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Transcript
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
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0
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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
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50
0
50
6 7 6.7
67 7 .8
67 7 .9
68 6 .8 0
69 2 .8
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6 93 .0
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6 9 4.0 7 00 .0
7 0 3.8 70 6.7
7 06 .8
7 06 .9
-50
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0
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7 09 .7
70 9 .8
70 9.9
7 10 .0 7 10 .7
71 0 .8
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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
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0
0
50
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7 19 .8
71 9 .9
72 0 .0
7 20 .1
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72 1.1
7 21 .2
72 1 .7
7 2 1.8
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72 2 .7
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72 3 .0
-50
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7 23 .1
7 23 .2
72 3 .8
72 3.9
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7 25 .8
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7 2 6.8
7 26 .9
7 27 .7
7 27 .8
72 7.9
-1 00
-5 0
0
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7 29 .7
7 2 9.8
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7 30 .0
7 30 .7
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73 0 .9
7 3 3.7
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7 33 .9
7 34 .7
7 34 .8
73 4.9
-1 00
-5 0
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50
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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
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0
-50
50
6y [mmag]
0
50
740.7
740.8
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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
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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
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Lüftinger T., Kochukhov O., Ryabchikova T., Weiss W. W., Ilyin I., 2007, these proceedings
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Ryabchikova T., Piskunov N., Kochukhov O., et al., 2002, A&A, 384, 545
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Ryabchikova T., Mashonkina L., Ryabtsev A., Kildiyarova R., Khristoforova M., 2007c, these proceedings
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Saio H., 2005, MNRAS, 360, 1022
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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. R., 2000, A&A, 356, 218
Bigot L., Dziembowski W. A., 2001, A&A, 391, 235
Cunha M. S., Gough D. O., 2000, MNRAS, 319, 1020
Cunha M. S., 2002, MNRAS, 333, 47
Cunha M. S., 2003, in Thompson M. J., Christensen-Dalsgaard J., eds, Stellar Astrophysical Fluid
Dynamics. Cambridge Univ. Press, UK, p. 51
Cunha M. S., 2005, J. Astrophys. Astron., 26, 213
Cunha M. S., Theado S., Vauclair S., 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. 359
Cunha M. S., 2006, MNRAS, 365, 153
Dziembowski W. A., Goode P. R., 1996, ApJ, 458, 33
Elkin V. G., Kurtz D. W., Mathys G., et al., 2005, MNRAS, 358, 665
Gough D. O., 2005, in Boweler S., The Roger Tayler Memorial lectures, Astronomy & Geophysics, special
issue, Royal Astronomical Society, p. 16
Hubrig S., Szeifert T., Schöller M., Mathys G., Kurtz D. 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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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. Comparison with the observed amplitude ratios and phase differences strongly
constrains these models in the convective envelope.
Acknowledgments. A. M. and J. M. acknowledge financial support from the Prodex-ESA
Contract Prodex 8 COROT (C90199).
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104
Theoretical aspects of g-mode pulsations in γ Doradus stars
DISCUSSION
Roxburgh: is there any way of trying to test your time-dependent convection model for
instance by comparing them to numerical simulations of convection?
Dupret: at this time, I think it would be difficult. We would have to isolate the high-order
gravity modes in the numerical simulations, which is a problem. I agree it would be interesting
but as far as I know, it hasn’t even been tried yet.
Marc-Antoine Dupret thoroughly involved in an entertaining discussion.
M.-A. 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.
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Bazot M., Bouchy F., Kjeldsen H., et al., 2007, A&A, submitted
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Bedding T. R., Kjeldsen H., 2006, Mem. Soc. Astron. Ital., 77, 384
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Bouchy F., Carrier F., 2002, A&A, 390, 205
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112
Observations of solar-like oscillations
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Carrier F., Bourban G., 2003, A&A, 406, L23
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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
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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. The lower panel of Fig. 5 displays the individual oscillatory
contributions from the two ionization stages of helium and from the sharp transition from
radiative to convective heat transport at the base of the convection zone.
Such seismic signatures complicate the measurement of the small frequency separation
δνn, which, in general, is used for calibrating stellar models to obtain their ages and initial
helium abundances. There is good reason to expect that by considering this oscillatory
signature in the calibration process a substantial improvement will be made for determining
stellar ages (e.g., Gough 2001).
Acknowledgments. I am grateful to Douglas Gough for many helpful discussions, and to
Hans-Günter Ludwig and Regner Trampedach for providing their results for Fig. 2. Support
by the Particle Physics and Astronomy Research Council is gratefully acknowledged.
G. Houdek
129
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Basu S., Mazumdar A., Antia H. M., Demarque P., 2004, MNRAS, 350, 277
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finding. ESA SP-485, Noordwijk, p. 65
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SP-624, Noordwijk, p. 28.1
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Dordrecht, p. 317
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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
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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.
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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.
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Observational Asteroseismology of slowly pulsating B stars
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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
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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
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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. Accretion raises the external
temperature distribution and changes external layers composition, but the underlying structure
should be similar to single stars. The models have been calculated by Arras, Townsley &
Bildsten (2006).
Acknowledgments. We thank HELAS for partial support that made our participation in
the conference possible.
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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. The National Center
for Atmospheric Research is a federally funded research and development center sponsored
by the U.S. National Science Foundation.
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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.
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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
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Fontaine G., Brassard P., Charpinet S., et al., 2003, ApJ, 597, 518
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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
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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).
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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
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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.
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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.
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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:
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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: [email protected]ffield.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]f.it
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.
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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.
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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
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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
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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
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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.
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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.
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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
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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.
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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
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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
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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.
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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!
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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.
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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).
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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.
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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