, in order to continue its function even in case of a breakdown, and multipurpose to carry out different astronomical experiments. The focal plane is equipped with a CCD (MaxCam, with KAF-0402E/ME, 768 × 512 pixels), photomultipliers, filterwheel and standard UBVRI filters, precision focuser, and liquid crystal interference filters. Electronics include a lock-in amplifier and a modulation and demodulation apparatus. Scientific goal for winter 2007 The Small IRAIT mission will provide a first test of astronomical measurements during the polar night. Similar tests have been performed in the last years by other groups, mainly devoted to site testing and measurements of atmospheric turbulence parameters (Aristidi et 316 Small IRAIT Telescope: photometry and asteroseismology at Dome C al. 2005, Agabi et al. 2006). Small IRAIT, with its multi-purpose focal plane instrumentation, will provide different kinds of tests. Three principal goals are foreseen: • instrumental tests to check operating conditions during the cold polar winter, with emphasis on remote control and communications • site qualification, which includes measurements of multiband extinction coefficients, transparency stability throughout the night, and sky magnitude in winter at different times during the night (for a previous study, refer to Kenyon et al. 2006) • test of stellar photometry, mainly devoted to asteroseismology. For this test we plan to get time series of β Hyi (V = 2.8). This should enable us to measure the scintillation as well as to detect the power excess of solar-like oscillations after roughly four weeks of observation. We further aim to obtain multi-colour time series of an open cluster with known variables. The winter mission will begin on the 1st of February 2007, when the telescope will be installed at Concordia Base. Acknowledgments. We wish to thank the Italian and French Polar Institutes (PNRA & IPEV) for logistics and financial support for the experiment and the mission. We wish to thank Laszlo Kiss and Tim Bedding (Sydney University, Australia) for constructive discussions and suggestions. References Agabi A., Aristidi E., Azouit M., et al., 2006, PASP, 118, 344 Aristidi E., Agabi A., Fossat E., et al., 2005, A&A, 444, 651 Kenyon S. L., Lawrence J. S., Ashley M. C. B., et al., 2006, PASP, 118, 924 Comm. in Asteroseismology Vol. 150, 2007 MONET, HET and SALT and asteroseismological observations and theory in Göttingen S. Schuh, F. V. Hessman, S. Dreizler, W. Kollatschny, W. Glatzel Institut für Astrophysik, Georg-August-Universität Göttingen, 37077 Göttingen, Germany Abstract The Göttingen stellar astrophysics group, headed by Stefan Dreizler, conducts research on extrasolar planets and their host stars, on lower-main sequence stars, and on evolved compact objects, in particular hot white dwarfs (including PG 1159 objects, magnetic WDs and cataclysmic variables), and subdwarf B stars. In addition to sophisticated NLTE spectral analyses of these stars, which draw on the extensive stellar atmosphere modelling experience of the group, we actively develop and apply a variety of photometric monitoring and time-resolved spectroscopic techniques to address time-dependent phenomena. With the new instrumentational developments described below, we plan to continue the study of variable white dwarfs (GW Vir, DB and ZZ Ceti variables) and in particular sdB EC 14026 and PG 1617 pulsators which already constitute a main focus, partly within the Whole Earth Telescope (WET/DARC), http://www.physics.udel.edu/∼ jlp/darc/) collaboration, on a new level. Additional interest is directed towards strange mode instabilities in Wolf Rayet stars. MONET MONET (http://monet.uni-goettingen.de) is a MOnitoring NEtwork of Telescopes consisting of two 1.2 m internet-operated telescopes with 40% of observing time reserved for school use. To improve physics and computer instruction in participating international schools, the Alfried Krupp von Bohlen und Halbach-Stiftung has awarded funds for the construction of these fully automatic robotic telescopes, which are built by Teleskoptechnik Halfmann. Our partner institutions, which host and run the telescopes, are the McDonald Observatory of the University of Texas at Austin and the South African Astronomical Observatory with its station at Sutherland. The first telescope (MONET/North) was erected at McDonald in December 2005. Remote observing has been put into operation and is routinely done, so that several scientific projects are now running to evaluate the performance of this new facility. The delivery of MONET/South into its already finished enclosure at Sutherland is scheduled for later this year and it should be commissioned in early 2007. MONET/South should be able to serve as a pathfinder telescope for SALT. The two MONET telescopes will not only represent a network by themselves: The HTN (http://www.telescope-networks.org) collaboration plans on joining a large variety of telescopes with different specific purposes in a Heterogeneous Telescope Network. It is also planned to use the MONET telescopes to participate in future WET/DARC (Whole Earth Telescope / Delaware Asteroseismic Research Center) campaigns. One of several primary goals of MONET during scientific use is the study of stellar variability. HET and SALT As a partner in these telescope projects, the Institute for Astrophysics Göttingen has guaranteed access to the HET (http://www.as.utexas.edu/mcdonald/het/het.html) and SALT 318 MONET, HET and SALT and asteroseismological observations and theory in Göttingen (http://www.salt.ac.za). The planned high time resolution in combination with the projected UV capabilities make SALT, in particular, attractive for studies of compact blue variable objects. Asteroseismology projects In the past, our contributions to sdB monitoring were predominantly obtained with Calar Alto observatory telescopes (e.g. the discovery and follow-up monitoring of the hybrid sdB pulsator HS 0702+6043, and part of the extensive monitoring of PG 1605+072 during the MultiSite Spectroscopic Telescope (MSST) campaign, and long-term monitoring of HS 2201+2610). As a special performance verification project for SALT, we currently are investigating the photometric stability of Wolf-Rayet stars with SALTICAM to test existing models that predict strange mode oscillations, and we obtain spectra with RSS to check classification and search for line profile variations. Acknowledgments. S. Schuh thanks the organizers for generous support. Hans Bruntt and Frank Grundahl enjoying a pleasantly warm Viennese evening. Comm. in Asteroseismology Vol. 150, 2007 A New Slovak Observatory 500 km from Vienna I. Kudzej,1 T. Dorokhova,2 P. Dubovsky,1 A. Ryabov,2 M. Vadila,1 N. Dorokhov,2 N. Koshkin 2 2 1 Vyhorlatsky Astronomical Observatory, Humenne, Slovakia Astronomical Observatory of Odessa National University, Odessa, Ukraine Vyhorlatsky Astronomical Observatory (VAO, Slovakia) and the Astronomical Observatory of Odessa National University (AO ONU, Ukraine) are developing a new observatory at the Kolonicke Sedlo (VAO KS) in the Vyhorlatsky mountains (latitude: 48o 57’ N, longitude: 22o 16’ E, altitude: 465 m). Figure 1: The percentage of photometric (grey blocks) and spectroscopic (black blocks) nights per month at Kolonicke Sedlo measured in 2006. This site has a unique atmospheric transparency for central Europe (the seeing is about 2.5 in the best nights), small light pollution (night sky brightness about 20m.5 per square second), and up to 120 − 130 nights per year are usable for photometry. At present the VAO KS is sufficiently equipped for astronomical observations: the work rooms possess electricity, computers, phone and internet. All other necessary facilities are provided. The 1 m telescope, which is the biggest astronomical instrument in Slovakia, is installed in a dome of 5 m diameter. The telescope has a focal ratio 1:12 and field of view 25’. Currently it is equipped with a high speed two-star photometer, an analogue of the photometer described by Dorokhov & Dorokhova (1994). A Ritchey-Chretien guider of 0.3 m diameter, 1:8 focal ratio and field of view 60’ works with a CCD autoguider. Furthermore we suggest to mount a CCD camera to the viewing 320 A New Slovak Observatory 500 km from Vienna Figure 2: The 1 m telescope equipped with the high speed two-star photometer. Left: the CCD autoguiding system mounted to the guider. channel of the photometer. In this way the third channel can be applied for autoguiding as well as for sky background or comparison stars measurements. Besides the main instrument at VAO KS some small telescopes, a Newton 11 inch, a Newton 14 inch, etc., work with MEADE DSI Pro CCD cameras. Such a set of instruments allows to carry out monitoring programs and detailed investigations of the temporal variations of the revealed phenomena. We now set up the complex, train the staff and students, and test and improve the performance of the photometer. The work is realized within the program context and standards of the global asteroseismic networks DSN (see, e.g., Breger & Handler 1993) and WET (Nather et al. 1990; Kalytis et al. 1993). A more detailed description of the site, observatory, and facilities is available at the website: http://www.astrokolonica.sk/ Acknowledgments. The work was supported by the Ukrainian MON grant No M/1532006 and the Slovak Ministry of Education grant SK-UA-01006. References Breger M., Handler G., 1993, Baltic Astron., 2, 468 Dorokhov N. I., Dorokhova T. N., 1994, Odessa Astronomical Publ., 7, 168 Kalytis R., Skipitis R., Karaliunas A., Dzindzeleta B., 1993, Baltic Astron., 2, 504 Nather R. E., Winget D. E., Clemens J. C., Hansen C. J., Hine B. P., 1990, ApJ, 361, 309 Comm. in Asteroseismology Vol. 150, 2007 Reflections on some aspects of ground-based observations for asteroseismology Christiaan Sterken Vrije Universiteit Brussel, Pleinlaan 2, B-1050 Brussels, Belgium Abstract We call attention to two problems of long-term observations: the problem of maintaining reliable and stable standardization, and the problem of securing sufficient power in terms of postdoctoral workers to carry out the workload. Introduction This meeting clearly illustrates that there is taking place a happy evolution in the study of pulsating stars, notably the gradual increase in the length of the time baseline of observations. In particular, the old habit to “observe many stars just a little bit” is gradually giving way to monitoring a more limited number of objects over much longer time baselines. The growing opinion that good science comes from long strings of data is a very positive development. That this has not always been the case, is testified by a statement from Paul Ledoux1 : “. . . I do not want to deny the importance of statistical relations that might be revealed by numerous but limited observations of a great number of objects. But it seems to me that real progress in the physical interpretation of a given type of variables depends essentially on detailed and at the same time complete and continuous observations of one typical star.” Indeed, many projects now cover an unprecedented extent in time coverage, and in precision. At the same time, surveys almost double the number of known members of a class of variables from one major meeting to the other. Wojtek Dziembowski underlined that mode identification relies on theory, and not only on observational data. Indeed, there is a long distance between delivering a complete and accurate frequency solution, and recognizing modes: much more is needed than good data and a frequency solution. Pulsation-mode identification heavily relies on sophisticated theories, and the increasing computational facilities soon will force us to deal with millions of models and tracks. But these complicated models are by far not the only theoretical aspect of asteroseismology: few observers realize that there is a tremendous impact of theoretical conceptions on so-called “observables”, i.e. quantities that are not observed directly, but always depend on theory, mainly through their calibration. The foregoing thoughts lead to the recognition of two problems. Problem I The bonus of extending the observational baseline has a drawback, though. It is not often realized that long time bases frequently lead to problems of standardization. Let me remind that standards are not just a set of constant stars needed for transforming one batch of data from one site to another: standards are a system of basic calibrators needed to guarantee 1 1956, letter to C. de Jager. 322 Reflections on some aspects of ground-based observations for asteroseismology the stability and consistency of the observational data, and to secure a reliable and stable (in time) mapping of the space of basic data (e.g. colour indices) onto the space of physical “observables” (e.g. Teff , [Fe/H], or even angular diameter). We must realize that existing standards and calibrations change with time, mainly because detectors change. Unfortunately, most of this is poorly documented. Moreover, almost every new observing facility (ground- and space based) creates a new standard that is not compatible with basic calibrations of stellar observables constructed a decade or longer ago. Last but not least, the acquisition of calibrated measurement is poorly taught during observer training. Problem II Referring to the shiny prospects ahead, someone said “We should all be in business for an extended period of time to come.” Yes, but. Have a look at the mode of funding of so many projects presented here: funding agencies provide huge amounts of support to acquire the data, money for organizing meetings, and travel support to populate these meetings. However, they do not provide long-term or even permanent research positions to guarantee that we shall ever be able to fully analyse and truly understand the new data flowing in. It is time to change these modes of funding, and perhaps we should use the momentum of these new networks to convince governments and funding agencies to invest more means in salaries for postdoctoral researchers. DISCUSSION Roxburgh: I agree with you that we should change the way of funding. But how? Sterken: By just trying. You have to insist, and I think that people like you, Michel and others are in a position to revert this tendency. As a postdoc, it is nice to travel etc., but it is not so nice when after a few years, when you understand what you are doing and you like what you are doing, you will have to stop. Metcalfe: I would like to point out that governments and funding agencies are not the only people to whom we should make these arguments. Two examples already exist: the Delaware Asteroseismic Research Center (which now operates the Whole Earth Telescope), and the Las Cumbres Observatory Global Telescope Network (also known as the Google network), are both privately funded. Shipman: There is actually a third example in the US that we are sometimes taking advantage of. This is the SMARTS organization which is running the smaller telescopes at Cerro Tololo in Chile. In part, these smaller telescopes networks, in particular the SONG project, are really trying to reduce operating costs. Another comment from my observations in the States is that when I am trying to make implicit longer-term commitments, I never mentioned the word tenure in connection with supporting the people associated with the project. I know that if I had mentioned that, I would have had no success at all in getting any money. Deupree: You need to appreciate the amount of time it takes senior people (or anybody else) to work for these sorts of changes. It takes many visits to the appropriate people to lobby for these changes - they cannot be made to happen quickly. With luck these types of changes can be made, but it usually requires significant sacrifices of time by senior personnel to make it happen. Sterken: That is true, but you need to invest a lot of time on grant applications anyway. If you are doing a long-term project and the funding stops after a few years, all this is lost. I agree that you must spend time on it, but only once to make this suggested change. Comm. in Asteroseismology Vol. 150, 2007 Discussion on ground-based asteroseismology led by Christiaan Sterken Vrije Universiteit Brussel, Pleinlaan 2, B-1050 Brussels, Belgium Dziembowski: I would like to ask Eric Fossat about the situation of human beings during the Antarctic night. How easily can be taken care of ill astronomers? How quickly can they be taken to hospital? Fossat: There is a doctor at the station with limited surgical equipment and capability, but if you are in real big trouble, there is absolutely no possible escape during 9 months and you have to be taken care at the station within these local possibility limits. During the daily routine, you have to take care that you get proper rest and you must be careful with breathing because you can freeze inside, which is very uncomfortable. Kaye: There has been some discussion about the automation of telescopes. At Fairborn Observatory, there are at least two that are operated by Vienna and there is a large collection operated by Tennessee State University, but all those are photometric. As far as I know, they work extremely well. The Tennessee State group is still trying to build an automatic spectroscopic telescope that is still not off the ground and they’ve been trying that for about eight years. So when we’re considering the possibility of automated telescopes for photometry we know how to do it, but it’s still non-trivial and it still requires people to actually go there when there are technical problems. With spectroscopy, I am not sure the problem has been solved, and the other half of that is, where do you put this? It’s likely that it is associated with a university which has students who would like to go to a telescope and use it. So, while in practice you can get a very high duty cycle on APTs, you could probably have something with a very high duty cycle and associated with a WET campaign, so that you get spectroscopy and photometry at the same time on the same object at a very dense collection. So when students actually go to the telescopes, they can take spectra of that object at a comparatively low duty cycle. Bedding: I have a question and a comment. The question is if there is any possibility that the bandwidth for communications will improve at Dome C? Fossat: Right now, the bandwidth is a few kB. The prospect is to improve that to 150 kB in two or three years. Mosser: In fact, it’s very easy to transmit time series, it’s just an email. Bedding: My comment is directed towards Frank’s talk, to point out the difference between photometry and spectroscopy for the detection of solar-like oscillations. In photometry, the background from granulation noise is higher than for spectroscopy. One can see = 3 modes in the velocities because of the lower background. Weiss: I got the impression that the spectrograph for SONG does not use a fibre. What was the argument for that? Grundahl: The configuration we chose is the safest (it is not the cheapest!). The reason for avoiding the fibre is that for the grating size we will use for the spectrograph you will get a lower efficiency. The use of a fibre has been tested with the iodine method, but I haven’t seen a performance of half a meter per second, which is our goal, in the literature. I think it is likely but it would have to go into a prototype. One thing I probably didn’t point out clearly is that by putting things into a Coude room, the only moving part that will experience weather is the telescope; everything else will be stationary. The only part that will move is the atmospheric dispersion corrector, and I think this is an important aspect for operations. 324 Discussion on ground-based asteroseismology Weiss: But that will be the same with a fibre. Grundahl: Yes. I am not saying this isn’t possible, but I think it is better without a fibre. Kaye: If you have a fibre-fed spectrograph and it will be automated, the potential for light loss in the fibre is much higher because of the way it’s going to operate. We saw that at the Multiple Mirror Telescope at the Hard Labor Creek Observatory, where they put nine 33-cm mirrors together to form one 1-m-class telescope, and the outer eight mirrors each fed a fibre to the spectrograph. The path of the fibre was very short but you lost a lot of light just because of the nature of the beast. If you want to have it mechanically simple, Frank’s layout is probably safe. Hatzes: Two comments on your prototype design. There’s a lot of reflections there, and if you want to make a 1-m telescope as efficient as possible you may not want to have a factor of 0.854 due to reflections in your light path. Another point about using the fibre: you may also want to estimate how much image stability will cost. Even if using the cell, if you have really really good seeing, you will get worse precision because the image will move around in the slit. There are a lot of trade-offs to consider. Grundahl: We expect to use these coatings that give higher reflectivity. After the third mirror in the telescope you have an optical window which will essentially close the system from there on. You can get these windows which have, say, at least 98% over the wavelength range that we are interested in. With respect to the movements of the star, this is of concern to me as well. Because the telescope is so small, you will get a fairly large slit which will help with the efficiency, but for the image motion we would actually like to use tip/tilt stabilization. At Keck Marcy and Butler achieve 1 m/s with an 0.9 arcsec slit in ∼0.6 arcsecond seeing. Mosser: With a Fourier tachometer, we avoid all these problems. We use a fibre, but under very different conditions. Think about Fourier tachometers, they are very efficient in these cases... Space-based asteroseismology Jørgen Christensen-Dalsgaard and Gerald Handler. Comm. in Asteroseismology Vol. 150, 2007 Asteroseismology with the WIRE satellite H. Bruntt School of Physics A28, University of Sydney, 2006 NSW, Australia Abstract I give a summary of results from the WIRE satellite, which has been used to observe bright stars from 1999–2000 and 2003–2006. The WIRE targets are monitored for up to five weeks with a duty cycle of 30–40%. The aim has been to characterize the flux variation of stars across the Hertzsprung-Russell diagram. I present an overview of the results for solar-like stars, δ Scuti stars, giant stars, and eclipsing binaries. Introduction The Wide-field Infra-Red Explorer (WIRE) satellite was launched on 4 March 1999 with the aim to study star-burst galaxies (Hacking et al. 1999). The mission was declared a failure only a few days after launch when it was realized that the hydrogen coolant for the main camera had leaked. Since May 1999 the star tracker on board WIRE has been used to measure the variability of bright stars (Buzasi et al. 2000). Previous reviews of the performance and science done with WIRE were given by Buzasi (2001, 2002, 2004), Laher et al. (2000), and Buzasi & Bruntt (2005). Observing with WIRE WIRE is in a Sun-synchronous orbit with a period that has decreased from 96 to 93 minutes from 1999 to 2006. Constraints from the pointing of the solar panels limits pointing in two roughly ±30◦ strips located perpendicular to the Sun-Earth line (Buzasi et al. 2000). In order to limit scattered light from the illuminated face of the Earth the satellite switches between two targets during each orbit. Each target has a duty cycle of typically 30–40%. The star tracker has a 52-mm aperture and a 5122 pixel SITe CCD. Windows of 8×8 pixels centred on the star are read out from the CCD at a cadence of 10 Hz. An example is shown in the left panel of Fig. 1. During the first few months of operation only the primary target was read out in the 10 Hz high cadence mode, but after refining the on-board software up to five targets were read out (each target read out at 2 Hz). In the right panel of Fig. 1 I show the distribution of x, y positions for 56 000 windows centred on the main target (α Cir). The FWHM of the distribution is just one hundredth of a pixel. One pixel on the CCD corresponds to about one arc minute. For details on the photometric pipeline and a discussion of scattered light see Bruntt et al. (2005). In the early WIRE runs from 2000–1 the field was slowly rotating which meant that the secondary targets moved across the CCD at timescales of one pixel every few days (depending on the distance from the main target which is centred on the CCD). These data are thus only of limited use since it is not possible to take flat fields. Due to lack of funding WIRE was put into sleep mode for about two years from September 2001 – November 2003. For the past three years WIRE has observed in a new mode where the secondary stars stay fixed on the same position on the CCD. As a consequence, the number of stars observed with high photometric precision has increased from a few dozen to more than two hundred. H. Bruntt 327 Figure 1: The left panel shows a CCD window from WIRE. The grey boxes mark the pixels used for determination of the sky background. The right panel shows the distribution of the x, y position of the central target from 56 000 CCD windows. An overview of stars observed with WIRE In Table 1 I list the brightest stars observed with WIRE from March 1999 to June 2006. There are 45 main sequence stars (luminosity class IV-V) on the left part of the table and 45 evolved stars on the right. I give the common name of each star (usually the Bayer designation), the Henry Draper number, V magnitude, and spectral class. This information was extracted from the simbad database. I have also marked the stars for which the analysis has been published √ (marked with a ) and the stars that are currently being analysed (marked with a ). In Fig. 2 I show the location in the Hertzsprung-Russell diagram of 200 stars observed with WIRE. In the following I will briefly discuss the main results for different classes of stars. Solar-like stars The first solar-like star observed with WIRE was α Cen (Rigil Kentaurus; G2V). Preliminary results based on the 50-d light curve observed in high-cadence mode were reported by Schou & Buzasi (2001), who could claim the first clear detection of the characteristic comb pattern of p modes in the star. This was confirmed in radial velocity by Bouchy & Carrier (2001, 2002). Bedding et al. (2004) identified 40 modes from a multisite radial velocity study, and Kjeldsen et al. (2005) constrained the lifetime of the modes to τ = 2.3+1.0 −0.6 days. The main limitation on the uncertainty of the lifetime is the limited time baseline. Fletcher et al. (2006) recognized this, made a refined analysis of the WIRE data set and measured a mode lifetime of τ = 3.9 ± 1.4 days which is in agreement with the result from the radial velocity survey. Karoff et al. (2007) applied the same method to the WIRE data of the evolved solar-like star β Hydri (G2IV). They found clear evidence of solar-like oscillations and measured a mode lifetime very similar to α Cen (τ = 4.2+2.0 −1.4 d). Like β Hydri, α CMi (Procyon; F5IV-V) is slightly more massive and more evolved than the Sun. Bruntt et al. (2005) found excess power in the power spectrum which they interpreted as a combination of granulation and solar-like oscillations. This was in disagreement with the null result by Matthews et al. (2004) based on 32 days of continuous photometry from the MOST satellite. As discussed by Bruntt et al. (2005), the noise level per data point in the MOST data was more than three times higher than in the WIRE data. This is likely due to high scattered light levels in the MOST data (see also Bedding et al. 2005). 328 Asteroseismology with the WIRE satellite Table 1: The brightest main sequence (left) and evolved stars (right) observed with WIRE. The name, HD number, √V magnitude, and spectral type are given. Stars whose observations have been published are marked by , while stars currently being analysed are marked by . √ √ √ √ √ √ √ √ Name α Cen α CMi α Aql α Vir β Cru α Leo λ Sco UMa β Aur α Pav δ Vel γ Leo σ Sgr β Leo β Cas δ Sco η Cen κ Vel ζ Oph α Col η Boo υ Sco β Hyi α Ara π Sco ζ Tau α Cir δ UMa δ Eri o Vel β Aql Eri ρ Sco π Lup ψ Cen μ Eri ρ Lup μ Ori Cep 90 Tau o Lup δ UMi γ Col τ 2 Lup ι Oph HD 128620 61421 187642 116658 111123 87901 158926 112185 40183 193924 74956 − 175191 102647 432 143275 127972 81188 149757 37795 121370 158408 2151 158427 143018 37202 128898 106591 23249 74195 188512 22049 142669 133242 125473 30211 128345 40932 211336 29388 130807 166205 40494 126354 152614 V 0.0 0.3 0.8 1.0 1.3 1.4 1.6 1.8 1.9 1.9 2.0 2.0 2.1 2.1 2.3 2.3 2.3 2.5 2.6 2.6 2.7 2.7 2.8 2.8 2.9 3.0 3.2 3.3 3.5 3.6 3.7 3.7 3.9 3.9 4.0 4.0 4.0 4.1 4.2 4.3 4.3 4.3 4.3 4.4 4.4 Type G2V F5IV-V A7V B1III-IV B0.5IV B7V B2IV+ A0p A2IV+ B2IV A1V K0 B2V A3V F2IV B0.2IVe B1.5Vne B2IV-V O9V B7IVe G0IV B2IV G2IV B2Vne B1V+ B2IV A5V A3V K0IV B3IV G8IV K2V B2IV-V B5V A0IV B5IV B5V A2V F0IV A6V B5IV A1Vn B2.5IV F7 B8V √ √ √ √ Name α Boo α Ori α UMa Car β CMa α UMi β UMi γ Dra α Lup κ Sco Peg β Peg α Peg Cyg γ Aql Vir η Peg ι1 Sco α Ind β Col φ Sgr G Sco κ Oph β Cep τ Sgr Cas ζ Cep θ 2 Tau ξ Hya γ Tau β Ind ξ Dra ν Eri ν 2 CMa υ Boo δ Cep − Q Sco π Aur CE Tau V761 Cen σ Lup ν 3 CMa ρ Cas 11 Cep HD 124897 39801 95689 71129 44743 8890 131873 164058 129056 160578 206778 217906 218045 197989 186791 113226 215182 161471 196171 39425 173300 161892 153210 205021 177716 11415 210745 28319 100407 27371 198700 163588 29248 47205 120477 213306 5848 159433 40239 36389 125823 127381 47442 224014 206952 V 0.0 0.6 1.8 2.0 2.0 2.0 2.1 2.2 2.3 2.4 2.4 2.4 2.5 2.5 2.7 2.8 2.9 3.0 3.1 3.1 3.2 3.2 3.2 3.2 3.3 3.3 3.4 3.4 3.5 3.7 3.7 3.7 3.9 4.0 4.1 4.1 4.2 4.3 4.3 4.4 4.4 4.4 4.4 4.5 4.5 Type K1.5III M2Iab K0Iab K3IIIva B1II/III F7 Ib-II K4III K5III B1.5III B1.5III K2Ib M2.5II-I B9III K0III K3II G8III G2II-III F2Iae K0IIICNv K2III B8III K2III K2III B2IIIeva K1IIIb B3III K1.5Iab A7III G7III K0III K1II K2III B2III K1III+ K5.5III F5Iab K2II-III K0IIIb M3II M2Iab B7IIIpva B2III K0II/III G2Ia0e K1III H. Bruntt 329 Figure 2: Hertzsprung-Russell diagram of about 200 stars observed with WIRE. Delta Scuti Stars Several δ Scuti stars have been monitored with WIRE. Poretti et al. (2002) made an analysis of the binary δ Scuti star θ 2 Tau (the primary is A7III) and found 12 frequencies which were in agreement with results by Breger et al. (2002) from a ground-based multisite campaign. The detection of a peak at high frequency seen in both the WIRE and ground-based data led Breger et al. (2002) to argue that this mode is real (i.e. not an alias or combination frequency) and likely due to oscillations of the secondary star in the θ 2 Tau binary system. Poretti et al. (2002) were the first to point out that WIRE is capable of doing time-series of the often neglected brightest stars in the sky, which are simply too bright for typical 0.5– 1.0-m telescopes normally used for multisite campaigns on δ Scuti stars (e.g. the DSN and STEPHI networks). Indeed, Buzasi et al. (2005) found seven low-amplitude (0.1–0.5 mmag) modes in α Aql (Altair; A7V), which is now the brightest δ Scuti star at V = 0.8. Bruntt et al. (2007a) combined WIRE photometry and Strömgren uvby ground-based observations in an attempt to identify the modes of the δ Scuti star Cep (F0IV). The spacebased data provided a superior spectral window and low noise level. Using the extracted frequencies from WIRE Bruntt et al. (2007a) measured the amplitudes and phases in the uvby filters from ground-based photometry. However, the limited amount of ground-based data made the accuracy of the amplitudes and phases too poor to be able to identify the 330 Asteroseismology with the WIRE satellite modes from phase differences and amplitude ratios (e.g. Garrido, Garcia-Lobo & Rodriguez 1990). Bruntt et al. (2007a) estimated that it would require more than 100 nights of data to obtain the accuracy on the phases and amplitudes to be able to identify the modes. B-type stars More than 35 β Cep and SPB stars have been observed with WIRE. Cuypers et al. (2002) confirmed the variability known from spectroscopy of β Cru (Mimosa; B0.5IV) and in addition found new low-amplitude modes (A 0.2−0.3 mmag). Cuypers et al. (2004) analysed WIRE data of the known multi-periodic β Cep star κ Sco (part of Girtab; B1.5III) and also detected low-amplitude modes not observed previously. Bruntt & Buzasi (2006a) gave preliminary results for λ Sco (Shaula; B2IV) which is a known triple system (Uytterhoeven et al. 2004). From spectroscopy it is known that λ Sco comprises two B type stars in a wide orbit (P 1083 d); one of these components has a low mass companion (P 5.95 d). After subtracting the β Cep pulsation Bruntt & Buzasi (2006a) could clearly see the primary and secondary eclipses in the close system. From their preliminary light curve analysis they constrained the masses and radii of the component stars. Giant stars The giant stars comprise around half of the targets observed with WIRE (cf. Fig. 2). This is because only the main target is chosen, while four additional secondary targets are selected automatically by the on-board computer based on the apparent brightness of stars in the field of view (about 8◦ square). Buzasi et al. (2000) claimed the detection of a comb-like pattern below 25 μHz (P > 0.5 d) associated with solar-like oscillations in α UMa (Dubhe; K0III). In addition, two significant peaks were found above the acoustic cut-off frequency (see Dziembowski et al. 2001; Guenther et al. 2000). Retter et al. (2003) also found a series of peaks around 4.1 μHz (P 2.8 d) in WIRE data of α Boo (Arcturus; K1.5III). However, their simulations of a pure noise source showed similar spacings as found in both α UMa and α Boo. The spacings reported in the two stars are Δν = 2.9 ± 0.3 μHz and Δν = 0.83 ± 0.05 μHz. This is uncomfortably close to the frequency resolution at 1/Tobs = 1.1 μHz and 0.6 μHz for the data sets of α UMa and α Boo, respectively. To conclude, the WIRE photometry of K giant stars shows clear evidence of excess power at low frequencies. In order to investigate whether this is due to solar-like oscillations and to find further evidence of a comb-like pattern, a larger sample of bright K giant stars is currently being analysed. Eclipsing binary stars Bruntt et al. (2006b) discovered that ψ Cen (A0IV) is a bright detached eclipsing binary (dEB), based on photometry from WIRE and the Solar-Mass Ejection Imager (Howard et al. 2006) on the Coriolis spacecraft. The ψ Cen system comprises a B9 and an A2 type star in an eccentric orbit (e = 0.55) with a long period (P = 38.8 d). Bruntt et al. (2006b) determined the fractional radii of the stars to just 0.1%. In addition they found evidence of g -mode oscillations in the primary star, despite the star being somewhat cooler than the predicted SPB instability strip. I am currently analysing spectra of ψ Cen to determine absolute radii and masses with accuracies better than 0.5%. Realizing the unique potential of WIRE to measure masses and radii of detached dEBs with unprecedented accuracy, a program has been started to monitor about a dozen known bright eclipsing binaries. Bruntt & Southworth (2007) presented preliminary light curves of the known Algol-type systems AR Cas (B4IV) and β Aur (Menkalinan; A2IV). H. Bruntt 331 Discussion I have given an overview of the different classes of stars observed with the WIRE satellite. It is interesting that a star tracker never designed for the purpose has in fact resulted in important discoveries. One important lesson learnt from WIRE is that accurate pointing (attitude control) is important when flat fields are not available. Also, it is of tremendous value to have the “raw data” in the form of individual CCD windows. With this in hand one can correct for instrumental effects like scattered light, sub-pixel drift etc. In the near future the dedicated photometry missions COROT and Kepler will provide high precision photometry with much longer time baselines (150 d for COROT; up to six years for Kepler) and nearly 100% duty cycle. This will be particularly interesting for long-period variables and may potentially solve the ambiguous results from WIRE for the K giants as was discussed here. However, less costly small satellites are also being planned (e.g., Weiss 2007) and will likely result in interesting science of bright stars. The WIRE results for δ Scuti stars and B-type stars point to the important fact that detailed comparison with theoretical models is not possible due to the lack of mode identifications. This must be considered carefully when planning ground-based support for the upcoming missions. Acknowledgments. It was Derek L. Buzasi (US Air Force Academy) who had the bright idea to use the failed WIRE satellite to do asteroseismology from space. I started working with DLB in 2003 and spent five months with his group at USAFA during 2004. Our collaboration has been very fruitful as we continue to monitor bright stars with WIRE. I received support from the Danish Research Agency (Forskningsrådet for Natur og Univers), the Instrument center for Danish Astrophysics (IDA), and the Australian Research Council. References Bedding T. R., Kjeldsen H., Butler R. P., et al., 2004, ApJ, 614, 380 Bedding T. R., Kjeldsen H., Bouchy F., et al., 2005, A&A, 432, L43 Bouchy F., Carrier F., 2001, A&A, 374, L5 Bouchy F., Carrier F., 2002, A&A, 390, 205 Breger M., Pamyatnykh A. A., Zima W., et al., 2002, MNRAS, 336, 249 Bruntt H., Kjeldsen H., Buzasi D. L., Bedding T. R., 2005, ApJ, 633, 440 Bruntt H., Buzasi D. L., 2006a, Mem. Soc. Astron. Ital., 77, 278 Bruntt H., Southworth J., Torres G., et al., 2006b, A&A, 456, 651 Bruntt H., Suarez J. C., Bedding T. R., et al., 2007a, A&A, 461, 619 Bruntt H., Southworth J., 2007b, in Hartkopf W., Guinan E., Harmanec P., Proc. IAU Symp. 240, Binary Stars as Critical Tools and Tests in Contemporary Astrophysics. Astron. Soc. Pac., in press (astro-ph/0610540) Buzasi D., Catanzarite J., Conrow T., et al., 2000, ApJ, 532, L133 Buzasi D. L., 2001, in Garcia Lopez R. J., Rebolo R., Zapaterio Osorio M. R., eds, ASP. Conf. Ser. Vol. 223, 11th Cambridge Workshop on Cool Stars, Stellar Systems and the Sun. Astron. Soc. Pac., San Francisco, p. 389 Buzasi D. L., 2002, in Aerts C., Bedding T. R., Christensen-Dalsgaard J., eds, ASP Conf. Ser. Vol. 259, Radial and Nonradial Pulsations as Probes of Stellar Physics. Astron. Soc. Pac., San Francisco, p. 616 Buzasi D. L., 2004, in Favata F., Aigrain S., Wilson A., eds, Stellar Structure and Habitable Planet Finding, 2nd Eddington Workshop. ESA-SP 538, Noordwijk, p. 205 Buzasi D. L., Bruntt H., Bedding T. R., et al., 2005, ApJ, 619, 1072 Cuypers J., Aerts C., Buzasi D., et al., 2002, A&A, 392, 599 332 Asteroseismology with the WIRE satellite Cuypers J., Buzasi D., Uytterhoeven, K., 2004, in Kurtz D. W., Pollard K. R., eds, ASP Conf. Ser. Vol. 310, Variable Stars in the Local Group, IAU Colloquium 193. Astron. Soc. Pac., San Francisco, p. 251 Dziembowski W. A., Gough D. O., Houdek G., Sienkiewicz R., 2001, MNRAS, 328, 601 Fletcher S. T., Chaplin W. J., Elsworth Y., Schou J., Buzasi D., 2006, MNRAS, 371, 935 Garrido R., Garcia-Lobo E., Rodrı́guez E., 1990, A&A, 234, 262 Guenther D. B., Demarque P., Buzasi D., et al. 2000, ApJ, 530, L45 Hacking P., Lonsdale C., Gautier T., et al., 1999, in Bicay M. D., Cutri R. M., Madore B. F., eds, ASP Conf. Ser. Vol. 177, Astrophysics with Infrared Surveys: A Prelude to SIRTF. Astron. Soc. Pac., San Francisco, p. 409 Howard T. A., Webb D. F., Tappin S. J., Mizuno D. R., Johnston J. C., 2006, J. Geophys. Res. (Space Physics), 111, A04105 Karoff C., Bruntt H., Kjeldsen H., Bedding T., Buzasi D. L., 2007, these proceedings Laher R., Catanzarite J., Conrow T., et al., Proc. of the 2000 AAS/AIAA Spaceflight Mechanics Meeting, AAS Publications Office, San Diego, p. 146 Matthews J. M., Kuschnig R., Guenther D. B., et al., 2004, Nat, 430, 51. Erratum: 2004, Nat, 430, 921 Poretti E., Buzasi D., Laher R., Catanzarite J., Conrow T., 2002, A&A, 382, 157 Retter A., Bedding T. R., Buzasi D. L., Kjeldsen H., Kiss L. L., 2003, ApJ, 591, L151. Erratum: 2003, ApJ, 596, 125 Schou J., Buzasi D. L., 2001, in Wilson A., ed., Proceedings of the SOHO 10/GONG 2000 Workshop: Helio- and asteroseismology at the dawn of the millennium. ESA SP-464, Noordwijk, p. 391 Uytterhoeven K., Telting J. H., Aerts C., Willems B., 2004, A&A, 427, 593 Weiss W. W., 2007, these proceedings DISCUSSION Kaye: Using WIRE to help understand 9 Aurigae would be useful. Many of us would find these additional data helpful, despite the fact that we still have single-site multicolour photometry of 9 Aurigae. Since nobody can figure out what it’s doing, it might be useful to put WIRE at it; it’s 5th magnitude and there are two frequencies at 0.8 and 0.3 c/d. Hatzes: you said WIRE has only a year left. Is this just because of lack of funding? Bruntt: It’s getting closer down to the Earth’s atmosphere. We don’t know exactly how long it has left. Matthews: For the eclipsing binary with the g mode, do you have evidence that it is tidally excited? Bruntt: No. Comm. in Asteroseismology Vol. 150, 2007 One small satellite, so many light curves: Examples of δ Scuti asteroseismology from the MOST space mission1 Jaymie M. Matthews Department of Physics & Astronomy, University of British Columbia, Vancouver, V6T 1Z1, Canada Abstract The skies are alive with the sound of music. The symphonies of δ Scuti stars, both postand pre-main sequence, offer more exciting potential for asteroseismology than ever before. Continuous precise light curves of δ Scuti stars obtained by the MOST (Microvariability & Oscillations of STars) space mission offer rich eigenspectra and accurate relative mode amplitudes to test models of stellar structure and nonlinear pulsation dynamics. Many of these δ Scuti pulsators have been discovered among the MOST Guide Star sample. One of them, HD 209775, exhibits more than 80 frequencies, rivalling FG Vir in its richness. The observed amplitude distribution is a test of theoretical mode growth rates and the histogram of frequency spacings places meaningful constraints on the stellar structure and evolutionary phase. MOST has also discovered at least two ”hybrid” pulsators, simultaneously exhibiting both δ Scuti p-modes and γ Doradus g-modes, doubling (or tripling) the number of known hybrids. MOST has also been used to target pre-main sequence pulsators (like those in the cluster NGC 2264), performing ’ultrasound’ of stellar embryos based on the acoustic oscillations. Austrianasteroseismology ”The Sound of Music” (Hollywood musical film version) is almost unheard of in Austria.2 But the sound of music from stars resonates clearly with Austrian astronomers like Prof. Michael Breger, whose ”recording studio” (FG Virginis Records?) has been one of the most successful multi-site photometric networks in history. It is fitting that this workshop in his honour on the future of asteroseismology should come at a time when space-based missions like MOST, WIRE and COROT are poised to test and extend the ideas about δ Scuti pulsation that Michael Breger and his team have explored as pioneers from the surface of the Earth. It is equally fitting that the scientific productivity of the Canadian MOST satellite reported in this workshop has been enhanced significantly by the addition of the Vienna ground station to its communications network and by the contributions of Prof. Werner Weiss and his team. MOST MOST (Microvariability & Oscillations of STars) is a Canadian Space Agency mission (Walker et al. 2003; Matthews et al. 2004) which was originally developed solely for asteroseismology of Sun-like stars, pulsating magnetic CP (rapidly oscillating Ap = roAp) stars and WolfRayet stars, through ultra-precise high-duty-cycle photometry. Since its launch in June 2003, 1 Based on data from the MOST satellite, a Canadian Space Agency mission, jointly operated by Dynacon Inc., the University of Toronto Institute for Aerospace Studies and the University of British Columbia, with the assistance of the University of Vienna. 2 ...and considered by most Austrians to be a cliché of the same magnitude as Canadians would consider the image of a Mountie riding a polar bear chasing a hockey puck into an igloo while eating a doughnut, eh. Well, okay, I admit, that’s actually a pretty genuine image of Canada. 334 Examples of δ Scuti asteroseismology from the MOST space mission the MOST scientific mission has broadened to include exoplanet search and exploration (e.g., Rowe et al. 2006) including the search for exoplanets of Earth size and mass (Croll et al. 2007; Miller-Ricci et al. 2007). Its capabilities have also broadened to enable precise photometry of the guide stars used for satellite attitude control, resulting to date in about 560 light curves of 480 different stars. This has led to the discovery of δ Scuti, γ Doradus and hybrid pulsators, as well as to g -modes among Be supergiants, and nonradial p-modes in red giants (Barban et al. 2007; Kallinger et al. 2007) MOST is a microsatellite (54 kg in mass) housing a CCD photometer fed by a 15-cm Maksutov telescope with a custom broadband optical filter (350 - 750 nm). Its polar Sunsynchronous orbit allows it to monitor stars within a near-equatorial Continuous Viewing Zone (CVZ) 54◦ wide continuously for up to two months. It is now also possible to monitor stars outside the CVZ with interruptions during each of the 101.4-min satellite orbits, giving very thorough coverage of stellar variability with timescales of a few hours. Point-to-point photometric precision ranges from about 100 ppm for the brightest targets (in Fabry Imaging mode) to a few mmag for targets as faint as V ∼ 11. The oscillations of a δ Scuti star: An Instability Strip tease One of the challenges of δ Scuti asteroseismology is that the theoretical eigenfrequency spectra of the stellar models are so richly populated that it is difficult to find a unique match to the observed frequencies without independent mode identifications. As someone remarked at this workshop, ”there is no simple pattern” to recognize in the low-degree, low-overtone pulsation frequencies of a δ Scuti star - no asymptotic comb of modes that stands out in the high-overtone oscillations of the Sun, α Cen A and B, and roAp stars like HD 24712 = HR 1217. But if you detect enough frequencies in a δ Scuti pulsator, there may indeed be a pattern lurking to be found. A case in point is one of the variable stars in the MOST Guide Star sample: HD 209775. One of the richest δ Scuti stars ever HD 209775 (V = 7.6) is an F0 star which was recognized as a δ Scuti variable by Henry & Henry (2000) based on about 10 hours of ground-based photometry. The star was being tested as a possible photometric comparison for the transiting exoplanet system HD 209458, but its pulsational variability makes it unsuitable for this role (see also Henry 2000). Xu et al. (2002) included HD 209775 in their study of the red edge of the instability strip. They derive from Strömgren photometry (Rodriguez et al. 2000) the star’s luminosity to be log L/L 0.749 and its effective temperature to be Teff 7490 K . T HD 209775 may not have been a suitable comparison star for HD 209458, but it served perfectly as one of five guide stars for MOST monitoring of the transiting exoplanet system, both during a trial run of 14 days during 1 − 15 September 2004 and a more extensive run of 44 days during 2 August − 15 September 2005. The 2005 run consisted of more than 369,000 individual exposures sampled every 10 seconds, covering over 1050 hours with only one gap of about 7 hours − 99.4% duty cycle. Details of the 2004 observations of HD 209458 are described by Rowe et al. (2006) and the 2005 data by Rowe et al. (2007, in preparation). The star was immediately recognizable as a multi-periodic δ Scuti variable, even in the raw data. Even the ”raw” MOST Guide Star photometry undergoes a first-order background removal on board the satellite. For the 2005 run, the stray light due to scattered Earthshine was very high during the first three weeks, and to be conservative, we removed about 25% of the data during each MOST orbit. For the final three weeks, the stray light levels were so modest that no data removal was deemed necessary. The overall result is a light curve with a net duty cycle of 84%. A long-term trend apparent in the other four guide stars in J. M. Matthews & the MOST Science Team 335 the field was removed from the photometry with a second-order polynomial fit, and the data were binned to a sampling rate of 2 minutes. Figure 1 shows this preliminary reduction of the 2005 light curve. Figure 1: MOST 2005 light curve of HD 209775. Top panel: All 44 days of photometry, binned at a sampling rate of once every 2 min. The y-axis is in units of relative variation from the mean, with brightness increasing upwards. Lower panels: Subsets of 1.5 days each, where the solid curves trace the multi-frequency fits to the data. 336 Examples of δ Scuti asteroseismology from the MOST space mission The reduced photometry was searched for periodicities through a discrete Fourier transform, nonlinear least squares fitting (with algorithms similar to Period04, developed under M. Breger’s supervision in Vienna) and bootstrapping techniques. The Fourier amplitude spectrum of the data is plotted in Fig. 2 and shows the abundance of frequencies in the range 0 − 35 c/d. There are 88 frequencies present in the δ Scuti p-mode range, whose peaks have an amplitude S/N greater than 3.6. The largest amplitude is only around 2 millimag. Figure 2: Fourier amplitude spectrum of the HD 209775 time series. The vertical dashed lines mark the orbital frequency of the MOST satellite and its first two harmonics. The inset is the spectral window of the time series, where two small sidelobe peaks are present, spaced by 14.2 c/d (the orbital frequency of MOST). Modelling growth rates and frequency separations HD 209775 joins FG Vir (Breger et al. 2005) as one of the richest multi-periodic δ Scuti stars ever observed. One advantage of detecting so many modes and combination frequencies in a single 45-day-long observing run is that it is possible to study the relative mode amplitudes in the envelope of excited peaks to test theories of pulsational growth rates. Indeed, such a rich eigenspectrum from a single observing sequence, prompted Moya, Goupil, Dupret, Michel and Baglin (cf. Matthews et al. 2007, in preparation) to construct models of HD 209775 from two evolutionary codes adapted specifically for asteroseismic studies: CESAM (Morel 1997) and CLES (Scuflaire 2005; see Miglio et al. 2007 for an application of CLES). In Fig. 3, the growth rates η for one model from the CESAM grid are compared to the observed range of frequencies in HD 209775. This model has M/M = 1.74, log Teff = 3.866 and log L/L = 1.087, and of the four models tested, has positive growth rates closest to the low end of the observed frequency range. The other models ranged in mass from 1.55 to 1.80 M and L/L from 0.753 to 1.137. J. M. Matthews & the MOST Science Team 337 The Hipparcos parallax of HD 209775 (10.17 ± 0.94 mas) and the apparent magnitude of the star indicate a luminosity of 0.85 ± 0.08L , less luminous than the model fit shown above. Note that only four models have been generated in this preliminary analysis and a more complete model grid will be explored. Figure 3: Growth rates of p-modes ( = 0, 1, 2 and 3) as a function of frequency for a CESAM model consistent with the observed parameters (and uncertainties) of HD 209775, compared to the observed frequency spectrum. The model parameters are given in the text. For a star like HD 209775, with no multicolour photometry nor spectral line profile variability data to identify individual modes, one effective way to compare the observed frequencies to models is through histograms of frequency differences (Breger et al. 1999, Goupil et al. 2000). Moya et al. computed the differences between the mean frequencies identified in the MOST photometry and counted the number of differences in a given interval to plot the number as a function of frequency difference, for different binning intervals (or widths). These can then be compared to theoretical histograms from the stellar model eigenspectra, including and neglecting rotational splitting. The best agreement in the preliminary analysis is shown in Fig. 4. The histogram method constrains the large frequency separation, which is essentially proportional to the dynamical time of the models. For HD 209775, the best fitting large separation Δν is around 50 μHz, corresponding to (R/R )3 /(M/M ) ∼ 5.6. Combined with the comparison of the model instability regions to the observed range of excited frequencies, the most luminous models agree best with the data. (More luminous δ Scuti stars are expected to exhibit more eigenmodes, but the better sampled histograms are not the reason for the better match found for the model shown.) Rotational splitting must be included to get a good match to the difference histogram with modes only up to = 3. (There was no published estimate of v sini for this star, so Artie Hatzes obtained for the MOST team a high-resolution spectrum of HD 209775 in September 2005 from the Tautenburg Observatory, yielding a rough estimate of v sin i = 75 ± 5 km/s.) The effects of metallicity have not been included in the preliminary analysis and a more complete investigation is underway. 338 Examples of δ Scuti asteroseismology from the MOST space mission Figure 4: Preliminary comparison of the frequency difference histograms (in 50-μHz bins) of the observed frequencies and the best matching model, which includes rotational splitting but requires only low-degree modes up to = 3. Hybrids and embryos MOST has discovered two new hybrid pulsators, which exhibit simultaneous oscillations consistent with δ Scuti p-modes and γ Doradus g -modes: BD+18 4914 (Rowe et al. 2006a) and HD 114839 (King et al. 2006). Both are Am stars. Only two hybrids were previously known: HD 209295 (Handler & Shobbrook 2002) and HD 8801 (Henry & Fekel 2005). The former is a close binary for which the authors argue that the g -modes are excited by tidal interaction. The latter is an Am star which is not known to be part of a binary system. The MOST additions to the hybrid sample - if demonstrated to be single stars - may point to the importance of the Am peculiarity to the hybrid pulsation phenomenon. There are other hybrid candidates in the MOST guide star sample and identifying them will help define the dual instability parameter space (Gruberbauer, MSc thesis, in preparation). The δ Scuti instability strip covers pre-main-sequence (PMS) evolutionary tracks as well as post-MS phases. MOST has also observed the pulsations of PMS stars, in particular two in the young open cluster NGC 2264: V588 Mon and V589 Mon. In December 2005 − January 2006, MOST monitored these stars and others in the cluster for about 48 days with nearly continuous time coverage. Segments of the PMS light curves are shown in Fig. 5. About 150 significant frequencies were identified in V588 Mon, of which about 90 are combination frequencies; in V589 Mon, ∼90 frequencies and ∼40 combinations. Asteroseismic analyses of the p-mode eigenspectra are underway (Kallinger et al. 2007, in preparation). Another PMS pulsator observed by MOST is the field star HD 142666, monitored for 11.5 days with a 70% duty cycle. HD 142666 (Zwintz et al. 2007, in preparation) exhibits pronounced variations like another PMS star UX Ori, attributed to a clumpy disk seen nearly edge-on, as well as δ Scuti pulsations. J. M. Matthews & the MOST Science Team 339 Figure 5: Five-day segments of the MOST light curves of the pulsating PMS stars V588 and V589 Mon in the cluster NGC 2264. The y-axes are in units of relative variation from the mean, with brightness increasing upwards. On the verge of breakthroughs The near future promises (1) additional rich δ Scuti and hybrid eigenspectra from the ultraprecise long-time-coverage photometry of MOST, WIRE, COROT, and Kepler, plus (2) precise line-profile variability data (and mode identifications) from multi-site high-resolution spectroscopic networks like SONG, and (3) improving models of pulsation with the effects of rotation. This is a combination that δ Scuti asteroseismologists have awaited for decades, and that Michel Breger and his colleagues have prepared us for with patient and meticulous observations and models over those same decades. Acknowledgments. Thanks, Mike! References Barban, C., Matthews, J. M. De Ridder, J., Baudin, J. F., Kuschnig, R., Mazumdar, A., Samadi, R. et al. 2007, A&A, in press Breger, M., Pamyatnykh, A. A., Pikall, H. & Garrido, R. 1999, A&A 341, 151 Breger, M. et al. 2005, A&A 435, 995 Croll, B., Matthews, J. M., Rowe, J. F., et al., Kuschnig, R., Walker, A., Gladman, B., Sasselov, D., Cameron, C., Walker, G. A. H., Lin, D. N. C., Guenther, D. B., Moffat, A. F. J., Rucinski, S. M. & Weiss, W. W. 2007, ApJ, in press Goupil, M. J., Dziembowski, W. A., Pamyatnykh, A. A., Talon, S. 2000, ASPC 210, 267 Handler, G. & Shobbrook, R. R. 2002, MNRAS 333, 251 Henry, G. W. 2000, ApJ 529, L41 Henry, G. W. & Fekel, F. C. 2005, AJ 129, 2026 Henry, G. W. & Henry, S. M. 2000, IBVS 4826 340 Examples of δ Scuti asteroseismology from the MOST space mission Kallinger, T., Guenther, D. G., Weiss, W. W., Matthews, J. M., Reegen, P., Hareter, M. et al. 2007, ApJ, submitted King, H., Matthews, J. M., Cameron, C., Rowe, J. F., Kuschnig, R., et al. 2006, CoAst 148, 28 Matthews, J. M., Kuschnig, R., Guenther, D. B., Moffat, A. F. J., Rucinski, S. M., Sasselov, D., Walker, G. A. H., Weiss, W. W. 2004, Nature 430, 51 Matthews, J. M., Kuschnig, R., Moya, A., Goupil, M.-J., Dupret, M.-A., Michel, E., Baglin, A. et al. 2007, in preparation Miglio, A., Montalban, J., Dupret, M.-A. 2007, MNRAS, 375, L21 Miller-Ricci, E., Rowe, J. F., Sasselov, D., Matthews, J. M. et al. 2007, ApJ, in press. Morel, P. 1997, A&A 124, 597 Rodriguez, E., Lpez-Gonzlez, M. J. & Lpez de Coca, P. 2000, A&AS 144, 469 Rowe, J. F., Matthews, J. M., Seager, S. et al. 2006, ApJ, 646, 1241 Rowe, J. F., Matthews, J. M., Cameron, C., Bohlender, D. A., King, H., Kuschnig, R. et al. 2006a, CoAst 148, 34 Rowe, J. F., Matthews, J. M., Seager, S. et al. 2007b, in preparation Scuflaire, R. 2005, in the 4th COROT/ESTA meeting (Aarhus, Denmark), http://www.astro.up.pt/corot/welcome/meeting Walker, G. A. H., Matthews, J. M., et al. 2003, PASP, Xu Y., Li Z.-P., Deng L.-C., Xiong D.-R. 2002, ChJAA 2, 448 Michael Gruberbauer, Thomas Kallinger and Jaymie Matthews - thinking about science? Comm. in Asteroseismology Vol. 150, 2007 CoRoT data contribution to stellar seismology E. Michel,1 A. Baglin,1 R. Samadi,1 F. Baudin,2 M. Auvergne 1 2 1 Observatoire de Paris, LESIA, UMR 8109, pl. J. Janssen, 92195 Meudon, France Institut d’Astrophysique Spatiale, CNRS/Univ. Paris XI, UMR 8617, 91405 Orsay, France Abstract At the time to submit papers for these proceedings, CoRoT will be launched in less than one month. The scientific programme, the instrument and the mission profile have been described in several places recently (e.g., Baglin et al. 2006, Michel et al. 2006a) and a dedicated volume (Fridlund et al. 2006) has been published, where these aspects are commented on in detail. In the present paper, we focus on a description of the nature and quality of the data expected from the CoRoT seismology observational programme. We thus first review a few specific aspects of the CoRoT instrument and mission profile necessary to have a clear idea of the nature and quantity of the data to come. Then, we produce data simulations for selected targets to illustrate the expected performance. In particular, we consider classical pulsators, extending the work initiated by Michel et al. (2006a) with solar-like pulsators. The instrument - main outline The instrument collects light through an off-axis telescope plus a dioptric objective giving access to a 3 × 2.7 degrees field of view for a 588 cm2 collecting area, equivalent to a 27 cm aperture. The focal plane hosts four CCDs (2k by 4k pixels) used in frame-transfer mode. Half of the field (two CCDs) is mainly devoted to the seismology programme of CoRoT. It is defocused (diameter of the star spot ∼ 18 px, i.e. ∼ 41 arcsec) and 10 target stars with 5.4 < mV < 9 can be observed simultaneously with a 1 second sampling time. By default, ten windows are read for targets and ten for background estimates. On-board realtime photometry is achieved. Part of these target window images can be downloaded for further refined analysis (6 to 10 among 10 with a 32 seconds sampling). The ”exoplanet field” is in focus and it is possible to observe 12 000 targets with 11 < mV < 16 at a sampling time of 512 s. Thanks to a prism put on the exo-field, each target image is slightly dispersed and for the brightest objects (mV < 14.5) three-colour information (white-blue-red) can be obtained. For a limited number of targets (∼ 500), a higher sampling rate can be used (32 s). Mission profile CoRoT’s mission profile is characterized by the possibility to dedicate long runs (up to 150 d) to a specific field. The price for this is that CoRoT observations are restricted to two observing zones defined as cones of 10 degrees on the sky, around Position C, roughly in the Galactic centre direction (α = 18o 50, δ = 0o ) and its opposite: Position A, roughly in the Galactic anticentre direction (α = 6h 50, δ = 0o ). The mission profile is thus built around successive 150 d long runs, alternatively in the centre and anticentre directions, separated by short runs (∼3 weeks) also in one of these accessible cones. 342 CoRoT data contribution to stellar seismology The observing program will start with an Initial Run (IR1) in the anticentre direction. Its duration is expected to be between 60 and 80 days, depending on the final operational schedule. The list of targets selected for this run features in particular: a solar-like pulsator on the Main Sequence, a known δ Scuti pulsator, two Am stars, two eclipsing binaries (one including a B5 star and the other an A0 star), an Ap star, and two giant stars. After this Initial Run, by mid-April, the satellite will be flipped by 180 degrees to observe the first Long Run field in the centre direction (LRC1). The selection of this field has been driven mainly by two known classical pulsators: a β Cephei and a δ Scuti star, but it also features two solar-like pulsator candidates: a relatively bright one (mV = 6.6) illustrative of the good candidates (criterion 2 as defined by Michel et al. 2006b) and the other one, fainter (mV = 7.7) being illustrative of criterion 0 (see Michel et al. 2006b), i.e. candidates for which detection of a significant number of modes is expected but with no guarantee on the precision of measured frequencies. After this first Long Run, a Short Run (SRC1) is planed in the same direction with a duration of 20 days. Then, around mid-October, the satellite will be flipped again to point to the Long Run LRA1, in the anticentre direction during 150 days, followed by a short run SRA1, and so on and so forth. The mission is planned for 3 years, but in the nominal scenario, there is no technical limitation to an extension. A preliminary observational programme has been settled for the first years of the mission (see Michel et al. 2006c). This list of objects which will be observed during 150 days in the four first Long Runs features: one O9 star, eleven B stars, including one known β Cephei and five Be stars, eleven A stars including two known δ Scuti pulsators (one being in an eclipsing binary) and two Ap stars, fourteen F stars including six solar-like candidates (one known solar-like pulsator), one δ Scuti star, one γ Doradus star, and three G stars including two solar-like candidates (one with a known planet). The two next Long Runs are known, but the definitive position and the list of targets is not settled yet. A projection of what the list could be after the 6 first Long Runs and the Initial Run is given in Fig. 1. As shown in Fig. 1, this sample gathers a significant set of objects scanning the Main Sequence and post Main Sequence stage for a large range of mass. Photometric performance in the Seismo field In this field, and in the range [0.1 mHz, 10 mHz], the instrumental noise has been kept below the photon noise, in the range of magnitude 5.4 <mV < 9 − 9.5, except for a few harmonics of the orbital period (at ω0 = 162 μHz, 2ω0 , 4ω0 , 5ω0 ) which will be kept as low as possible by corrections. In this context, the photometric precision obtained with CoRoT is σ = 0.6 ppm in 5 days for a mV = 5.7 target (σ1s ∼ 4 × 10−4 and 0.156 ppm2 /μHz). For a mV = 9 target, these numbers become σ = 2.75 ppm in 5 days (σ1s ∼ 1.8 × 10−3 and 3.26 ppm2 /μHz). Performance in terms of eigenfrequency measurements In order to illustrate the expected performance in terms of precision on frequency measurement, we complete and develop the work presented by Michel el al. (2006a). We use the simulation tool Simu-LC developed in the framework of the CoRoT Seismology Working Group (http://www.lesia.obspm.fr/∼corotswg) and described by Baudin et al. (2006). This tool takes into account granulation noise estimates following Harvey (1985) and photon noise in the CoRoT framework. For solar-like pulsators, it also takes into account theoretical mode excitation rates following Samadi & Goupil (2001) and theoretical mode damping rates from Houdek et al. (1999). E. Michel, A. Baglin, R. Samadi, F. Baudin and M. Auvergne 343 Figure 1: HR diagram of the targets to be observed during the Initial Run and Long Runs Detection level and precision on frequency measurement A major aspect of the CoRoT performance is the possibility to detect very low amplitude oscillations. In order to give a flavour of this, we use a statistical test proposed by Appourchaux et al. (2000): r ln(T ) + ln(Δ) − ln(P), where T is the total duration of the observations (in seconds), Δ is the range of frequency searched for oscillation peaks (in Hz) and P is the probability to get at least one peak due to noise larger than r times the local mean, in the power spectrum. For solar-like oscillations, assumed to have lifetimes shorter than the observations, it was shown by Appourchaux (2004) that the test can be refined and optimized to better take into account the fact that the mode profile is resolved. But for simplicity, we here will use the same test as previously described, giving a bottom line for detection performance. As by Michel et al. (2006a), for cases illustrative of a solar-like pulsators, the 1-σ precision on frequency determination is estimated following Libbrecht (1992), while for the cases illustrative of classical pulsators, the estimate of the precision is given following Koen (1999). 344 CoRoT data contribution to stellar seismology Solar-like pulsators The case of solar-like pulsators has already been considered by Michel et al. (2006a) for CoRoT Long Runs. These authors selected two objects. On one hand, HD 49933 (mV = 5.7), to be observed during LRA1, is representative of the best (brightest) candidates. On the other hand, HD 49385 (mV = 7.9), also to be observed during LRA1, is representative of solar-like pulsators candidates for which, according to current theoretical amplitude estimates, one can expect detection of a significant number of peaks, but no guarantee of a high precision of the frequency measurement. Simulations presented by Michel et al. (2006a) show that for HD 49933, the expected precision on frequency measurements goes from ∼ 0.15 μHz to ∼ 0.3 μHz when granulation noise estimate is taken into account. For HD 49385, the expected precision is about 0.4 − 0.5 μHz with a lower relative influence of the potential contribution of granulation noise. During an Initial Run HD 49933 is also scheduled for Initial Run IR1, to be observed during 60 to 80 days at the very beginning of the observational program. The synthetic power spectrum corresponding to the simulation of a 60-day run on HD 49933 is presented in Fig. 2. For the photon noise only and for the photon noise plus the granulation noise contributions, we compute a 99% confidence level of detection following the statistical test described previously, with T = 60 days, Δ = 5 mHz, and P = 1%. We notice that even with the granulation noise as estimated here, a large amount of the oscillation peaks is detected with a confidence level higher than 99%. Figure 2: Simulation of the power spectrum expected for HD 49933 (observed during 60 days), including photon noise (dark grey), and granulation noise (light grey) estimates as described in the text. The 99% confidence levels of detection are drawn as lines associated with the photon noise only (dark grey), and the photon noise plus granulation noise (light grey). E. Michel, A. Baglin, R. Samadi, F. Baudin and M. Auvergne 345 Figure 3 illustrates the expected precisions estimated following Libbrecht (1992) and for different cases: a) The reference case: the precision of frequency determination is established considering only photon noise and taking 1 μHz as a fixed value for line widths. The excitation rates are computed following Samadi & Goupil (2001). b) As case a, but line widths are from Houdek et al. (1999). c) As case b, but granulation noise contribution is also considered. The results presented in Fig. 3 can be directly compared with those obtained for a 150-day run (Michel et al. 2006a, Fig. 5). As could be expected, the present precisions are significantly larger in all cases a, b and c. They however remain below ∼ 0.5 − 0.6μHz. Figure 3: Lower panel: simulation of the pure seismic signal expected for HD 49933. Upper panel: Estimates of the 1-σ precision on the determination of eigenfrequencies, for cases a, b and c (resp. triangles, diamonds, stars) as described in the text. Classical pulsators In order to illustrate the expected performance for classical pulsators, we have selected the example of HD 49294 (mV = 7, v sin i = 111 km/s), located in the δ Scuti instability strip, but for which preparatory surveys have not revealed variability at the mmag level (Poretti et al. 2005). Contrary to solar-like pulsations, classical pulsators show auto excited pulsations and since eventual amplitude and phase variations are still an open question it seems representative enough to use the work hypothesis that these oscillations are constant in amplitude and coherent in phase over a time span longer than the CoRoT observations. In addition to this, there is no theoretical prediction either of amplitudes for these objects. Observations from the ground reveal modes with amplitudes down to the detection threshold 10−3 (1000 ppm), occasionally a few hundreds of ppm. For our simulation, we thus decided to consider arbitrary amplitudes of 100 ppm, i.e. peaks below what is currently detected from the ground. 346 CoRoT data contribution to stellar seismology During a Long Run Figure 4 illustrates such a simulation for HD 49294, a relatively bright object (mV = 7). Here again, photon noise alone is represented in dark grey, while the photon noise plus granulation noise estimate is represented in light grey. In each case, the 99% confidence level for detection is represented by a line. It is computed following the previous definition, for T = 150 d, Δ = 1 mHz, and P = 1%. Peaks above this limit are attributed to the star with a probability higher than 99%. The present case illustrates that here again, for bright objects, granulation noise, as estimated here, might be an important component for the final performance. Considering photon noise only, the 99% confidence level for detection is around 2 ppm, while including the granulation noise contribution, it is about 10 ppm in the domain of interest. This still corresponds to a gain by a factor larger than 50 to 100 compared with what is currently obtained from the ground. Figure 4: Simulation of the power spectrum expected for HD 49294, mV = 7, (observed during 150 days), including photon noise (dark grey), and granulation noise (light grey) estimates as described in the text. The 99% confidence level of detection are drawn as lines associated with photon noise only (dark grey), and photon noise plus granulation noise (light grey). Besides the detection of the modes, it is interesting also to investigate the precision expected on frequency measurement for the detected modes. Following Koen (1999), all modes detected above the 99% confidence level are expected to have their frequency measured with a precision better than ∼ 1/(10 T ), where T is the duration of the run (in seconds). In the present case, this means that all the peaks detected above the 99% confidence level will have their frequency measured with a precision better than 0.01 μHz. This confirms the conclusion by Michel et al. (2006b) that such data will provide very valuable material for time/frequency analysis. E. Michel, A. Baglin, R. Samadi, F. Baudin and M. Auvergne 347 For a fainter object during a Short Run If HD 49294 were fainter (e.g. mV = 9.5, at the faint edge of the range of magnitudes considered in the Seismo field) and observed during a Short Run (20 days), the simulation provides the results shown in Fig. 5. We see that the detection threshold is between 10 and 20 ppm if only photon noise is considered and around 30 ppm including the present granulation noise estimate. Here again, this represents a significant gain (larger than 10) compared with current data. Following the same prescriptions as in the previous sections, but with T = 20 d, the precision on frequency measurement is expected to be better than 0.065 μHz for the modes above the detection threshold. These results confirm the great interest of observing classical pulsators, even rather faint ones, during long and short runs. Figure 5: Same as Fig. 4, but for mV = 9.5 observed during a Short Run (20 d) Conclusion CoRoT is about to be launched and to bring a wealth of data expected to reveal a unique sight on stellar oscillations. It is our conviction that it will contribute to answer several open questions and lead to reconsider several aspects of the field of stellar structure and evolution, with consequences in numerous connected fields of research. Since the leading objective of this meeting was to discuss how to organize the future of stellar seismology, we have found it appropriate to illustrate, as precisely as possible at this stage, what will be the contribution of CoRoT data to this future, in terms of star sample and expected characteristics of the data. References Appourchaux T., Fröhlich C., Andersen B., et al., 2000, ApJ, 538, 401 Appourchaux T., 2004, A&A 428, 1039 Baglin A., Michel E., Auvergne M., et al., 2006, in Fletcher K., ed., SOHO 18/GONG 2006/HelAs I: Beyond the spherical Sun. ESA SP-624, Noordwijk, p. 34.1 348 CoRoT data contribution to stellar seismology Baudin F., Samadi R., Appourchaux T., Michel E., 2006, in Fridlund M., Baglin A., Conroy L., Lochard J., eds, 2006, The CoRoT Mission, Pre-Launch Status, Stellar Seismology and Planet Finding. ESA-SP 1306, Noordwijk, p. 403 Fridlund M., Baglin A., Conroy L., Lochard J., eds, 2006, The CoRoT Mission, Pre-Launch Status, Stellar Seismology and Planet Finding. ESA-SP 1306, Noordwijk Harvey J., 1985, in Rolfe E., Battrick B., eds, Future Missions in Solar, Heliospheric and Space Plasma Physics. ESA-SP, 235, Noordwijk, p. 199 Houdek G., Balmforth N. J., Christensen-Dalsgaard J., Gough D. O., 1999, A&A, 351, 582 Koen C., 1999, MNRAS, 309, 769 Libbrecht K. G., 1992, ApJ 387, 712 Michel E., Samadi R., Baudin F., et al., 2006a, Mem. Soc. Astron. Ital., 77, 539 Michel E., Baglin A., Auvergne M., et al., 2006b, in Fridlund M., Baglin A., Conroy L., Lochard J., eds, 2006, The CoRoT Mission, Pre-Launch Status, Stellar Seismology and Planet Finding. ESA-SP 1306, Noordwijk, p. 39 Michel E., Deleuil M., Baglin A., 2006c, in Fridlund M., Baglin A., Conroy L., Lochard J., eds, 2006, The CoRoT Mission, Pre-Launch Status, Stellar Seismology and Planet Finding. ESA-SP 1306, Noordwijk, p. 473 Poretti E., Alonso R., Amado P. J., et al., 2005, AJ, 129, 2461 Samadi R., Goupil M. J., 2001, A&A, 370, 136 Comm. in Asteroseismology Vol. 150, 2007 Microsatellites W. W. Weiss Institute of Astronomy, University of Vienna, 1180 Vienna, Austria Abstract Asteroseismology is the most efficient method for investigating the interior of stars and for testing current theories of stellar structure and evolution. One of the most important ingredients for this research field are pulsation eigenfrequencies of the target stars. The determination of such frequency spectra poses a challenge to observers, as the amplitudes can be extremely small and the frequencies need to be known to high accuracy. These requirements call for long and uninterrupted photometric data sets with a high duty cycle, and a reduction of all noise sources to achieve the photon noise limit in the optimum case. Already since the early days of asteroseismology two strategies were followed to pursue this goal: establishment of observatory networks on ground, and photometry from space. While various observatory networks are working successfully since 20 years and more, attempts to launch a dedicated space photometer were unsuccessful until June 2003, when MOST was brought into orbit. The potential of the stable space environment for photometry, however, was demonstrated already by, e.g., HST, WIRE, the IUE star tracker, but no large continuous photon noise limited data sets with a large duty cycle could be obtained with these satellites. With MOST already in orbit, COROT, due for launch end of December 2006, and Kepler in 2008, the situation has recently improved dramatically. Largely unnoticed by the asteroseismological community another technical development boosted the potential for space photometry: 3-axes stabilized nanosatellites. These satellites with less than 10 kg mass and typically a shape of a cube with not more than 30 cm in size basically can be built by students, launched and operated from rather small University institutes. The total budget needed is comparable to the costs of a smaller auxiliary instrument of one of the larger observatories. We in Austria have embarked together with our colleagues from Canada (Universities of Montreal, Toronto, and Vancouver) on the development of a network of up to four nanosatellites, called BRITE-Constellation. The two Austrian components are already funded. This ensemble of satellites will be launched in 2008 and will allow high precision two-colour photometry of bright and luminous stars. This group of objects is particularly interesting as it determines largely the ecology of our Universe. Comm. in Asteroseismology Vol. 150, 2007 Asteroseismology with the Kepler mission J. Christensen-Dalsgaard,1,2 T. Arentoft,1,2 T. M. Brown,3 R. L. Gilliland,4 H. Kjeldsen,1,2 W. J. Borucki,5 D. Koch 5 1 Institut for Fysik og Astronomi, Aarhus Universitet, DK-8000 Aarhus C, Denmark 2 Danish AsteroSeismology Centre, DK-8000 Aarhus C, Denmark 3 Las Cumbres Observatory, 6740B Cortona Dr, Goleta, CA 93117, USA 4 Space Telescope Science Institute, Baltimore, MD 20771, USA 5 NASA Ames Research Center, Moffett Field, CA 94035, USA Abstract NASA’s Kepler mission will fly a photometer based on a wide-field Schmidt camera with a 0.95 m aperture, staring at a single field continuously for at least 4 years. Although the mission’s principal aim is to locate transiting extrasolar planets, it will provide an unprecedented opportunity to make asteroseismic observations on a wide variety of stars. Plans are now being developed to exploit this opportunity to the fullest. Introduction The Kepler mission was selected for NASA’s discovery programme in 2001, with a launch now planned for November 2008. The goal of the mission is to search for extrasolar planetary systems with the transit method, by detecting the slight decrease in the brightness of a star as a planet in orbit around it passes in front of the star. This is probably the most efficient method to detect substantial numbers of planets of modest size, and a key goal of the mission is in fact the search for ‘Earth analogs’, planets of roughly Earth size in year-long orbits around solar-like stars. More generally, planets in the ‘habitable zone’, where conditions are such as to allow liquid water, are emphasized; thus the mission is a key component of NASA’s Exploration Roadmap. These goals require very high differential photometric precision and observations of a given field for several planetary orbits, i.e., several years. Also, to achieve a reasonable probability for the detection of planets a very large number of stars must be observed, requiring a large field of view of the photometer. The requirements for planet-transit detection also make the Kepler mission very well suited for asteroseismology. The photometric precision required to study solar-like oscillations is similar to that needed to detect Earth-size planets, and the large field ensures that a very substantial number of interesting targets will be available, both solar-like pulsators and other types of pulsating stars. Consequently an asteroseismic programme is being established within the Kepler project. Pulsations are found in stars of most masses and essentially all stages of evolution. The frequencies are determined by the internal sound-speed and density structure, as well as rotation and possibly effects of magnetic fields, and the amplitudes and phases are controlled by the energetics and dynamics of the near-surface layers, including effects of turbulent convection. Observationally, the frequencies can be determined with exceedingly high accuracy compared with any other quantity relevant to the internal properties of the stars. Analysis of the observed frequencies, including comparison with stellar models, allows determination of the properties of the stellar interiors and tests of the physics used in the model computation (e.g. Kjeldsen & Bedding 2004). Stars showing oscillations similar to those observed in the Sun are particularly promising targets for asteroseismology, owing to the large number of generally well-identified modes J. Christensen-Dalsgaard et al. 351 that can be observed. Also, the extensive experience from analyses of solar oscillations can be applied in the analysis of data for these stars, which have oscillation periods of minutes to hours. Furthermore, the properties of the oscillations (amplitudes, frequencies, mode lifetimes) show long-term variations caused by stellar activity. Here we give a brief description of the Kepler mission and the planned asteroseismic investigations. Further details on the mission were provided by Basri et al. (2005) and Koch et al. (2006), as well as on the mission web page (http://kepler.nasa.gov/sci/). Kepler instrumentation The Kepler photometer is a classical Schmidt design with a 0.95 m diameter corrector passing light to a 1.4 m primary and then on to the focal plane mounted near the instrument centre (see Fig. 1). The focal plane is populated with 42 CCDs with 2200 columns and 1024 rows each that will be read out through two amplifiers per CCD. Pixel sizes of 27 μ will provide full-well depths of approximately 1.0 ×106 electrons for these backside-illuminated, thinned and anti-reflection coated devices. The resulting pixel scale of 3.98 arcsec results in a large field of view subtending over 100 square degrees. The spacecraft is three-axis stabilized with an expected jitter of less than 1 per cent of the pixel scale. Since tight focus in not required for obtaining optimal time-series photometry the individual CCD modules are allowed to have significant focus offsets relative to each other easing integration of this large focal plane. Modules with the best focus will have point spread functions (PSF) with full width at half maximum (FWHM) less than one pixel resulting in undersampling, while other modules with larger focus offsets will provide PSFs with FWHM of about two pixels resulting in critical sampling of the PSF. On the other hand, focus stability will be tightly constrained. Figure 1: Primary components of the Kepler Photometer shown in cut-out. For a higher resolution, colour version see http://kepler.nasa.gov/sci/. This web site provides a wealth of technical and scientific information about the mission. 352 Asteroseismology with the Kepler mission The Kepler observing programme A single field near right ascension 19.4 h and declination 44◦ N will be monitored for the full 4-year mission (with option for a 2-year extension). The spacecraft will be in an Earth-trailing heliocentric orbit, similar to Spitzer . To keep the solar arrays illuminated and the focal-plane radiator pointed towards deep space the spacecraft is rotated 90◦ every three months. Figure 2 shows the CCD coverage superposed on the sky in the Cygnus-Lyra region; the CCD layout is four-fold symmetric so that the quarterly roll will not change the sky coverage. Transfer of the accumulated data to ground stations, in the form of small images around each target, will require body-pointing the high-gain antenna once per month resulting in data gaps less than one day, in addition to the similar gaps at the quarterly rolls. Figure 2: Region of galaxy to be monitored with Kepler showing in detail the layout of the 42 science CCDs. From http://kepler.nasa.gov/sci/. The primary Kepler science searching for transits of Earth-like planets will be fulfilled by collecting data on 170 000 stars for the first year, reduced to 100 000 later as high-noise stars are dropped, to accommodate the lower data rates as the spacecraft drifts away from the Earth. These targets will range in magnitude from about 9th to 15th with the design point J. Christensen-Dalsgaard et al. 353 being the ability to detect the 85 parts-per-million (ppm) transits of an Earth analog. The design point is a combined differential photometric precision of less than 20 ppm in 6.5 hours (half the length of a central passage of an Earth analog) for a V =12 G2V host when all noise terms are included, assuming an intrinsic 10 ppm noise from the solar-like star. In order to accumulate the 5 × 109 electrons at 12th mag without saturating the CCDs, they will be read out every 2.5 to 8 seconds (exact value yet to be set) and accumulated on board into 30-minute sums. For the extrasolar planet detection, targets that are dwarfs are strongly preferred over giants; hence a full ground-based, multi-band photometric screening will be completed before launch, capable of providing a target list dominated by F, G and K dwarfs with as many M dwarfs, to a limit of V =16 in this case, as possible. Due to the 30-minute observing cadence asteroseismology from these primary observations will be limited to red giants that have slipped through the screening process (or intentionally left in), and classical oscillators for which this long cadence allows Nyquist sampling. The capability of Kepler to provide also excellent results for asteroseismology on solar-like stars has been recognized from the time of initial mission proposals, and a small complement of 512 targets that can be changed on a quarterly basis will be followed with 60-second data accumulations. For detailed study of solar-like oscillations the goal should be to reach a mean photon-noise level in the amplitude spectrum of 1 ppm after three months; this requires the collection of 1012 electrons per month, which will occur at V =11.4. Stars brighter than this, with photon noise below 1 ppm per month, are likely the prime targets for asteroseismology. Such targets are saturated in individual readouts; however, experience from HST observations has been that saturated data can support near photon-noise-limited differential time-series photometry, with a detector set-up such as will be used for Kepler . At V =9, usually taken to be the bright limit for Kepler observations, the photon-noise limit will be ∼70 ppm per minute, and experience from HST and simulations for Kepler suggest that we should be able to do better than 100 ppm per minute, allowing the mean noise level over a three-month data segment to reach less than 0.5 ppm in the amplitude spectrum. Early in the mission the 512 one-minute cadence targets will be dedicated to those deemed best for asteroseismology. After the detection of planet candidates from the 170 000 longcadence targets, many of these providing high S/N will be switched to the short cadence to allow refinement of transit shape, timing of transits for detection of other planets, and also for asteroseismology, since a prime motivator for the latter is the exquisite refinement of stellar parameters (especially radius) thereby obtained. A substantial number of targets will be reserved for asteroseismology throughout the mission, however. Asteroseismology with Kepler The solar-like oscillations are characterized by a great deal of regularity that relates directly to stellar parameters. This includes in particular the so-called large and small frequency separations (e.g. Christensen-Dalsgaard 2004). Extracting these quantities from the oscillation signal allows precise determinations of stellar radii (relative accuracy of 2 – 3 per cent); also, ages can be determined with a precision of better than 5 – 10 per cent of the total main sequence lifetime, although the accuracy may be somewhat compromised by uncertainties in stellar physics and composition. We are currently developing techniques for extracting this information; the large separation can be determined from the power spectrum of the timeseries using cross-correlation and peak comb analysis, and having obtained that, the small separation can be obtained by a folding of the power spectrum based on the large separation. The solar-like oscillations occur in stars across the HR diagram, with increasing amplitudes and decreasing periods for increasing luminosity (e.g. Kjeldsen & Bedding 1995). In order to test our ability to extract stellar parameters using solar-like oscillations, we calculated oscillation spectra from theoretical stellar models, and simulated 1-year Kepler time-series including 354 Asteroseismology with the Kepler mission Luminosity (Solar Units) 10.0 1.0 0.1 Detection limit >14 Detection limit >13 Detection limit >12 Detection limit ~12 7500 7000 6000 5000 Effective Temperature 4000 Figure 3: HR diagram of calculated models, with masses in solar units, indicating the limiting magnitudes to which the correct large separation could be retrieved from simulations of one year of Kepler data (see text). stochastic excitation of the oscillations, realistic levels of photon-noise, and granulation. We calculated time-series for a total of 99 models in the mass-range 0.7 – 1.5M from the main sequence to the giant branch. For each one, we added noise corresponding to V = 9 − 14 in steps of 0.2 mag, and for each magnitude value we simulated 10 time-series using different random numbers for generating the noise. We then used the analysis briefly discussed above to extract the large frequency separation to find, for each model, the limiting magnitude to which we could extract the correct separation in all 10 realizations of the noise. The results are shown in Fig. 3: from one year of Kepler data we will be able to determine the large separation, and hence stellar radii, in a very large fraction of the relevant stars in the Kepler field observed at the one-minute cadence. We also expect to be able to determine the small separation in most of the cases where we could determine the large separation, but this has not yet been quantified in any detail. However, for asteroseismology we will be able to go much further. Using the Kepler timeseries we will be able to extract the individual oscillation frequencies, measure amplitudes, phases and mode life-times, and use this information to interact with theoretical stellar modelling to measure stellar masses, luminosity, radii, ages, effective temperatures and rotation for each of the observed stars, as well as test the details of the physics of the stellar interiors. We finally note that the time scale of pulsation varies widely between different types of stars. For several types of the classical variables (such as Cepheids), as well as for solar-like oscillations in giant stars, the pulsation periods are so long that the low-cadence data will be sufficient for detailed asteroseismic investigations. The long-term, continuous observations of Kepler will allow the determination of frequencies to very high precision. J. Christensen-Dalsgaard et al. 355 The Kepler Asteroseismic Investigation (KAI) The Kepler Asteroseismic Investigation will be arranged around the Kepler Asteroseismic Science Operations Centre (KASOC), which will be established at the Department of Physics and Astronomy, University of Aarhus. An agreement is being established to define the details of this part of the Kepler project. The relevant Kepler data will be transferred from the Data Management Centre at Space Telescope Science Institute to KASOC; the data will be high-pass filtered, or in other ways modified, so as to contain no information about planet transits. At the KASOC amplitude spectra will be determined and the frequencies and other properties of the stellar pulsations will be extracted. Also, a preliminary asteroseismic analysis will be made to determine global parameters of the stars, such as radius, mass and age. Further detailed analyses will be carried out to determine properties of the stellar interiors and test stellar modelling, particularly for the relatively bright targets with high signal-to-noise ratio. The quantity and quality of asteroseismic data expected from Kepler are overwhelming: time series extending over months to years for several thousand stars are expected. Also, very substantial development of procedures for data analysis and data interpretation has to take place before the start of the mission, and detailed ground-based observations are needed to characterize the prime targets of the asteroseismic investigation. These efforts far exceed the capabilities of KASOC and the directly involved Co-Investigators of Kepler . Consequently, we shall establish a Kepler Asteroseismic Science Consortium (KASC), with broad community participation, to help with the preparations and take part in the analysis of the data. A call will be made early in 2007 for applications to join the KASC, requesting indication of the contributions to be made to the project and the planned use of the data. Conclusion The Kepler mission promises unique opportunities for asteroseismology, in terms of the number and variety of stars that can be studied with very high differential photometric precision. This will provide a comprehensive overview of stellar properties across a large part of the HR diagram, including information about the excitation and damping of the modes, and detailed information about the internal structure of a substantial number of stars. Also, the long period over which the Kepler field will be observed offers the possibility of studying frequency variations associated with possible stellar activity cycles; thus a parallel investigation of the activity of stars in the Kepler field through measurement of the H and K indices (e.g. Baliunas et al. 1998) is highly desirable. Kepler will follow two years after the launch of the CoRoT mission which shares many of the characteristics of Kepler , including very high photometric precision and observations over relatively long periods. Thus a collaboration with the CoRoT asteroseismic project would be very valuable; this could include experience with the optimal analysis of the time series to determine the oscillation frequencies, as well as improved information about the expected amplitudes and lifetimes of the modes in the potential Kepler targets. The asteroseismic investigations based on the Kepler data will be very valuable for the exo-planet part of the mission. As demonstrated above, we expect to determine accurate radii for a substantial fraction of the planet-hosting stars discovered from planetary transits; this will substantially improve the determination of the planet radii from the properties of the transits. Also, in many cases the asteroseismic data will provide estimates of the age of the star, of obvious value to the understanding of the evolution of planetary systems. However, in the present context the main importance of the data is obviously their great potential value for our understanding of stellar structure and evolution. 356 Asteroseismology with the Kepler mission References Baliunas S. L., Donahue R. A., Soon W., Henry G. W., 1998, in Donajue R. A., Bookbinder J. A., eds, ASP Conf. Ser. Vol. 154, Activity Cycles in Lower Main Sequence and POST Main Sequence Stars: The HK Project. Astron. Soc. Pac., San Francisco, p. 153 Basri G., Borucki W. J., Koch D., 2005, New Astronomy Rev., 49, 478 Christensen-Dalsgaard J., 2004, Solar Physics, 220, 137 Kjeldsen H., Bedding T. R., 1995, A&A, 293, 87 Kjeldsen H., Bedding T. R., 2004, in Danesy D., ed., Proc. SOHO 14/ GONG 2004, Helio- and Asteroseismology: Towards a Golden Future. ESA SP-559, Noordwijk, p. 101 Koch D., Borucki W., Basri G., et al., 2006, in Hartkopf W. I., Guinan E. F., Harmanec P., eds, Proc. IAU Symp. 240, Binary Stars as Critical Tools and Tests in Contemporary Astrophysics, Cambridge University Press, #21 DISCUSSION Roxburgh: Will you just have access to 500 windows or all the data? Christensen-Dalsgaard: I think that initially we’ll just be having 512 windows, although we have to negotiate on the giant stars. Asteroseismology with Kepler will actually be of some help to identify the giant stars because we will be measuring the large separations. So we will have some giant star data to play with. There is also a guest observer program, that is separate from this, and that will allow also studying ”uninteresting” stars like B stars that some people tend to like. Bedding: This mission will also provide excellent parallaxes for the main sequence stars from the astrometry. Christensen-Dalsgaard: That’s a very important point. We will be getting very precise, and maybe even very accurate, parallaxes from the Kepler data, so we should be able to get sufficiently accurate distances to determine the luminosities of the stars. From the photometry we should also be able to see rotation from spots on the surface, so we can compare this to pulsational spacings due to rotation. Metcalfe: Did you say what is the policy and timeline for data release, and how this compares to the other space telescopes? Christensen-Dalsgaard: The data-release scheme is very complicated and I was not able to discuss it. A complication is that it has to allow for enough time to detect and identify the planet transits, and for that you need at least three transits. There is hefty document that discusses all the rules on when and how the data are going to be released. However, I hope that we shall be able to operate with a simpler scheme for the asteroseismic data, managed through the Kepler Asteroseismic Science Operation Centre. Aerts: I was thinking about the 3-minute integrations for the Gamma Dor stars. You should get them! Christensen-Dalsgaard: Of course. We will use the Northern ASAS to start looking for candidates in the fields. Comm. in Asteroseismology Vol. 150, 2007 The PLATO mission concept Ian Roxburgh,1,2 Claude Catala 2 and the PLATO consortium3 1 Astronomy Unit, Queen Mary, University of London, Mile End Road, London E14NS, UK 2 LESIA, Observatoire de Paris, Place Jules Janssen, 92195 Meudon, France Abstract PLATO is a project for a future space mission that is intended to be submitted in response to the upcoming ESA ”Cosmic Vision” announcement of opportunity. The science goal of PLATO is to provide a solid observational basis to understand the formation and evolution of stars and their planetary systems. This goal will be achieved by determining statistically the distribution of sizes and orbits of exoplanets, down to sub-earth sized planets and up to orbits at several AU, and the properties of their parent stars through asteroseismology. The observational concept of PLATO is based on ultra-high precision photometry from space. The strategy is to identify a sample of more than 100 000 bright stars, and to perform on all of them a long-term high precision monitoring in white-light visible photometry. This monitoring will be used on one hand to search for and characterize planetary transits in front of these stars, and on the other hand to detect and analyse oscillations of the same stars and thus probe their internal structure and dynamics. The requirements for such a mission are challenging: a very wide field-of-view, near 900 square degrees, as well as a large effective collecting area, of the order of 1 m2 , are necessary to monitor simultaneously a sufficiently large sample of bright stars, with a sufficient photometric precision. The duration of the monitoring must be of at least 5 years. We present an example of instrumental concept compliant with these requirements. It involves a large number of small pupil optics, each one illuminating its own large format focal plane. Although challenging, this concept builds on heritage from previous missions and previous studies, and presents a low technological risk. Detailed industrial studies of the proposed mission are currently being undertaken by Astrium and by Alcatel/Alenia, and the final form of the mission concept to be submitted to ESA will doubtless draw heavily on these studies. Due to secrecy agreements with these companies we are not permitted, at this time, to discuss the current stage of their studies. Introduction A full and deep understanding of stellar formation and evolution is central to much of astrophysics. In particular, stars are the basic ”clocks” with which we can measure ages of stellar systems within our galaxy, and thus set up and calibrate age estimators in the Universe on larger scales. For instance, dating stellar members of the different components of galactic structure, such as bulge, halo, thin disk, thick disc, would lead to fundamental advances in our understanding of galactic structure formation and evolution. Stars are also responsible for most of the chemical evolution of the Universe, elements being created and destroyed by nuclear burning in their deep interiors, before they are subsequently 3 The current PLATO team consists of: C. Aerts, S. Aigrain, E. Antonello, T. Appourchaux, M. Auvergne, A. Baglin, P. Barge, M. A. Barstow, F. Baudin, P. Boumier, A. C. Cameron, C. Catala, J. Christensen-Dalsgaard, G. Cutispoto, H. Deeg, M. Deleuil, S. Desidera, J.-F. Donati, B. H. Foing, J. Gameiro, R. Garcia, R. Garrido, K. Horne, A. F. Lanza, A. C. Lanzafame, A. Lecavelier des Etangs, A. Léger M. Mas-Hesse, S. Messina, G. Micela, E. Michel, M. Monteiro, B. Mosser, A. Noels, I. Pagano, G. Piotto, E. Poretti, H. Rauer, T. Roca-Cortes, D. Rouan, I. Roxburgh, J. Schneider, K. Strassmeier, S. Turck-Chièze, S. Vauclair, A. Vidal-Madjar, W. W. Weiss, P. Wheatley. Support from the wider community will be sought when the mission concept is more precisely defined. 358 The PLATO mission concept ejected into the interstellar medium at the end of the stars’ lives. A clear and reliable understanding of stellar formation and evolution is therefore essential to our description of chemical evolution of galaxies and of the Universe. A good knowledge of the evolution of cool solar-type stars is also crucial for our understanding of the past and future evolution of the sun and solar system. Finally, stellar interiors constitute laboratories for studying physical processes such as e.g. convection or nucleosynthesis in extreme conditions that cannot be reproduced on Earth. The question of the existence of life outside the Earth has been of concern to mankind for several thousand years. Today, one decade after the discovery of the first giant exoplanet, and with the prospect of detecting soon the first telluric exoplanets after the launch of CoRoT (Baglin et al. 2002) in 2006, then of Kepler (Borucki et al. 2003) a couple of years later, we are entering the era when scientific answers to this fundamental question can be envisaged. Planet formation and evolution theory is at the centre of this problem. In order to understand the origin of life and to determine whether and where life is likely to exist elsewhere in the Universe, a full and reliable understanding of planet formation and evolution is absolutely necessary. Understanding the processes of star and planet formation and the subsequent evolution of stellar interiors, stellar surfaces and of planetary systems is thus a prerequisite for future progress in most areas of astrophysics and in the scientific and philosophical approaches of the origin of life in the Universe. Star and planetary system evolution Theory of stellar evolution has undergone major progress in the last decades. In particular, improvements in the description of opacities, equation of state and thermonuclear reaction rates have resulted in a better agreement between models and observations. In spite of this progress in our understanding of microscopic physics in stellar interiors, our description of some physical processes controlling stellar structure and evolution is subject to major uncertainties. Convection and various other mixing and transport processes are poorly understood and yet play a major role in stellar evolution. Some of these processes, such as mixing and diffusion in stellar cores for main sequence stars, are crucial in determining their evolution timescales, and therefore need to be understood and taken into account for measuring stellar ages. Our current poor knowledge of some (if not all) of these processes is usually compensated in our modelling by some poorly constrained parametrization, and therefore the resulting stellar ages are model dependent and often unreliable. One of the consequences of this unsatisfactory modelling is that the ages of the oldest globular clusters are still very uncertain, and for some values of the model free parameters can still be higher than the estimated age of the Universe (van den Bergh 1995, Clementini & Gratton 2002, Krauss & Chaboyer 2003). Additionally, the relatively large adopted value of the core overshooting parameter needed to fit young open cluster data (e.g., Mermilliod & Maeder 1986) is in contradiction with recent asteroseismic estimates of 0.1 (expressed in the local pressure scale height) for this parameter for field β Cephei stars (Aerts et al. 2003, Pamyatnykh, Handler & Dziembowski 2004). This clearly points out that our current knowledge of convective and rotational mixing processes inside massive stars is very incomplete, resulting in huge uncertainties in stellar masses and ages of supernova progenitors. In general, uncertainties in convective overshooting lead to uncertainties in the ages of open clusters up to a factor of two (e.g., Perryman et al. 1998). Considering these difficulties and uncertainties, it must be admitted that the age ladder of the Universe, which rests on stellar age estimates, is still highly unreliable. Our modelling of stellar interiors and stellar evolution therefore needs to be seriously improved. The situation for the Sun has evolved considerably with the advent of helioseismology, I. Roxburgh, C. Catala and the PLATO team 359 which has provided precise insight into the properties of the solar interior (e.g. ChristensenDalsgaard 2000). The inversion of solar oscillation frequencies has led to the determination of the sound speed in most of the Sun, providing detailed tests of models of solar internal structure. The analysis of frequency splittings has provided measurements of the solar internal rotation to very high accuracy. Based on this very positive experience, it is clear that asteroseismic investigations, i.e. measurements of oscillation frequencies, amplitudes and lifetimes of a large number of stars of various masses and ages constitute the only and necessary tool to develop and operate to constrain efficiently our modelling of stellar interiors, and improve our understanding of stellar evolution (e.g., Roxburgh 2004). Similarly, we do not yet have a sufficient understanding of planetary system formation and evolution. Detections of giant exoplanets in the past decade have revealed a large variety and complexity of configurations in exoplanetary systems, which was totally unexpected. Major questions and uncertainties remain, which hamper our progress in understanding the formation and evolution of planetary systems. The distribution of characteristics of exoplanets and of their orbits is unknown. In particular, we have no indication on the distribution of planets with sizes and masses significantly smaller than those of gaseous giant planets. The extension of our knowledge of the frequency and characteristics of exoplanets toward lower masses, down to terrestrial planets, may reveal further surprises. The first planets with masses corresponding to those of icy planets have been discovered in the past year, but their nature (Very large rocky cores? Remnants of evaporated giant planets?) remains at present obscure. Although some important information will be obtained by CoRoT and later on Kepler, a full statistical description of exoplanetary systems, down to masses and sizes of a fraction of those of the Earth, will be out of reach of these upcoming missions. Yet such a description is a prerequisite for any decisive advance in this field. In particular, it is only through the tight constraints derived from a full and reliable knowledge of the properties of planets, their orbits and their parent stars that we will progress in our understanding of the mechanisms controlling orbital eccentricities and planet migration (Namouni 2005). The connection between giant planets and the metallicity of their parent stars is still mysterious, and its investigation also requires good statistical knowledge of planet and parent star properties. In particular, asteroseismology has the potential to measure directly the chemical composition difference between the inner part and the external convective zone of a star, that would be present if the high metallicity of planet hosts was due to the ingestion of planetary material (Bazot & Vauclair 2004). Necessary observational constraints We clearly lack observational constraints for studying the formation and evolution of stars, of their planetary systems, and of their magnetic fields. These problems being intimately related, their investigations must optimally be conducted jointly. In other words, the constraints that we need to gather on the distribution of planet characteristics, on the internal structure of stars and their evolution, and on the distribution and strength of magnetic fields at the surface of stars, must be obtained by observing the same sample of stars. The best way to obtain the distribution of exoplanet sizes and orbital elements is certainly the observation of planetary transits by long-term monitoring in ultra-high precision visible photometry. The same instrumental technique can also be used to detect and measure stellar oscillation modes in order to probe their internal structure via asteroseismology. This approach is at the centre of the CoRoT mission. The science objectives outlined above clearly necessitate space-based observations. First, the ultra-high photometric precision needed to detect planetary transits from small- and medium-size telluric planets, as well as to detect and measure low amplitude stellar oscillations, cannot be achieved from the ground because of scintillation noise. Second the very 360 The PLATO mission concept high duty cycle needed to avoid side lobes in the oscillation power spectra and to optimize the transit detection probability, also calls for space-based observations. Proposed observational concept The basic observational concept proposed here consists in following these three complementary approaches on the same stars. The strategy is to identify a sample of more than 100 000 stars, and to perform on all of them a long-term high precision monitoring in visible light, with the following objectives: • search for planetary transits in broadband visible intensity measurements; characterize the detected transits (depth, duration, period, shape,...) and derive the characteristics of the transiting planets and their orbits; • detect oscillation modes in broadband visible intensity measurements; measure their frequencies, amplitudes and lifetimes, and derive constraints on internal structure and internal rotation, e.g. via inversion techniques. These objectives can be met using the same set of visible photometric observations. Because we need to detect stellar oscillations at least down to solar-like oscillation amplitudes (typically a few ppm), the visible light photometric observations must be performed on stars that are bright enough that such oscillations can be comfortably detected against photon noise. For reasonable values of the instrument pupil size, the limiting magnitude for such observations is around mV = 11. The search for planetary transits around such bright stars requires a very wide field in order to counterbalance the relatively small density of such stars in the sky. For a wide choice of pointing directions, one can find typically 140 stars brighter than mV =11 per square degree. The specification for the planetary transit objective would therefore be to monitor a field of at least 30◦ × 30◦ , in order to include about 100 000 such stars. Such a large number of relatively bright stars would provide us with an unbiased stellar sample in terms of mass, age, metallicity, rotation. It would also include members of open clusters of various ages, as well as old Population II stars. The duration of the monitoring to be performed on these stars must be of at least 5 years. With such a long duration monitoring, we will be able to detect and characterize planets with orbital periods up to several years. We will also reach a very high precision in the frequency measurements for asteroseismology, and get the opportunity to study changes in mode amplitudes and frequencies along stellar activity cycles. The detection of earth and sub-earth sized planet transits, as well as the detection and analysis of solar-like oscillations imply stringent requirements in terms of visible photometric precision: photometric noise levels as low as 2 × 10−5 in 1 hr for stars with mV = 11 are necessary for the foreseen exoplanet studies, while a resulting photometric noise level in Fourier space of 10−6 in 2 weeks for stars with mV = 11 is a prerequisite for asteroseismology of solar-like stars in the same sample. These demanding requirements impose a large collecting area, of the order of 1 m2 . An example of instrumental concept In this section, we present an instrumental concept that would meet the requirements listed above. We stress that this is nothing other than an illustrative example, and that alternative options are possible, and are currently being considered in industrial studies by Astrium and Alcatel/Alenia and will doubtless influence the final version of the mission concept to be I. Roxburgh, C. Catala and the PLATO team 361 submitted to ESA. At the present time these studies are subject to a secrecy agreement and so unfortunately their results cannot be presented here. The major difficulty comes from the need to cover a very wide field (30◦ ), with a large collecting area (1m2 ). One solution is to use a large number of small pupil, short focal length optics. The short focal length made possible by the use of small pupils yields a wide optical field, while the large number of unit elements ensures a large effective collecting area. Figure 1: An example of instrumental configuration. The instrument includes 100 refractors with pupils of 100 mm all looking at the same 30◦ × 30◦ field. Each visible refractor has its own focal detector, made of one single 12k × 12k visible detector, with 5 μm pixels, or a mosaic of smaller detectors, covering up the available 6 cm focal plane. This illustrative example of instrumental concept (Fig. 1) calls for some technological developments and changes in design. For example it is probably necessary to use reflecting telescopes to reduce the mass, the development of large format, small pixel CCDs is certainly a challenging issue to be studied in detail in the coming months and years. Other points to be studied in relation to this concept include miniaturized electronics and powerful on-board computing facilities. Note however that most of these developments will build on heritage from previous missions and/or previous studies, such as Gaia or Eddington, so that the concept presented here can certainly be developed at low technological risk. Advantages of the proposed concept Exoplanet science Our proposed observational concept concentrates on the observation of a large number of bright and nearby stars to search for planetary transits. The relatively short distance to the targets is compensated by the very large field size, to finally allow us to probe a large volume of the galaxy. This is in contrast to previous approaches, such as CoRoT, Kepler or Eddington, which are designed to survey a large volume of the galaxy by observing faint and distant stars in a much smaller field. 362 The PLATO mission concept Because the present concept focuses on bright and nearby stars, still providing a fully unbiased sample, the use of a large collecting area on relatively bright targets will yield high signal-to-noise ratios in the light curves, thus allowing us to detect small planets, and to characterize the transit shapes with a higher precision. In addition, the brightness of the surveyed stars makes possible their subsequent observation in high resolution spectroscopy. The proximity of some of these objects also provides us with the opportunity of performing detailed astrometric follow-up observations, as well as interferometric imaging of the detected planets. Stellar interiors The seismological observations of the proposed concept will give us the possibility to study stellar oscillations down to solar-like level for more than 100 000 stars, of all masses and ages. This is a considerable step forward compared to currently planned missions: it represents more than 1000 times the stellar sample monitored by CoRoT, and more than five times the sample that was planned for the Eddington mission. This impressive star sample represents a significant fraction of the targets that will be observed by Gaia/RVS, and for which we will provide an estimate of their age. The age observable, missing from the Gaia/RVS science, will complete nicely the space and velocity-space coordinates provided by Gaia, and bring us a full characterization of the surveyed galactic populations. Finally, the proposed five-year duration will yield very high precision on oscillation frequencies, and thus a very good precision on internal structure and rotation. Summary and conclusion The observational concept proposed in this paper will allow us to study at the same time and on the same targets two fundamental problems of today’s astrophysics: the characterization of exoplanets and stellar evolution. In order to meet these fascinating and challenging objectives, we need to survey a very wide field and monitor more than 100 000 stars at a time, to reach a very high precision photometry in the visible, and to perform very long duration monitoring. This concept has its place within an overall European roadmap for the study of star and planet evolution. As of the end of 2006, the pioneering mission CoRoT will open the way by looking for the first telluric exoplanets and by performing the first high precision seismology studies of a few bright stars. The mission concept we have described here goes far beyond that of the Eddington mission (sadly cancelled by ESA due to budgetary constraints) and as a consequence, is more challenging from a technical point of view, thus requiring a new mission concept assessment study. The very large number of targets will allow us to study the broad context of the life of stars and planets from one mission for hundreds of thousands of stars in our Galaxy at once. Gaia will provide the most complete investigation of stellar fundamental parameters for millions of stars. The concept we propose here will complete this view by (i) providing a measurement of the age of a significant fraction of the Gaia targets, (ii) investigating the internal structure and rotation of stars of all masses and ages, (iii) characterizing with high accuracy exoplanetary systems together with their central stars. The statistical knowledge acquired on exoplanetary systems by missions like CoRoT, and the mission concept proposed here, can be used to optimize the strategy of future interferometric imaging missions such as Darwin and subsequent more ambitious interferometric missions such as that submitted to ESA by Catala and Roxburgh (2005) in response to their call for ideas for the future science programme of ESA. I. Roxburgh, C. Catala and the PLATO team 363 References Aerts C., Thoul A., Daszyńska J., et al., 2003, Sci, 300, 1926 Baglin A., Auvergne M., Barge P., et al., 2002, in Favata F., Roxburgh I. W., Galadi D., eds, Stellar Structure and Habitable Planet Finding, 1st Eddington Workshop. ESA-SP 485, Noordwijk, p. 17 Bazot M., Vauclair S., 2004, A&A, 427, 965 Borucki, W. J., Koch, D. G., Basri, G. B., et al., 2003, in Deming D., Seager S., eds, ASP Conf. Ser. Vol. 294, Scientific Frontiers in Research on Extrasolar Planets. Astron. Soc. Pac., San Francisco, p. 427 Catala C., Roxburgh I. W., 2005, Response to RESA’s call for ideas for future space missions Christensen-Dalsgaard J., Däppen W., Dziembowski W. A., Guzik J. A., 2000, in C. Ibanoglu, ed, Variable Stars as Essential Astrophysical Tools. Kluwer, Dordrecht, p. 59 Clementini G., Gratton R., 2002, European Review, Vol. 10, p. 237 Krauss L. M., Chaboyer B., 2003, Sci, 299, 65 Mermilliod J. C., Maeder A., 1986, A&A, 158, 45 Namouni F., 2005, AJ, 130, 280 Pamyatnykh A. A., Handler G., Dziembowski W. A., 2004, MNRAS, 350, 1022 Perryman M. A. C., Brown A. G. A., Lebreton Y., et al., 1998, A&A, 331, 81 Roxburgh I. W., 2004, in Favata F., Aigrain S., Wilson A., eds, Stellar Structure and Habitable Planet Finding, 2nd Eddington Workshop. ESA-SP 538, Noordwijk, p. 23 van den Bergh S., 1995, Sci, 270, 1942 Comm. in Asteroseismology Vol. 150, 2007 Dynamos, Asteroseismology, and the Stellar Imager C. J. Schrijver,1 K. G. Carpenter,2 M. Karovska 3 1 Lockheed Martin Adv. Techn. Center, Solar and Astrophysics Lab., Palo Alto, CA 2 Exoplanets and Stellar Astrophysics Laboratory, NASA’s GSFC, Greenbelt, MD 3 Smithsonian Astrophysical Observatory, Cambridge, MA Abstract The ultra-sharp images of the Stellar Imager1 (SI) will revolutionize our view of many dynamic astrophysical processes: The 0.1 milli-arcsec resolution of this deep-space telescope will transform point sources into extended sources, and simple snapshots into spellbinding evolving views. SI’s science focuses on the role of magnetism in the Universe, particularly on magnetic activity on the surfaces of stars like the Sun and on the subsurface flows that drive this activity. SI’s prime goal is to image magnetically active stars with enough resolution to map their evolving dynamo patterns and their internal flows. By exploring the Universe at ultra-high resolution, SI will also revolutionize our understanding of the formation of planetary systems, of the habitability and climatology of Earth as well as distant exoplanets, and of many magneto-hydrodynamically controlled structures and processes in the Universe. Introduction The Stellar Imager (SI) is a UV-optical, space-based interferometer designed to enable 0.1 milli-arcsecond (mas) spectral imaging of stellar surfaces and asteroseismic exploration of stellar interiors, and the high-resolution exploration of the Universe in general. The key science goals of the SI mission are (1) to study the evolution of stellar magnetic dynamos from the very formation of stars and planetary systems onward to the final stages of stellar evolution; (2) to complete the assessment of external solar systems begun by the planetfinding and imaging missions by observing their central stars in detail; and (3) to study the Universe at ultra-high angular resolution from the internal structure and dynamics of stars and interacting binaries to extreme conditions in, e.g., active galactic nuclei and in black hole environments. The resolving power of SI makes it a unique tool for a variety of scientific research areas in general astrophysics, including magnetically active stars, stellar interiors in stars outside solar parameters, infant star-disk systems, hot stars, cool giant and supergiant stars, supernovae and planetary nebulae, interacting binaries, active galactic nuclei, quasars, black-hole environments, etc. Here, we focus on stellar magnetic activity, and on the internal stellar dynamics that drives dynamos in the Sun and stars. Stellar Magnetic Activity The recognition of the importance of the Sun’s variability has led to the development of an International Living With A Star program and its research infrastructure. At the core of that program is the Sun’s magnetic field: what causes the Sun to be magnetically active, and how can we develop reliable forecasting tools for this activity and the associated space weather and climate changes on Earth? The Stellar Imager aims to make crucial contributions to this 1 See http://hires.gsfc.nasa.gov/si/ for details on the Stellar Imager mission. C. J. Schrijver, K. G. Carpenter, M. Karovska 365 Figure 1: Simulations of SI’s imaging capabilities for 30 mirror elements, and a visualization of stellar interior flows. field, warranting its status as a Landmark Discovery Mission in the 2005 roadmap for NASA’s Heliophysics Division. The principal cause of all solar variability is its magnetic field. This intangible and unfamiliar fundamental force of nature is created in the convective envelope of the Sun by a process that we call the dynamo. There is at present no quantitative model for stellar dynamos that is useful to forecast solar activity or even to establish the mean activity level of a star based on, say, its mass, age, and rotation rate. The nonlinear differential equations for the coupling of the vectors of turbulent convection and magnetic field cannot be solved analytically. Nor can the cycle dynamo be simulated numerically in its entirety; full numerical coverage would require some 1018 grid points, which is a factor of order a billion beyond present computational means. Hence, both analytical and numerical studies necessarily make approximations that simplify or ignore much of the physics. Furthermore, even the approximating models are of a richness and diversity that there is no consensus on the model properties, or even on the set of processes that are important in driving the dynamo. Numerical research will undoubtedly make significant advances in the coming years, but only the comparative analysis of many Sun-like stars with a range of activity levels, masses, and evolutionary stages will allow adequate tests of complex dynamo models, validation of any detailed dynamo model, and exploration of the possible spatio-temporal patterns of the nonlinear dynamo. The studies of average activity levels of stars have helped us piece together what some of the essential ingredients to dynamo action are on the largest scales. For example, we know that a dynamo associated with stellar activity operates in all rotating stars with a convection zone directly beneath the photosphere. In single stars, the dynamo strength varies smoothly, 366 Dynamos, Asteroseismology, and the Stellar Imager Table 1: SI mission and performance parameters Parameter Max. mirror separation Effective focal length Diameter of mirrors Wavelength coverage Spectral resolution Angular resolution Optical surfaces Phase corrections Time to image stellar surface No. of pixels on star Time to map int. flows Seismology cadence Minimum field of view Min. detectable flux Operational orbit Operational lifetime Accessible Sun angle Combiner dry mass Mirrorsat dry mass Reference platform Total propellant S/C control Pointing control Value B = 100-1000 m 1-10 km 1-2 m λ 1200-3200Å λ 3200-5000Å 10Å(lines);100Å(cont.) 50 μas-208μas actuated to μm-nm to λ/10 < 5 h for solar type < 1 d for supergiant ∼ 1000 Rotation period 1 minute > 4 milli-arcsec 5. × 10−14 ergs/cm2 /s 200×800 Mm; 180 d 5 y (req.) - 10 y (goal) 70◦ ≤ θ ≤ 110◦ 1455 kg 65 -120 kg 200 kg 750 kg mm-cm level 3 μas up to 1000 s Notes 500 m typical Scales with B Up to 30 mirrors Wavefront sensing in optical only Scales with λ/B for path lengths Surface imaging Sun-like at 4 pc. Set by target Internal structure 10Å band at 1550Å at Sun-Earth L2 Entire sky in 180 d 1 req.; 2 optional up to 30 satellites for operations Formation flying and mostly monotonically, with rotation rate, at least down to the intrinsic scatter associated with stellar variability. It also depends on some other unknown stellar property or properties. For main sequence stars, for example, the primary factor in determining activity resembles the convective turnover time scale at the bottom of the convective envelope. But no such dependence holds if we test the relationship on either evolved stars or on tidally-interacting compact binary systems. Apparently, other parameters, as yet unidentified, play a role, such as surface gravity and tidal forces. The variations of stellar and solar activity on time scales of years also remain a mystery. The Sun shows a relatively regular heartbeat with its 11-year sunspot cycle, even as cycle strength and duration are modulated. Such a pattern is not the rule among the cool mainsequence stars, however. Instead, we find a variety of patterns in their activity, in which only one in three of these stars show cyclic variations like those of the Sun. For truly active stars, various variability patterns exist, but generally no unambiguous activity cycle is seen. It would take hundreds of years to validate a solar dynamo model using only observations of the Sun, given its irregular 11-year magnetic heartbeat and the long-term modulations. Key to successfully navigating the route to a workable, predictive dynamo model is the realization that in order to understand the solar dynamo, we need a population study; that is, we need to study the dynamo-driven activity in a sample of stars like the Sun, and compare it to observations of younger stars, older stars, and stars in binary systems, etc. Thus, the SI will enable us to test and validate solar dynamo models within a decade, rather than requiring a century or more if we used only the Sun. C. J. Schrijver, K. G. Carpenter, M. Karovska 367 The potential for a breakthrough in our understanding and our prediction ability lies in spatially-resolved imaging of the dynamo-driven activity patterns on a variety of stars. These patterns, and how they depend on stellar properties (including convection, differential rotation and meridional circulation, evolutionary stage/age), are crucial for dynamo theorists to explore the sensitive dependencies on many poorly known parameters, to investigate bifurcations in a nonlinear 3-dimensional dynamo theory, and to validate the ultimate model. Direct, interferometric imaging - the goal of the Stellar Imager - is the only way to obtain the required information on the dynamo patterns for stars of Sun-like activity. Alternative methods that offer limited information on spatial patterns on much more active stars fail for a Sun-like star: a) rotationally-induced Doppler shifts in such stars are too small compared to the line width to allow Zeeman-Doppler imaging, b) the activity level is insufficient to lead to significant spectral changes associated with magnetic line splitting, c) rotational modulation measurements leave substantial ambiguities in the latitude distributions, locations and sizes of spots, and cannot be used to measure dispersal of field across the stellar surface. The direct imaging by SI of stellar activity will overcome these problems. Equally importantly, the asteroseismic observations planned with SI will determine the internal properties of stellar structure and rotation, thus directly providing crucial information relevant to the physical operation of the dynamo mechanism. Imaging magnetically active stars and their surroundings will also provide us with an indirect view of the Sun through time, from its formation in a molecular cloud, through its phase of decaying activity, during and beyond the red-giant phase during which the Sun will swell to about the size of the Earth’s orbit, and then toward the final stages of its evolution as a Planetary Nebula and a white dwarf relic. Asteroseismology: from dynamo to fundamental physics The SI mission will allow us not only to image the surfaces of stars, but also to sound stellar interiors using spatially resolved asteroseismology to measure internal structure, differential rotation, and large-scale circulations; this will provide accurate knowledge of stellar structure and evolution and complex transport processes, and will impact numerous branches of (astro)physics. Helioseismology has given us an extremely detailed view of the solar interior. These results are of great importance to our understanding of the structure and evolution of stars, and of the physical properties and processes that control this evolution. At the time of the launch of the SI, seismic investigations of other stars will have been undertaken by several space missions, including MOST and COROT. However, a number of key issues will remain open. These preceding missions will only observe low-degree modes, through intensity variations in light integrated over the stellar disks. Such point-source observations will provide information about the global properties of solar-like stars, which allows the study of global structure, including, e.g., gravitational settling of helium and large-scale mixing processes. SI observations, however, will allow us to expand the discovery space far beyond that: modes of degree as high as 60 should be reachable with an array of N = 10 elements, increasing as N 2 for larger arrays. By analogy with the Sun, in solar-like stars this will allow inferences with good radial and reasonable latitude resolution to be made in the radiative interior and the lower part of the convective envelope, for both structure and the patterns and magnitudes of the differential rotation with depth and latitude. With a careful choice of target stars SI observations will allow us to obtain such detailed information about the interiors of stars over a broad range of stellar parameters, in terms of mass, age and composition. Studies of the internal rotation as a function of mass and age will provide unique information about the evolution of stellar internal rotation with age, in response to the activity-driven angular-momentum loss in stellar winds. This will provide stringent constraints on models of the rotational evolution, elucidating the processes responsible for transport of angular mo- 368 Dynamos, Asteroseismology, and the Stellar Imager mentum in stellar interiors; these studies are also fundamental to the understanding of the dynamo processes likely responsible for stellar activity. By correlating the rotation profile with the profile of the helium abundance, as reflected in the seismically inferred sound speed, an understanding can be achieved of the rotationally-driven mixing processes in stellar interiors. This is of great importance for calibrating the primordial abundances in the Universe as well as to the improvement and validation of stellar evolution models. For example, the data will provide constraints on the convective overshoot at the base of the convective envelope which also contributes to the mixing. The resulting understanding can then be applied to the mixing and destruction of lithium, finally providing the means to relate the observed lithium abundance in old halo stars to the primordial lithium content of the Universe. For stars slightly more massive than the Sun the data, combined with the more extensive data on low-degree modes likely available at the time from earlier missions, will allow detailed investigations of the properties of convective cores and related internal mixing; an understanding of these processes is essential to the modelling of the evolution of massive stars, leading to the formation of supernovae. The initial trade-off studies performed described in the Vision Mission study report1 will need to be complemented by others to balance the scientific needs with the overall SI design and operations. Here, we point out that at a minimum we can say that n ∼ 9 optical elements are needed to adequately measure the magnitude of the differential rotation, with mapping resolution increasing rapidly with n: The minimum number of mirror elements required for SI follows from the need to measure the differential rotation to better than a fraction f of the stellar rotation period P. An n-element interferometer that can observe in k independent optical channels, can measure sectoral modes up to no more than azimuthal order m = kn(n − 1)/4. For a desired frequency resolution of mf /P Hz, the observing interval should exceed 4P/fm. When √ SI observes a full rotation in order to complete its surface mapping, this results in n > ∼ 2/ fk, so that for, say, f = 0.02, n > ∼ 9. Increasing the number of interferometer elements allows a shorter integration period needed to measure internal rotation rate, although it must necessarily remain a substantial fraction of the rotation period in order to be able to separate the frequencies in Fourier space. The asteroseismic resolution that can be achieved at a given location within a star approximately equals the local wavelength λ = cs /ν, where cs is the sound speed and ν is the cyclic frequency. Thus the resolution improves from the stellar centre to the surface as the sound speed decreases. The best resolution is obtained at the lower turning depth of the most shallowly penetrating modes for given ν, i.e., those with highest azimuthal order m. There, near the surface, the resolution is approximately λ ≈ 2πR∗ /m. For an SI design with n = 9 and k = 3, we thus find a depth resolution of ∼81 000 km, or 40% of the depth of the convective envelope in a Sun-like star, which poorly constrains differential rotation with depth within the envelope. For an SI design with with n = 30 and k = 3, the depth resolution is ∼ 7000 km or ∼ 3%, so that the differential rotation can be mapped accurately with depth throughout the envelope. Within the total observing period, the net fraction of the time spent on the target star must exceed ∼ 50%, although alternating intervals of ∼ 12 h on a pair of stars nearby on the sky would suffice; that strategy would double the number of stars that can be studied in this way. Mission architecture The current baseline architecture concept for SI (summarized in Table 1) is a space-based, UVoptical Fizeau interferometer with up to 30 one-meter primary mirrors, mounted on formationflying mirrorsats, distributed over a parabolic virtual surface with a diameter that can be C. J. Schrijver, K. G. Carpenter, M. Karovska 369 varied from 100 m up to as much as 1000 m, depending on the angular size of the target to be observed. The individual mirrors are ultra-smooth, UV-quality flats and are actuated to produce the extremely gentle curvature needed to focus light on the beam-combining hub that is located at the prime focus from 1 − 10 km distant. The focal length scales linearly with the diameter of the primary array: a 100 m diameter array corresponds to a focal length of 1 km and a 1000 m array with a focal length of 10 km. The typical configuration has a 500 m array diameter and 5 km focal length. A one-meter primary mirror size was chosen to ensure that the primary stellar activity targets can be well observed with good signal/noise. Sizes up to two meters may be considered in the future, depending on the breadth of SI science targets, e.g., some fainter extra-galactic objects may need larger mirrors, but those will come at a cost to the packaging for launch, the number of launches needed, and total mission cost. The mirrorsats fly in formation with a beam-combining hub in a Lissajous orbit around the Sun-Earth L2 point. The satellites are controlled to mm-micron radial precision relative to the hub and the mirror surfaces to 5 nm radial precision, rather than using optical delay lines inside the hub for fine tuning the optical path lengths. A second hub is strongly recommended to provide critical-path redundancy and major observing efficiency enhancements. The observatory may also include a “reference craft” to perform metrology on the formation, depending on which metrology design option is chosen (see full Vision Mission study report at the SI home page1 for more details). The full SI mission may be built up by starting with a small number of optical elements, perhaps utilizing both interferometry and high-resolution spectroscopy. Adding optical elements increases image quality and time resolution. SI status, technology roadmap, and timeline SI is currently a mission concept that has been listed in three successive strategic planning documents of the Sun-Earth Connections (now Heliophysics) Division of NASA’s Science Mission Directorate, most recently as a Landmark Discovery Mission, and is mentioned in the 2005 roadmap of the Exploration of the Universe Division as a possible “Pathways to Life Observatory.” SI’s scientific rationale needs to be further developed to demonstrate its unique potential for studying the multitude of potential targets in the Universe. Its focus on dynamos and internal flows of Sun-like stars requires further evaluation of its discovery potential by imaging and asteroseismology. To meet those demands, we have the support of an international team of experts in a growing Mission Concept Development Team1 . Many spacecraft engineering challenges exist which are a natural consequence of the defined science goals of the SI mission. Among the most significant, we identify telescope pointing, formation flying and mirror configuration, wavefront sensing and metrology, exposuretime limitations, and mission lifetime. SI shares these challenges with other missions in NASA’s strategic plans; SI can therefore benefit from the studies performed, and expertise developed for its precursor missions. Rapidly advancing technologies may enable an SI precursor mission by 2015 and the full mission by 2025. DISCUSSION Roxburgh: about 1.5 years ago, there was a sketch of a project submitted to ESA in response to their call for ideas for of their Cosmic Vision 2015 program, which has in fact been written up in the COROT book by Claude Catala. Moskalik: what kind of budget do you envision for this kind of project? 100 million dollars? 370 Dynamos, Asteroseismology, and the Stellar Imager Schrijver: We are talking about 10 - 30 spacecraft that would each cost at least 5 - 10 million Euro, plus a beam combiner, launch, etc. It’s not cheap. But for a stepping stone mission we have to ask for something that’s of the order of half a billion. If you go to the full scale thing, it’s going to be 2 - 4 times that. It may be less than JWST, but it’s not a cheap mission. Fossat: this morning I showed the concept of a photometric interferometer of thirty-nine telescopes in the Antarctic. Doing the same in space seems to be extremely difficult to me. Schrijver: it doesn’t matter how we are going to create an interferometer of this type. We need to come up with appealing science reasons from this entire community to make any of them happen because we compete against people who are talking about the age of the universe, the nature of dark matter and dark energy, the end of stars and formation of planetary systems. We need to demonstrate and march as united as we can and then see what we can get. Comm. in Asteroseismology Vol. 150, 2007 The ground-based counterpart of the CoRoT asteroseismic observations from space K. Uytterhoeven,1 E. Poretti 1 and the COROT SGBOWG 1 INAF-Osservatorio Astronomico di Brera, Merate (LC), Italy The CoRoT mission (Michel et al. 2006, 2007) needs a significant amount of ground-based observing time to achieve its science goals. Ground-based asteroseismology has progressed under several aspects (from single- to multi-site campaigns, closer matching between observed frequencies and mode identification, tighter collaboration between observers and theoreticians, etc.). The scientific cases of the δ Sct variable FG Vir (more than 75 frequencies identified; Breger et al. 2005) and of the β Cep variable ν Eri (Ausseloos et al. 2004; De Ridder et al. 2004) can be considered as the frontiers of the ground-based techniques. A large observational effort has been made in the past decades to extract sets of frequencies from photometry (light and colour data) and spectroscopy (line-profile and radial-velocity variations), often combined together. Now, observations from space constitute the natural development of all the progress made by the asteroseismic community, both in the development of methods and of techniques and in the description of the stellar interiors. CoRoT is expected to introduce a dramatic increase in the number of identified frequencies. CoRoT targets cover the whole Main Sequence with the goal to monitor a broad variety of pulsational and other variability mechanisms. For the pulsators, the CoRoT photometry will give us access to low-degree modes, at an amplitude level three orders of magnitude smaller than the current one. However, the complete frequency spectrum is necessary to investigate the stellar interior, including rotation. Therefore, we need to accompany the CoRoT photometric time series with spectroscopic observations, since, in spectra with a resolution ∼50 000, modes with degrees as high as = 10 can be detected through the analysis of the line-profile variations. In moderate and fast rotators, spectral resolution translates into spatial resolution by disentangling different stripes of the stellar surface. As a result, non-radial modes produce line-profile perturbations visible as “moving bumps” in the line profiles. A detailed analysis of the line-profile variations allows us to identify corresponding modes because the shape and the behaviour of the variations depend on the properties of the modes. Indeed, such line-profile analyses have been successfully carried out for several classes of non-radially pulsating stars. To combine the photometric and spectroscopic approaches, we applied to obtain telescope time at different observatories. In particular, a Large Programme has been granted at the [email protected] ESO-MPI instrument, focused on the δ Sct, γ Dor, β Cep and Be stars among the CoRoT targets. Sixty nights (15 in each semester, split into two strings of 10 and 5 consecutive nights separated by at least 10 days) will be devoted to the CoRoT programme in four consecutive ESO Periods, covering the first 1.5 years of the CoRoT lifetime. FEROS is a very solid baseline for the observations of δ Sct, γ Dor, β Cep and Be stars, having been used in the past (e.g., Zima et al. 2006). Moreover, other Large Programmes will be carried out at the Observatoire de Haute Provence (using the new [email protected] instrument; PI P. Mathias) and at the Calar Alto Observatory (using the [email protected] instrument; PI P. Amado). Normal proposals on specific targets will be submitted to the Nordic Optical Telescope (FIES and SOFIN instruments) and Telescopio Nazionale Galileo (SARG instrument) to supply complementary data to those of the ESO, OHP and Calar Alto Large Programs. Therefore, we feel ready to accompany the CoRoT mission with the best observational ground-based effort, in order that as much information as possible can be extracted from this huge (scientific, financial and manpower) effort that the astronomical community is undertaking. 372 The ground-based counterpart of the CoRoT asteroseismic observations from space Acknowledgments. The Seismology Ground-Based Observations Working Group (SGBOWG) involves a wide participation and know-how from researchers in different Institutes: A. Baglin, C. Catala, E. Michel, M. Floquet, M. J. Goupil, A. M. Hubert, Y. Lebreton, A. Moya, C. Neiner, (Meudon Observatory), C. Aerts, M. Briquet, M. Desmet, W. Zima (Leuven University), P. Amado, R. Garrido, S. Martı́n-Ruiz, J. C. Suárez (IAA Granada), L. Mantegazza, E. Poretti, M. Rainer, K. Uytterhoeven (INAF-OABrera), P. Mathias (OCA Nice) and F. X. Schmider (Nice University). K. Uytterhoeven acknowledges the support of the European Community under the Marie Curie Intra-European Fellowship, Contract 024476– PrepCOROT. References Ausseloos M., Scuflaire R., Thoul A., Aerts C., 2004, MNRAS, 355, 352 Breger M., Lenz P., Antoci V., et al., 2005, A&A, 435, 955 De Ridder J., Telting J. H., Balona L. A., et al., 2004, MNRAS, 351, 324 Michel E., Samadi R., Baudin F., et al., 2006, Mem. Soc. Astron. It., 77, 539 Michel E., Baglin A., Samadi R., Baudin F., Auvergne M., 2007, these proceedings Zima W., Wright D., Bentley J., et al., 2006, A&A, 455, 235 Comm. in Asteroseismology Vol. 150, 2007 Discussion on space-based asteroseismology led by Annie Baglin Observatoire de Paris, LESIA, UMR 8109, pl. J. Janssen, 92195 Meudon, France Baglin: We know the very near future of space asteroseismology very well and we know how to handle it. We hope that CoRoT will be launched successfully. The next step is to use the data in the most efficient way. Then the Kepler asteroseismology program is to follow, and this is the near future for us. But after that, it’s extremely unclear and even very opaque, so nothing may happen for a long time as Jørgen said. At least from the European side, there seems to be a lack of funding for new important, new-generation space missions dedicated to stellar physics. The idea of imaging stars, which was mostly born in the States, leads certainly into a very bright future. We will probably have to combine all the efforts, the knowledge, and the money of the whole planet to do that. But that’s still very far; we have to do something in between. This is an open question that I would like to discuss now. Certainly MOST has shown the way of how to work on a very cheap level. This is certainly a way to do something from space on a larger basis, to increase the number of projects. The other way is to rely on ground-based observations. Science asks for both space and ground. We have to say everywhere and claim that we need both, that the information we get is different and complementary. It is difficult but it’s probably easier to fund a ground based project for at least several years. Even in this discussion, which is mostly dedicated to space, we need to think about what we can do from the ground. What is your feeling after this meeting, where we made the effort to discuss all these projects that we have in hands and how do you think that we should move on? What strategy should be developed? Kjeldsen: I think that right now is actually a bad moment to think what we should do next in space. We now have all these nice simulations, but we actually have no data yet except for a few missions like MOST and WIRE. So I think in a few years from now, when we actually have the CoRoT data and the Kepler data, of course we will find that things don’t look like the simulations we did and that there will be lots of things that we would have liked to do differently. And that will be the point where we can say what we shall do in the future. I think at the moment it’s about analysing the data that the next step is. How are we actually going to use all these many many data? That’s where the planning effort should be put at the moment, and not at the next space missions especially because there seems no way to pay for this. Roxburgh: Part of me agrees with you, but part of me does not because it takes twenty, twenty-five years to get a space mission from concept to launch. We should not stop thinking and agitating. Logically you should first analyse all the data from, e.g., Kepler, by which time it will be 2015. And then, another twenty years after that, the next mission is due. So, in reality, you need to start planning now. A mission like CoRoT was first thought about in 1981! Baglin [to Kjeldsen]: I partly agree with you, but we have to do both. The question is, how much energy do you have to put into each task? But I would like to keep from what you said, that there is a need for a stronger organization to get the best science out of the data we will get and I am not sure that we are ready for that. As you say, it’s an enormous amount of data. 374 Discussion on space-based asteroseismology Schrijver: It is a very complex thing that we have to think about what we might be doing twenty years from now even as we actually have to decide now because of the long process ahead. But I would like to stress that this community must think about it rather than letting ESA or NASA as organizations separately decide through their committees. You should form a consensus in your community about a few key things you want to do. It’s the most important thing to do to get things the way you want. The first step is to decide what’s important! Frandsen: Based on my experience with space projects, where I have seen three failures, starting with PRISMA, then STARS and Eddington, I think we need to think about something different, and Karel’s project is maybe the way. Stellar imaging as a solution is really new, and we won’t be alone in that area because there are many astronomers who would love to see imaging data. If we can do something that cannot be done from the ground, and we have the possibility to go to the UV, this could be a point to convince the responsible people that this is new and interesting. My advice therefore is to go to something different; interferometry might be such a case. Kaye: Does anyone know about the optical interferometers that were on range? Schrijver: Yes, they are still being developed. In terms of imaging of stars, however, they don’t have the required baseline and they have to be reconfigured rapidly in order to cover Fourier space. That’s why we are asking for something that’s really challenging. But people are still working on a ground-based system with something in the range of two to five or six optical elements. Baglin: VLTI is working. It’s not foreseen to do seismology, but there could be some attempts with this kind of array. Matthews: Picking up on Søren’s statement: One of the things that benefited MOST and that helped to get it funded so quickly was that we did not have to co-opt the entire community. We were not competing to take money off other Canadian space astronomers; we got money from a space technology pot that no other astronomer ever thought of using. We needed no peer-review, which was a big factor. One other thing one has to take into account, depending on how expensive the mission is: You have to get everybody in your community for support on board, because it’s going to be a major chunk of investment for the community. There are examples of specialized missions at lower budgets in which one can identify a certain science goal, like Werner’s demonstration of the BRITE nanosats. There are certain dedicated focused things that one can consider, that may probably get funding without having to have that sort of political support. One should also always keep those in mind to check the skyscape for some more ambitious missions. The community has to decide what the priorities are, but we have to realize that our community is a subset of a much larger community who also needs to buy into that, if we want, say, half a billion Euro to go for. Roxburgh: If we look at the European mission Eddington, it was more successful than earlier proposals that were not funded. But what also happened at the time was the increasing emphasis on planets. The same is true in recent times. From that I learnt we really ought to be thinking about projects that share with some other areas of astronomy, not just on our own, and something that was equally practicable and wanted by others. Shipman: What Ian just said reminded me of Artie’s talk. We can do planets as a byproduct of everything else that we are doing. Artie mentioned that incidentally, but he found planets! So we have at least part of our hat on that. I think we need to think of other things where we can hang our hat on. Just one example: g-modes probe the interior of stars. Why should we want to do that? Well, the size of the core of some stars determines stellar lifetimes, which tells us about stellar populations, which is going to tell us about - a-ha! the evolution of the universe. These kind of things I haven’t heard a great deal about here. Roxburgh: Really, the planets is what has gotten us this far. Kepler: We have lost the ability to work in the ultraviolet for hot stars. The application of ultraviolet data is much wider in stellar seismology than in other areas, and no one mentioned A. Baglin 375 this possibility here. Matthews: I agree with Kepler entirely. The original concept for the Canadian microsat by Slavek Rucinski was for an ultraviolet imaging telescope. It turned out not to be really practical in terms of its mass, etc., and it eventually became MOST. But that led to a project called UVIT and we are now collaborating with the Indians on their ASTROSAT. There are some science drivers here for ultraviolet time-resolved photometry from space of pulsating stars. In fact we are encouraging everyone who is interested to supply proposals and potential targets because this is going ahead. Kjeldsen: I hope that we really find out with these missions that we don’t understand anything inside stars. The worst that can happen is that we confirm everything, that things look like we thought, we measure the ages of stars and basically the theory was OK, because no one will fund another mission doing that. We have to go out and make sure to convince people doing dark matter etc. that stars were not understood in the right way. It changes our view on what physics is, and we may end up in the situation that people are much more willing to support us at the next step. But we have to understand first what these missions really can do. We promised to do asteroseismology but if you look on where we really changed the understanding of the evolution of the universe and so on, we haven’t gone where we promised yet, but we hope that space missions can do that. We have to make sure that the whole community can use all these space data. If we make another effort to spread all these data to students around the whole world, they will all learn the way seismologists study stars. Then we will have a much better chance to fund the next mission. Weiss: I think not every country is in the same situation. Where there is a space agency, there are usually two different budget items. Usually the astronomers don’t have direct access to space money and vice versa. It helps if you have a very successful satellite. Then you can go to the other agency and say, we have lots of data, lots of potential science, that the other agency has paid for, and now we need money to work on them. You can do that in countries where you have such a structure; not all have it. Baglin: I think there are lots of ideas that came out of this discussion. I would suggest that we continue along these lines to develop the future. It is probably best to gather the different ideas of the community, to compare them and to decide what to do. Thank you! Other types of pulsators Gerald Handler showing how his head feels at the end of the meeting ( = |m| = 16). Comm. in Asteroseismology Vol. 150, 2007 Indication of pulsation in young Brown Dwarfs M. Marconi,1 V. Ripepi,1 M. Oliviero,1 L. Errico,1 M. Magrı́,1 A. Vittone,1 F. Palla,2 S. Bernabei 3,4 1 INAF-OACapodimonte,Via Moiariello 16, 80131, Napoli, Italy INAF-OAAarcetri, Largo E. Fermi, 5, I-50125, Firenze, Italy 3 INAF-OABologna, Via Ranzani 1,40127 Bologna, Italy 4 Univ. de La Laguna, Avda. Astrofisico F. Sánchez sn, 30071 La Laguna, Spain 2 Abstract Preliminary results of a project devoted to the detection of pulsation in young brown dwarfs are presented. In particular, we show the light curve and frequency analysis for the first candidate, CFHT BD3 in the Taurus-Auriga association. Future plans are briefly discussed. Introduction New classes of pulsators have been recently discovered or predicted and could be confirmed and classified with the advent of space missions like COROT. As an example, Palla & Baraffe (2005, hereinafter PB05) have theoretically predicted the existence of pulsating young Brown Dwarfs (BDs) during the central deuterium burning phase, with typical time scales ranging from ∼1 h for 0.02 M to ∼ 5 h for 0.1 M . Furthermore, PB05 identify possible candidates for pulsational variability among known BDs in nearby star forming regions whose location in the HR diagram falls within or close to the instability strip. To test this suggestion, we have started a program dedicated to the observation of potentially interesting candidates. In particular, during winter 2005 we used the Asiago (1.8 m) and Loiano (1.5 m) telescopes to observe CFHT BD2 and CFHT BD3, two BDs in the Tau-Aur association that fall into the PB05 instability strip (see Fig. 1). Unfortunately, we were only able to observe for one night at each site (separated by 10 days), for a total of 7.8 h and 4.2 h of observing time in Asiago and Loiano, respectively. Results The observations have been carried out in the I band only, due to the faintness of the target stars in bluer filters. Concerning Asiago data, the photometric data of five sufficiently bright (∼ 0.5 − 1.5 mag brighter than the targets) and stable stars have been combined to obtain an artificial comparison star with a rms scatter of ∼ 2 mmag (see the left panels of Fig. 2). The time series for the target stars were calculated by adopting differential photometry with respect to the artificial comparison star. As a result, CFHT BD2 does not show significant light variations in the present data. Conversely, CFHT BD3 is more interesting. As shown in the upper-left panel of Fig. 2, the light curve is indicative of periodic variability. The periodogram analysis (see upper-right panel) yields f ∼ 5.0 ± 2.4 d−1 (period range 3 − 7 h), with an amplitude of 8 mmag and S/N ∼ 5. For comparison, we report in the lower-left and right panels of Fig. 2 the light curve and DFT of another star present in the field (named star #24) with a magnitude comparable to that of CFHT BD3. We see that the noise can hardly be responsible for the light variability displayed by CFHT BD3. As for the Loiano data, the poor length of the time series prevents us from obtaining reliable results. However, a Fourier analysis of the data on CFHT BD3 presents an indication of a marginally significant (S/N ∼ 3.6) periodicity on a time scale shorter than the Asiago observations, ∼15 d−1 (period ∼ 1.5 h). 378 Indication of pulsation in young Brown Dwarfs Figure 1: The location of CFHT BD2 and BD3 in the HRD. Triangles: data from Briceño et al. (2002). Circles: data from Grosso et al. (2007). Shaded region: predicted D-burning instability strip of PB05. Evolutionary tracks and isochrones are from Baraffe et al. (1998). Isoperiod curves (in hr) are also shown. Figure 2: From left, panel 1: Full and empty dots show the Asiago data for CHFT BD3 and for the artificial comparison star, respectively; the solid line is a fit to the data; panel 2: DFT for BD3; panels 3 and 4: as panels 1 and 2, respectively, but for star #24. Conclusions These preliminary data indicate that CFHT BD3 in Tau-Aur might be a periodic variable with a period in the range ∼3-7h. This interval is larger than the one expected from pulsation models by PB05, given the BD location in the HR diagram (i.e. ∼2 h, see Fig. 1). Considering the large uncertainty of the period determination, we must wait for more extended time series observations for a firm conclusion. In any case, only the detection of persistent periodic, or possibly multi-periodic, light variations with time scale of few hours in CFHT BD3 and similar candidates can offer the evidence that the observed variations can be ascribed to pulsation instead of other mechanisms (such as BD rotation, spot modulation) that have been invoked to explain fast variability observed in some BDs (e.g. Caballero et al. 2004). Acknowledgments. We thank the Asiago and Loiano Observatories for their help with the observations. Partial financial support was provided by PRIN-INAF 2005 under the project “Stellar clusters as probes of stellar formation and evolution” (P.I. Francesco Palla). References Baraffe I., Chabrier G., Allard F., Hauschildt P. H., 1998, A&A, 337, 403 Briceño C., Luhman K. L., Hartmann L., Stauffer J. R., Kirkpatrick J. D., 2002, ApJ, 580, 317 Caballero J. A., Béjar V. J. S., Rebolo R., Zapatero Osorio M. R., 2004, A&A, 424, 857 Grosso N., Briggs K. R., Güdel M., et al., 2007, A&A, in press Palla F., Baraffe I., 2005, A&A, 432, L57 Comm. in Asteroseismology Vol. 150, 2007 RR Lyrae stars: The changing light curve shape during the Blazhko cycle E. Guggenberger,1 K. Kolenberg 1,2 2 1 Institute of Astronomy, University of Vienna, 1180 Vienna, Austria Instituut voor Sterrenkunde, Katholieke Univ. Leuven, Celestijnenlaan 200 D, B-3001 Leuven, Belgium Abstract High-precision multisite photometry was used for a detailed investigation of the bump occurring before minimum light in the light curves of the two RRab Blazhko stars RR Lyr and SS For. For both stars, the phase of the bump was found to be variable with a period equal to the Blazhko period, with the bump occurring at an earlier phase around Blazhko minimum and at higher values during maximum. Target Stars For the analysis on the star SS For, we used mmag precision data from our campaigns in the years 2004 and 2005 as well as the best 311 data points from the All Sky Automated Survey, ASAS (Pojmanski 2002). Data from our campaign comprise a total of 1218 points gathered in 50 nights with a typical scatter of a few millimag per point, while the ASAS data show a typical scatter of 0.03 mag. For more details on the data set see Kolenberg et al. (2007). Using a Blazhko period of about 34.7 days we created 20 overlapping phase bins of 0.1 of the Blazhko period. For each of those the phase of the bump maximum was measured and plotted against the Blazhko phase. Both phase and amplitude of the bump were found to be variable. The first question arising is whether this variability of bump phase is a common phenomenon among (Blazhko) RR Lyr stars. Therefore we performed the same test on a similar data set of RR Lyr (Kolenberg et al. 2006). 14702 data points gathered in 98 nights over a period of 421 days were used for the investigation. With a scatter of 0.01–0.02 mag the data were less accurate than in the case of SS For. The Blazhko period found from the data set was 39 days. The results concerning the bump turned out to be comparable. Results • For both stars the phase of the bump maximum is variable with a period identical to the Blazhko period • For both stars the smallest value of the bump phase is reached near Blazhko minimum, while the largest value is reached near maximum pulsation amplitude. • For SS For the phase of the bump varies between 0.65 and 0.85 (i.e. 20 per cent of the pulsation period!), for RR Lyr between 0.67 and 0.75 with the total light curve maximum set to zero phase. • For SS For the phase variation is non-sinusoidal and is characterized by a slow progress to lower phases (’to the left’) and a quicker motion to higher phases after the Blazhko minimum. 380 The changing light curve shape during the Blazhko cycle • The bump is stronger in the B filter than it is in V, as it is clearly visible in a (B-V) diagram. • In SS For the bump is most distinct during Blazhko minimum and almost vanishes around Blazhko maximum. For RR Lyr we cannot find any noteworthy dependence of the bump strength on the Blazhko phase. Conclusions In both examined stars, the bump moves back and forth in the phase diagram during a Blazhko cycle. Models for Blazhko RR Lyrae stars should therefore allow the bump phase to be variable. To clarify the bump behaviour, high-resolution spectroscopic data covering the bump at different Blazhko phases are needed. It will be necessary to investigate a larger sample of Blazhko and non-Blazhko stars to find out whether a variable bump is a common phenomenon. Future studies will also focus on the relation between the Blazhko phase and the occurrence of the hump in the ascending branch of the light curve. Acknowledgments. Part of this investigation has been supported by the Austrian Fonds zur Förderung der wissenschaftlichen Forschung, project number P17097-N02. References Kolenberg K., Smith H. A., Gazeas K. D., et al., 2006, A&A, 459, 577 Kolenberg K., Guggenberger E., Medupe R., et al., 2007, MNRAS, in press Pojmanski G., 2002, Acta Astron., 50, 177 Comm. in Asteroseismology Vol. 150, 2007 Photometric campaigns for the Blazhko Project K. Kolenberg,1,2 E. Guggenberger 1 and the Blazhko collaboration3 2 1 Institute of Astronomy, University of Vienna, 1180 Vienna, Austria Instituut voor Sterrenkunde, Celestijnenlaan 200D, 3001 Heverlee, Belgium A large fraction of the RR Lyrae stars are modulated on time scales of typically tens to hundreds of days. Though this phenomenon, denoted the Blazhko effect, has been discovered a century ago (Blazhko 1907), there is still no consensus on its cause. The Blazhko Project is an international collaboration focused on understanding the modulation. We discuss some results of the photometric multi-site campaigns so far, and their implications for the models proposed to explain the Blazhko effect. Figure 1: Light curves of three Blazhko stars monitored by the Blazhko Project, folded with their respective pulsation periods Since the study of Blazhko phenomenon is still in an experimental phase, the observational approach seems to be the most effective way to cast more light on it. Simultaneous photometric and high-resolution spectroscopic data combined with mode identification techniques devised for RR Lyrae stars are likely to give clues. This is the approach adopted by the Blazhko Project. Our photometric data were recorded with photomultipliers and CCD cameras using 15 different telescopes in the range of 0.25 to 1.0 m and have a precision ranging from 2 up to 15 mmag. A dozen selected targets have been observed so far from both hemispheres yielding over 1500 hours of photometric data. For instance, a combined photometric (Kolenberg et al. 2006) and spectroscopic campaign was devoted to RR Lyr in 2004. We also carried out detailed observations and analyses of southern field Blazhko targets (see also Fig. 1). Multi-site campaigns involving observatories at complementary longitudes allow for a quasi-continuous coverage of the light variations. It is crucial to sufficiently cover both the pulsation cycle (typically around half a day) and the longer Blazhko cycle. More details can be found on the dedicated Blazhko Project website (http://www.univie.ac.at/tops/blazhko/). Some implications of our photometric studies are summarized below. Changing Blazhko periods, as observed in several stars (e.g., Kolenberg et al. 2006, LaCluyzé et al. 2004) challenge the models linking the modulation period directly to the rotation of the star. Features in the light curve such as the hump and bump (Guggenberger 3 The collaborators who contributed to the described photometric data (in alphabetical order): Ozan Aksu, Berahitdin Albayrak, Paul Beck, Michel Breger, Asli Elmaslı, Antonio Garrigós Sánchez, Kosmas Gazeas, Dieter Husar, Patricia Lampens, Patrick Lenz, Jan Lub, Andreas Leitner, Thebe Medupe, Tim Mokgwetsi, Boitumelo Ngwato, Ibrahim Ozavcı, Holger Pikall, Johannes Puschnig, Piet Reegen, C. W. Robertson, Lukas Schmitzberger, Selim O. Selam, Bob Shobbrook, Horace Smith, Nermin Deniz Ulus, Paul Van Cauteren 382 Photometric campaigns for the Blazhko Project & Kolenberg 2006) show variability in phase with the Blazhko period. Nonlinear convective pulsation models for RR Lyrae stars (Feuchtinger 1999) involving only radial modes cannot easily reproduce the observed Fourier parameters at different Blazhko phases (Pikall, private communication). The nonlinear behaviour of the radial mode, especially strong in RRab stars, complicates an identification of the nonradial modes supposed to be responsible for the Blazhko effect. Whereas high-resolution spectra provide more information on the pulsation modes (see, e.g., Kolenberg 2002, for a spectroscopic mode identification), photometric data are easier to obtain in sufficient amounts. Photometric mode identification in RR Lyrae stars is hampered by the incomplete knowledge of the phase-amplitude relation of the temperature and displacement variations, and its applicability is still being tested. Data obtained in different photometric passbands are crucial to increase the discriminating power. Acknowledgments. Part of this investigation has been supported by the Austrian Research Fund, project number P17097-N02. References Blazhko S. N., 1907, Astron. Nachr., 175, 325 Feuchtinger M. U., 1999, A&A, 351, 103 Guggenberger E., Kolenberg K., 2006, Comm. Asteroseis., 148, 21 Kolenberg K., 2002, PhD Thesis, University of Leuven Kolenberg K., Smith H. A., Gazeas K. D., et al., 2006, A&A, 459, 577 LaCluyzé A., Smith H. A., Gill E.-M., et al., 2004, AJ, 127, 1653 Patrick Lenz and Katrien Kolenberg in the final stages – of preparing their posters. Comm. in Asteroseismology Vol. 150, 2007 RR Lyrae stars in M4 G. Kopacki,1 S. Frandsen 2 2 1 Institute of Astronomy, University of Wroclaw, Poland; [email protected] Department of Physics and Astronomy, University of Aarhus, Denmark; [email protected] Abstract A large CCD photometry observing campaign in search of p mode oscillations in K giants (see Frandsen et al., these proceedings) has produced very high quality time series data for the RR Lyrae stars and other variables in the globular cluster M4. New variables have been found and the known RR Lyrae stars have been better characterized. Non-radial modes in globular cluster RR Lyrae stars Until now only ten RR Lyrae stars with non-radial modes detected from the Fourier analysis were known in globular clusters (Clement and Rowe 2000, Kopacki et al. 2003). All of them are of the RRc type, which is not surprising since these stars have shorter pulsation and modulation periods and are much easier to discover. Recently, however, Benkő et al. (2006) determined through Fourier analysis modulation periods for 13 RRab stars in M3. Non-radial modes in pulsators in M4 Using our data we performed a frequency analysis of the observed RR Lyrae stars. We find non-radial modes both in RRc and RRab variables. As expected, these modes appear to be components of a doublet or triplet structure. It should be noted that the equidistant triplet structure in the power spectrum may result from modulation of the purely radial mode only. In RRab stars we detect strong interaction between radial and non-radial pulsations evidenced by the occurrence of many combination frequencies. Interestingly, all Blazhko RRc stars in our sample are located in the colour – magnitude diagram (see Fig. 1) at the blue edge of the instability strip only. In the period – amplitude diagram, given in Fig. 2, these stars also occupy a distinctive position being the stars with the shortest periods and lowest amplitudes among all RR Lyrae stars in M4. References Benkő J., Bakos G., Nuspl J., 2006, MNRAS, 372, 1657 Clement C. M., Rowe J., 2000, AJ, 120, 2579 Kopacki G., Kolaczkowski Z., Pigulski A., 2003, A&A, 398, 541 384 RR Lyrae stars in M4 13.0 V [mag] 13.2 13.4 13.6 13.8 0.2 0.3 0.4 0.5 0.6 0.7 (V-R) [mag] Figure 1: Horizontal branch of M4 in the V vs. (V − R) colour-magnitude diagram. RRab stars are represented by filled diamonds, RRc stars with filled circles. Variables exhibiting the Blazhko effect are indicated with open diamond symbols. 1.4 V Range [mag] 1.2 1.0 0.8 0.6 0.4 0.2 0.0 -0.6 -0.5 -0.4 -0.3 -0.2 -0.1 log ( Period / d ) Figure 2: V range of variability as a function of period for RR Lyrae stars in M4. The meaning of symbols is the same as in Fig. 1. For comparison, the RR Lyrae stars of M53 are shown with squares. Comm. in Asteroseismology Vol. 150, 2007 Physical parameter determination of seven RR Lyrae stars in Bootes J. H. Peña,1 A. Arellano,1 J. P. Sareyan,2 R. Peña,1 M. Alvarez 1 1 Instituto de Astronomı́a, UNAM, México D.F., México 2 Observatoire de la Cote d’Azur, France Abstract uvby β photoelectric photometry of the RR Lyrae stars AE, RS, ST, TV, TW, UU, and XX Bootis has been acquired in order to determine the physical parameters of the stars. We used the correlation between the Fourier parameters derived from the light curves and the physical parameters such as the absolute magnitude Mv , intrinsic colour (B − V )0 and metal abundance [Fe/H]. Once reddening has been determined, unreddened indices are obtained and Teff and log g followed along the cycle, using a comparison with the theoretical models given for our determined metallicity. Analysis Our knowledge on stellar evolution comes from a direct comparison between the observational determination of the star’s basic physical parameters (i.e. Teff , g , luminosity, metallicity and eventual pulsation periods) and models. In the case of the RR Lyrae variables, some of the goals can be attained from the relationships that have been developed by Kovács & Jurcsik in several papers (Jurcsik & Kovács 1996, Kovács & Jurcsik 1996, 1997, Jurcsik 1998). As Kovács & Walker (2001) state in their review paper, this method is empirical and based on the assumption that the period and the shape of the light curve are directly correlated with the physical parameters. Since we have obtained simultaneous uvby β photoelectric photometry, the precise variation of these parameters along the cycle can be determined for each star. The observations were all taken at the Observatorio Astronómico Nacional, Mexico. The 1.5m telescope, to which a spectrophotometer was attached, was used in all seasons. The physical parameters can be determined with the ad-hoc models. From the data of several photometric campaigns we obtained uvby β photometry, which was used to calculate the physical parameters of each star. The fit with our observations has been considered as reasonable when the rms error is the same order of magnitude as the detected amplitude. Reddening has been estimated by considering different objects in the same direction. Once reddening has been fixed, the unreddened Strömgren indices give the variation along the cycle of the effective temperature and surface gravity. These results are summarized in Table 1 which reports the physical parameters. The last two columns list the number of data points and the standard deviation of the residuals. Acknowledgments. This paper was partially supported by Papiit IN108106. This article has made use of the SIMBAD database operated at CDS, Strasbourg, France and ADS, NASA Astrophysics Data Systems hosted by Harvard-Smithsonian Center for Astrophysics. 386 Physical parameter determination of seven RR Lyrae stars in Bootes Table 1: Physical parameters from the calibrations for studied RR Lyrae stars ID RS ST TW UU XX AE TV [Fe/H] -0.281 -1.306 -1.227 -0.487 -0.282 -1.293 -1.877 Teff (K ) 6889 6444 6569 6795 6649 7370 7200 Mv 1.00 0.71 0.82 0.88 0.89 0.61 0.34 log L/L 1.48 1.62 1.58 1.54 1.53 1.68 1.79 log P -.423 -.206 -.274 -.340 -.236 -.502 -.505 Type AB AB AB AB AB C C data points 43 39 33 25 34 138 500 References Jurcsik J., 1998, A&A, 333, 571 Jurcsik J., Kovács G., 1996, A&A, 312, 111 Kovács G., Jurcsik J., 1996, ApJ, 466, L17 Kovács G., Jurcsik J., 1997, A&A, 322, 218 Kovács G., Walker A. R., 2001, A&A, 371, 579 José Peña and Margit Paparó in intensive discussions. σ 0.057 0.088 0.124 0.084 0.055 0.018 0.014 Comm. in Asteroseismology Vol. 150, 2007 List of participants Conny Aerts, Katholieke Universiteit Leuven, Belgium, [email protected] Amir Ahmad, Armagh Observatory, Northern Ireland, [email protected] Pedro Amado, Instituto de Astrofisica de Andalucia - CSIC, Spain, [email protected] Victoria Antoci, University of Vienna, Austria, [email protected] Torben Arentoft, University of Aarhus, Denmark, [email protected] Annie Baglin, Observatoire de Paris, France, [email protected] Andrzej Baran, Mt. Suhora Observatory, Poland, [email protected] Michael Bazot, University of Aarhus, Denmark, [email protected] Paul Beck, University of Vienna, Austria, [email protected] Tim Bedding, University of Sydney, Australia, [email protected] Zsofia Bognar, Konkoly Observatory, Hungary, [email protected] Pierre-Olivier Bourge, Université de Liège, Belgium, [email protected] Michel Breger, University of Vienna, Austria, [email protected] Runa Briguglio, University of Rome La Sapienza, Italy, [email protected] Maryline Briquet, Katholieke Universiteit Leuven, Belgium, [email protected] Hans Bruntt, University of Sydney, Australia, [email protected] Stéphane Charpinet, Observatoire Midi-Pyrénées, France, [email protected] Jørgen Christensen-Dalsgaard, University of Aarhus, Denmark, [email protected] Victor Costa, Instituto de Astrofisica de Andalucia - CSIC, Spain, [email protected] Orlagh Creevey, High Altitude Observatory, USA, [email protected] Margarida Cunha, Universidade do Porto, Portugal, [email protected] Jan Cuypers, Royal Observatory of Belgium, [email protected] Jadwiga Daszyńska-Daszkiewicz, Wroclaw University, Poland, [email protected] Peter De Cat, Royal Observatory of Belgium, [email protected] Aliz Derekas, University of Sydney, Australia, [email protected] Joris De Ridder, Katholieke Universiteit Leuven, Belgium, [email protected] Maarten Desmet, Katholieke Universiteit Leuven, Belgium, [email protected] Robert Deupree, Saint Mary’s University, Canada, [email protected] Tatyana Dorokhova, Odessa National University, Ukraine, [email protected] Marc-Antoine Dupret, LESIA, Observatoire de Paris, France, [email protected] Wojtek Dziembowski, Warsaw University Observatory, Poland, [email protected] Joe Eggen, Missouri State University, USA, [email protected] Eric Fossat, Universite de Nice, France, [email protected] Søren Frandsen, University of Aarhus, Denmark, [email protected] Lars Freyhammer, University of Central Lancashire, UK, [email protected] Rafael Garrido, Instituto de Astrofisica de Andalucia - CSIC, Spain, [email protected] Mélanie Godart, Université de Liège, Belgium, [email protected] Jose Miguel Gonzalez Perez, Instituto de Astrofisica de Canarias, Spain, [email protected] Douglas Gough, University of Cambridge, UK, [email protected] Frank Grundahl, University of Aarhus, Denmark, [email protected] Elisabeth Guggenberger, University of Vienna, Austria, [email protected] Gerald Handler, University of Vienna, Austria, [email protected] Artie Hatzes, Thüringer Landessternwarte, Germany, [email protected] 388 List of participants Günter Houdek, University of Cambridge, UK, [email protected] Santosh Joshi, Inter-Univ. Centre for Astronomy & Astrophysics, India, [email protected] Alexander Kaiser, University of Vienna, Austria, [email protected] Christoffer Karoff, University of Aarhus, Denmark, karoff@phys.au.dk Steve Kawaler, Iowa State University, USA, [email protected] Anthony Kaye, George Mason University, USA, [email protected] S. O. Kepler, Universidade Federal do Rio Grande do Sul, Brasil, [email protected] Dave Kilkenny, South African Astronomical Observatory, South Africa, [email protected] Seung-Lee Kim, Korea Astronomy and Space Science Institute, Korea (South), [email protected] Laszlo Kiss, University of Sydney, Australia, [email protected] Hans Kjeldsen, University of Aarhus, Denmark, [email protected] Oleg Kochukhov, Uppsala University, Sweden, [email protected] Katrien Kolenberg, University of Vienna, Austria, [email protected] Geza Kovacs, Konkoly Observatory, Hungary, [email protected] Igor Kudzej, Vihorlat Observatory, Slovakia, [email protected] Friedrich Kupka, Max-Planck-Institute for Astrophysics, Germany, [email protected] Don Kurtz, University of Central Lancashire, UK, [email protected] Holger Lehmann, Thüringer Landessternwarte, Germany, [email protected] Patrick Lenz, University of Vienna, Austria, [email protected] Pilar López de Coca, Instituto de Astrofisica de Andalucia - CSIC, Spain, [email protected] Denise Lorenz, University of Vienna, Austria, [email protected] Catherine Lovekin, Saint Mary’s University, Canada, [email protected] Theresa Lüftinger, University of Vienna, Austria, [email protected] Marcella Marconi, Osservatorio Astronomico di Capodimonte, Italy, [email protected] Susana Martin-Ruiz, Instituto de Astrofisica de Andalucia - CSIC, Spain, [email protected] Philippe Mathias, Observatoire de la Cote d’Azur, France, [email protected] Jaymie Matthews, University of British Columbia, Canada, [email protected] Travis Metcalfe, High Altitude Observatory, USA, [email protected] Gabriela Michalska, Wroclaw University, Poland, [email protected] Eric Michel, Observatoire de Paris, France, [email protected] Joanna Molenda, Wroclaw University, Poland, [email protected] Michael Montgomery, University of Texas, USA, [email protected] Thierry Morel, Katholieke Universiteit Leuven, Belgium, [email protected] Pawel Moskalik, Nicolaus Copernicus Astronomical Center, Poland, [email protected] Benoı̂t Mosser, Observatoire de Paris, France, [email protected] Andres Moya, Instituto de Astrofisica de Andalucia - CSIC, Spain, [email protected] Anjum Mukadam, University of Washington, USA, [email protected] Artur Narwid, Wroclaw University, Poland, [email protected] Atsuko Nitta, Subaru Telescope, USA, [email protected] Raquel Oreiro Rey, Instituto de Astrofisica de Canarias, Spain, [email protected] Roy Østensen, Katholieke Universiteit Leuven, Belgium, [email protected] Alexey Pamyatnykh, Nicolaus Copernicus Astronomical Center, Poland, [email protected] Margit Paparó, Konkoly Observatory, Hungary, [email protected] Ernst Paunzen, University of Vienna, Austria, [email protected] Jose Peña, Instituto de Astronomia, UNAM, Mexico, [email protected] Andrzej Pigulski, Astronomical Institute, Wroclaw Univ., Poland, [email protected] Karen Pollard, University of Canterbury, New Zealand, [email protected] Blazej Popielski, Warsaw University Observatory, Poland, [email protected] Ennio Poretti, INAF - Osservatorio Astronomico Brera, Italy, [email protected] List of participants 389 Judi Provencal, University of Delaware, USA, [email protected] Janine Provost, Observatoire de la Cote d’Azur, France, [email protected] Pierre-Olivier Quirion, University of Aarhus, Denmark, [email protected] Suzanna Randall, European Southern Observatory, Germany, [email protected] Mike Reed, Missouri State University, USA, [email protected] Cristina Rodrı́guez López, Instituto de Astrofisica de Andalucia - CSIC, Spain, [email protected] Angel Rolland, Instituto de Astrofisica de Andalucia - CSIC, Spain, [email protected] Markus Roth, Max-Planck-Institut für Sonnensystemforschung, Germany, [email protected] Ian Roxburgh, University of London, UK, [email protected] Alessandra Ruoppo, Osservatorio Astronomico di Capodimonte, Italy, [email protected] Tanya Ryabchikova, Institute of Astronomy RAS, Russia, [email protected] Mikhail Sachkov, Institute of Astronomy RAS, Russia, [email protected] Sophie Saesen, Katholieke Universiteit Leuven, Belgium, [email protected] Hideyuki Saio, Tohoku University, Japan, [email protected] Karel Schrijver, Lockheed Martin Advanced Technology Center, USA Sonja Schuh, Universität Göttingen, Germany, [email protected] Harry Shipman, University of Delaware, USA, [email protected] Radoslaw Smolec, Nicolaus Copernicus Astronomical Center, Poland, [email protected] Joana Claudia Sousa, Universidade do Porto, Portugal, [email protected] Dennis Stello, University of Sydney, Australia, [email protected] Chris Sterken, University of Brussels VUB-WE-OBSS, Belgium, [email protected] Juan Carlos Suárez, Instituto de Astrofisica de Andalucia - CSIC, Spain, [email protected] John Telting, Nordic Optical Telescope, Spain, [email protected] Alfred Tillich, Universität Erlangen, Germany, [email protected] Jean-Claude Valtier, Observatoire de la Cote d’Azur, France, [email protected] Maja Vučković, Katholieke Universiteit Leuven, Belgium, [email protected] Werner Weiss, University of Vienna, Austria, [email protected] Don Winget, University of Texas, USA, [email protected] Duncan Wright, University of Canterbury, New Zealand, [email protected] Wolfgang Zima, Katholieke Universiteit Leuven, Belgium, [email protected] Konstanze Zwintz, University of Vienna, Austria, [email protected] 390 List of participants Denise Lorenz says goodbye after three hard days of work.

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