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Magnetic fields and mass loss in massive stars Cover illustration by Annesas Appel Magnetic fields and mass loss in massive stars Magneetvelden en massaverlies van zware sterren Academisch Proefschrift ter verkrijging van de graad van doctor aan de Universiteit van Amsterdam, op gezag van de Rector Magnificus prof. mr. P. F. van der Heijden, ten overstaan van een door het college voor promoties ingestelde commissie, in het openbaar te verdedigen in de Aula der Universiteit op woensdag 7 februari 2007, te 14:00 uur door Roald Sander Schnerr geboren te Amsterdam P ROMOTIECOMMISSIE P ROMOTOR prof. dr. H. F. Henrichs O VERIGE LEDEN prof. dr. E. P. J. van den Heuvel prof. dr. L. Kaper prof. dr. M. van der Klis dr. A. de Koter prof. dr. F. Leone prof. dr. S. P. Owocki prof. dr. H. C. Spruit dr. E. Verdugo Faculteit der Natuurwetenschappen, Wiskunde en Informatica ISBN-10: 90-6464-079-3 ISBN-13: 978-90-6464-079-7 Now this is not the end. It is not even the beginning of the end. But it is, perhaps, the end of the beginning. Winston Churchill C ONTENTS 1 2 3 Introduction 1.1 Magnetic fields . . . . . . . . . . . . . . . . . . . . . 1.2 Massive stars . . . . . . . . . . . . . . . . . . . . . . . 1.3 Magnetic fields in massive stars . . . . . . . . . . . . 1.3.1 Indicators of the presence of magnetic fields 1.4 Notes on polarisation . . . . . . . . . . . . . . . . . . 1.4.1 A photon as a wave . . . . . . . . . . . . . . 1.4.2 The Stokes parameters I, Q, U and V . . . . 1.4.3 Zeeman splitting of spectral lines . . . . . . . 1.4.4 The Least-Squares Deconvolution method . 1.4.5 The design of spectropolarimeters . . . . . . 1.5 This thesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1 2 2 3 8 8 9 10 11 12 13 On the reliability of stellar magnetic field measurements based on the Least Squares Deconvolution method 2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2 Synthetic spectra . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3 The classical method to measure Beff . . . . . . . . . . . . . . . . . . . . 2.3.1 Recovering the geometry . . . . . . . . . . . . . . . . . . . . . . 2.4 The Least-Squares Deconvolution method . . . . . . . . . . . . . . . . . 2.4.1 Basics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.4.2 Underlying assumptions . . . . . . . . . . . . . . . . . . . . . . . 2.4.3 Zeeman patterns . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.4.4 Continuum determination . . . . . . . . . . . . . . . . . . . . . . 2.5 Measurements of Beff with the LSD method . . . . . . . . . . . . . . . . 2.6 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 20 21 21 22 24 24 25 25 25 25 28 Discovery of the magnetic field in the pulsating B star β Cephei 3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2 Experimental setup and observations . . . . . . . . . . . . . 3.3 Data reduction and results . . . . . . . . . . . . . . . . . . . . 3.3.1 Correction for fringes . . . . . . . . . . . . . . . . . . 33 34 36 40 40 i . . . . . . . . . . . . . . . . . . . . . . . . C ONTENTS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41 41 44 45 45 49 52 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59 60 61 61 62 62 63 64 Numerical simulations of UV wind-line variability in magnetic B stars: β Cephei 5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.2 The UV behaviour and magnetic field of β Cep . . . . . . . . . . . . . 5.3 Line profile calculations using SEI . . . . . . . . . . . . . . . . . . . . 5.3.1 Solving the transfer equation in the comoving frame . . . . . 5.4 A phenomenological model . . . . . . . . . . . . . . . . . . . . . . . . 5.5 2D-MHD simulations . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.5.1 Evolution of the simulations . . . . . . . . . . . . . . . . . . . 5.5.2 Calculating line profiles from 2D-MHD models . . . . . . . . 5.5.3 Understanding the line profiles . . . . . . . . . . . . . . . . . . 5.6 An X-ray ring model . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.7 Conclusions and discussion . . . . . . . . . . . . . . . . . . . . . . . . Appendix A: X-ray emission from a ring . . . . . . . . . . . . . . . . . . . . Appendix B: X-ray variability due to star occultation . . . . . . . . . . . . . . . . . . . . . . . . . . 67 68 69 70 72 73 75 76 78 81 81 83 84 85 . . . . . . . . . . 89 90 91 91 92 95 97 97 98 99 101 3.4 3.5 4 5 6 3.3.2 Effect of the spectral line list . . . . . . 3.3.3 Limits of integration . . . . . . . . . . Period analysis . . . . . . . . . . . . . . . . . 3.4.1 UV stellar wind period . . . . . . . . . 3.4.2 Magnetic properties . . . . . . . . . . 3.4.3 Pulsation period and system velocity Conclusions and discussion . . . . . . . . . . On the Hα emission from the β Cephei system 4.1 Introduction . . . . . . . . . . . . . . . . . . 4.1.1 The binary components . . . . . . . 4.2 Observations and data reduction . . . . . . 4.3 Results . . . . . . . . . . . . . . . . . . . . . 4.3.1 The source of the Hα emission . . . 4.3.2 The spectra of the individual stars . 4.4 Conclusions and discussion . . . . . . . . . . . . . . . . Attempts to measure the magnetic field of the pulsating B star ν Eridani 6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.2 Observations and data analysis . . . . . . . . . . . . . . . . . . . . . . 6.2.1 IUE observations . . . . . . . . . . . . . . . . . . . . . . . . . . 6.2.2 Spectropolarimetry . . . . . . . . . . . . . . . . . . . . . . . . . 6.2.3 Modeling the Stokes V and N profiles . . . . . . . . . . . . . . 6.3 Results and discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.3.1 UV variability . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.3.2 Magnetic field measurements . . . . . . . . . . . . . . . . . . . 6.3.3 Constraining the magnetic field . . . . . . . . . . . . . . . . . . 6.4 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ii C ONTENTS 7 8 9 Magnetic field measurements of OB-type stars 7.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . 7.2 Indirect magnetic-field indicators and target selection 7.2.1 Indirect indicators . . . . . . . . . . . . . . . . 7.2.2 Target selection . . . . . . . . . . . . . . . . . . 7.3 Observations & data reduction . . . . . . . . . . . . . 7.3.1 Determining the spectral properties . . . . . . 7.3.2 Measuring the effective magnetic fields . . . . 7.4 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.4.1 The magnetic calibrators . . . . . . . . . . . . . 7.4.2 Magnetic field measurements . . . . . . . . . . 7.4.3 Radial velocities and pulsations . . . . . . . . 7.5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105 106 107 109 116 119 119 120 121 121 122 126 126 Magnetic field measurements of O stars with VLT/FORS1 8.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . 8.2 Observations & Method . . . . . . . . . . . . . . . . . 8.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.4 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137 138 139 139 141 Radio observations of candidate magnetic O stars 9.1 Introduction . . . . . . . . . . . . . . . . . . . . 9.2 Observations & data reduction . . . . . . . . . 9.2.1 Distances and mass-loss rates . . . . . . 9.3 Results . . . . . . . . . . . . . . . . . . . . . . . 9.3.1 ξ Per . . . . . . . . . . . . . . . . . . . . 9.3.2 α Cam . . . . . . . . . . . . . . . . . . . 9.3.3 15 Mon . . . . . . . . . . . . . . . . . . . 9.3.4 λ Cep . . . . . . . . . . . . . . . . . . . . 9.3.5 10 Lac . . . . . . . . . . . . . . . . . . . 9.4 The effects of clumping in stellar winds . . . . 9.5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 147 148 149 150 150 151 152 153 153 153 153 154 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Nederlandse Samenvatting 159 English Summary 165 Dankwoord 169 Publication list 171 iii C ONTENTS iv C HAPTER 1 I NTRODUCTION 1.1 Magnetic fields Within many astrophysical contexts, magnetic fields have been found to play a role. Over the last decades, fields have been discovered in all stages of stellar evolution and on scales from single stars to whole galaxies. From the µG to mG fields in galaxies (e.g. Beck et al. 1996) and star forming molecular clouds (Crutcher 1999), to 10 1 – 104 G fields in planets and stars, and to 106 –1015 G fields in white dwarfs and neutron stars (see, e.g., Wickramasinghe & Ferrario 2000; Manchester 2004). Star forming molecular clouds have magnetic fields that are likely important in the formation process (Crutcher 2005). The young, low-mass T Tauri stars are observed to have magnetic fields that guide accreting material from the inner part of the accretion disk to the magnetic poles (e.g Valenti & Johns-Krull 2004), and recently several of the more massive Herbig Ae/Be stars were also found to posses magnetic fields (Hubrig et al. 2004; Wade et al. 2005; Hubrig et al. 2006c,b; Catala et al. 2006). On the main sequence, magnetic fields are frequently found in late-type stars, which are thought to have dynamo generated fields, and in the chemically peculiar Ap/Bp stars. The chemical peculiarities in these stars are related to their strong magnetic fields. Only recently magnetic fields have been found in the more massive O and early B-type stars (see Section 1.3). At all scales the magnetic fields are thought to be either generated by dynamo processes, or to be of a fossil origin. The origin of the magnetic fields on the largest scales, scales of galaxies and larger, is a fundamental cosmological question (see, e.g., Vallée 2004; Giovannini 2004). The magnetic fields in the Ap/Bp stars of several hundred G to tens of kG are likely of a fossil origin. The field strengths show no correlation with the stellar rotation periods, which would be expected in the case of dynamo generated fields. Recently, a stable magnetic field configuration for these stars has been found using numerical simulations (Braithwaite & Spruit 2004; Braithwaite & Nordlund 2006). Previously, the lack of a known stable configuration was a strong argument against the fossil field theory. It has also been proposed that the fields in the Ap/Bp stars are the origin of those in the white dwarfs (Wickramasinghe & Ferrario 2005) and that the magnetic fields found in neutron stars are related to the 1 C HAPTER 1 more massive counterparts of the Ap/Bp stars such as θ 1 Ori C (Ferrario & Wickramasinghe 2005). A possible scenario of the evolution of magnetic fields is that the fossil fields that are present in all interstellar material, are amplified during star formation, and further amplified during the final collapse of the star, resulting in the observed magnetised white dwarfs and neutron stars. Such a flux conserving scenario agrees with the magnetic fluxes observed in main sequence stars, and in white dwarfs and neutron stars, but the magnetic fluxes observed in molecular clouds tend to be on the high side. Apparently, some magnetic diffusion takes place during star formation. 1.2 Massive stars Massive stars end their evolution, with a final supernova explosion, as neutron stars or black holes. The initial masses of these stars range from ∼8–10 M to perhaps 100 M or more, which corresponds to spectral types earlier than about B2. Due to their enormous luminosities of more than ∼104 L , massive stars are able to drive a stellar wind by the opacity in the absorption lines of the ions in the wind (e.g. Lamers & Cassinelli 1999). The mass-loss rates due to these line-driven winds are around 10−10 –10−5 M year−1 , with typical terminal velocities of a few hundred to a few thousand km s−1 . Although massive stars are much more rare than lower mass stars, they are very important for the structure and evolution of the interstellar material and galaxies. Due to their high temperatures and luminosity they are a main source of ionising radiation. They evolve very rapidly and eject large amounts of mass into their surroundings, both through their winds and the final supernova explosion, which makes them an important source of heavy elements, momentum and energy for their environment. The launch of satellites with UV spectrographs, such as Copernicus, the International Ultraviolet Explorer (IUE), the Far Ultraviolet Spectroscopic Explorer (FUSE) and the Hubble Space Telescope (HST), enabled the study of the winds of massive stars. These winds were found to be highly variable (Howarth & Prinja 1989; Kaper et al. 1996; Fullerton 2003). Some well-observed stars were found to show periodic or cyclic behaviour on a timescale of a few days, which is comparable to the rotation timescale. In principle such variability could be related to non-radial pulsations, but as no non-radial pulsations with sufficiently long periods were found in these stars (de Jong et al. 1999; Henrichs 1999), these variations are thought to be due to corotating magnetic fields. 1.3 Magnetic fields in massive stars It has long been assumed that massive stars do not have magnetic fields, as they lack the convective outer mantle prevalent in lower mass stars. However, since Babcock 2 I NTRODUCTION Table 1.1: Properties of the known magnetic massive stars, excluding chemically peculiar Ap/Bp stars. The magnetic field strength Bp is the strength at the magnetic pole of the (approximately) dipolar field. Spec. type Mass Bp rotation period reference (M ) (Gauss) (days) θ1 Ori C O4-6V 45 1100±100 15.4 Donati et al. (2002) HD 191612 O6-8 ∼40 ∼1500 538a Donati et al. (2006a) τ Sco B0.2V ∼15 ∼500 41 Donati et al. (2006b) ξ 1 CMa B1III 14 ∼500 <37 Hubrig et al. (2006a) β Cep B1IV 12 360±40 12.00089 Henrichs et al. (2000) V2052 Oph B1V 10 250±190 3.63883 Neiner et al. (2003b) ζ Cas B2IV 9 340±90 5.37045 Neiner et al. (2003a) ω Ori B2IVe 8 530±200 1.29 Neiner et al. (2003c) a To be confirmed Star (1947, see also Babcock 1958) it is known that the intermediate mass Ap/Bp stars have strong magnetic fields, which, except perhaps those with the lowest masses, have radiative envelopes. In recent years a handful of massive stars with magnetic fields have been found. The first massive star of which the magnetic field was detected was β Cephei (Henrichs et al. 2000), followed by several other B (Neiner et al. 2003a,b,c; Hubrig et al. 2006a; Donati et al. 2006b) and O-type stars (Donati et al. 2002, 2006a). A summary of the properties of massive stars with magnetic fields is given in Table 1.1. 1.3.1 Indicators of the presence of magnetic fields∗ As detecting the magnetic field of a massive star requires a significant effort using dedicated instruments, a careful selection of targets is essential. The most successful indicator of the presence of magnetic fields has been periodic variability observed in UV wind lines. Unfortunately only a limited sample of massive stars has timeseries of observations with satellites capable of UV spectroscopy such as Copernicus and IUE, which allow to resolve periodic variability in UV wind lines. A serious limitation on finding new magnetic massive stars is the current lack of a high resolution UV spectrograph available for such studies. 1.3.1.1 UV wind-line variability The periodic stellar wind behaviour as observed in the known magnetic B stars is an extremely reliable indicator for the presence of a magnetic field. Fig. 1.1 gives several examples of the C IV line as observed with the IUE satellite over about 15 ∗ This section is partly based on Henrichs, Schnerr, & ten Kulve (2005). 3 C HAPTER 1 6 4 B2V He strong P = 9.5 d B ≈ 1 kG 4 σobs/σexp B7IIIp He weak P = 21.6 d B ≈ 300 G –500 0 500 1000 1500 Velocity (km s–1) (stellar rest frame) –500 0 500 1000 1500 Velocity (km s–1) (stellar rest frame) 3 B1 V 1 0 6 4 2 0 –1000 ζ Cas HD 3360 C IV Wavelength (Å) 103 spectra 1548 1552 B2 IV 2 1 0 3 2 1 0 –1000 V2052 Oph HD 163472 C IV IUE Wavelength (Å) 41 spectra 1544 1548 1552 σobs/σexp Flux (10–10 erg cm–2s–1Å–1) 1 α Scl HD 5737 C IV Wavelength (Å) 29 spectra 1548 1552 6 0 4 2 0 –1000 2 –500 0 500 1000 1500 Velocity (km s–1) (stellar rest frame) IUE Flux (10–10 erg cm–2s–1Å–1) –500 0 500 1000 1500 Velocity (km s–1) (stellar rest frame) IUE 1544 2 3 0 8 6 4 2 0 –1000 IUE 1544 6 ω Ori HD 37490 C IV Wavelength (Å) 80 spectra 1544 1548 1552 B2 Ve 4 2 0 6 4 2 0 –1500 –1000 –500 0 500 1000 Velocity (km s–1) (stellar rest frame) σobs/σexp σobs/σexp 0 6 4 2 0 –1000 B1 IVe σobs/σexp 2 4 β Cep HD 205021 C IV Wavelength (Å) 81 spectra 1548 1552 σobs/σexp 8 Flux (10–9 erg cm–2s–1Å–1) 10 IUE 1544 Flux (10–9 erg cm–2s–1Å–1) HD 184927 C IV Wavelength (Å) 30 spectra 1548 1552 Flux (10–10 erg cm–2s–1Å–1) Flux (10–11 erg cm–2s–1Å–1) IUE 1544 –500 0 500 1000 1500 Velocity (km s–1) (stellar rest frame) Figure 1.1: Typical examples of magnetic signatures in stellar wind behaviour in the C IV line of known magnetic B stars. Left: two chemically peculiar stars; a He-strong star (top) and a He-weak star (bottom). Middle/right: four magnetic massive B stars: β Cep, V2052 Oph, ζ Cas and the classical Be star ω Ori. In each figure the upper panel shows an overplot of all available IUE spectra (except for ω Ori), often taken over many rotational cycles. The lower panel displays the ratio of the observed variation to the expected variation (due to the noise), showing the velocity range in the stellar rest frame within which significant variations occur (Henrichs et al. 1994). Note that the whole profile moves up and down, approximately symmetrically with respect to zero velocity, except for ω Ori, in which the stellar wind changes occur at much higher velocities. years. All the stars shown are oblique rotators, i.e. they have a large scale magnetic field that does not vary in time, corotates with the star, and of which the axis is not aligned with the rotation axis. As a result of the corotating magnetic field both the emission and absorption components of the line profile increase and decrease in flux periodically. This behaviour is modelled and discussed in more detail in Chapter 5. The geometry of the wind and orientation of the magnetic field and rotation axes can in principle be derived from magnetic field measurements and the variable equivalent width of the wind lines. Note that in all observed cases the maximum wind absorption (maximum equivalent width) occurs when the magnetic equator passes the line of sight (Blong = 0, see Fig. 1.2). The rotation period can be determined from 4 5 P=12.00075(11) days ζ Cas B2 IV P = 5.37045(8) d, Tmin = 2446871.89(5) Tmin=2449762.05(6) 3 4 EW (C IV) 3 2 1 0 2 1 –1 IUE 1978–1995, 81 spectra 150 100 50 0 –50 –100 –150 –200 TBL 1998–2001, 48 spectra –250 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 UV phase IUE 1978 – 1995, 103 spectra 100 50 Blong(G) Blong(G) EW(C IV) [–700, 800]km/s I NTRODUCTION 0 –50 –100 TBL 2001 – 2002, 118 spectra –150 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 UV phase 2 Figure 1.2: Upper panels: equivalent width of the C IV stellar wind line measured in IUE spectra of β Cep (left) and ζ Cas (right) as a function of rotational phase. The deepest minimum at phase 0 corresponds to the maximum emission. Lower panels: Magnetic data as a function of the UV phase with a best-fit sine curve. Note that there is no significant difference in zero phase between the UV and magnetic data and that the field crosses zero at the EW maxima (Henrichs et al. 2000; Neiner et al. 2003a). The strictly periodic wind variations similar to those in Bp stars led to the discovery of the magnetic field in these two stars. these measurements. Once the period is known, the v sin i of the star yields the inclination. Using the relation between the measured maximum and minimum field strength and β, the angle between the rotation axis and the axis of the magnetic field (Preston 1971): r= cos(β + i) Bmin = , Bmax cos(β − i) (1.1) allows a determination of β. From observations with the IUE satellite, it can be seen that at least 60% of the O stars, 17% of the non-chemically peculiar B stars, and all of the Bp stars show variability in their wind-lines (Henrichs et al. 2005, see also Howarth & Prinja 1989). For the stars that have large scale, dipole-like magnetic fields (the Bp stars, β Cep, ζ Cas, τ Sco and θ 1 Ori C), this variability is likely due to material that is guided by the magnetic field, which corotates with the star (see Chapter 5). In these cases the timescale of the variability coincides with the rotation period. However, in some cases the variability shows a timescale comparable to the rotation period of the star, but is not strictly periodic. 5 C HAPTER 1 Table 1.2: Classes of wind line variability to identify magnetic candidates from the sample of ten Kulve (2004, see also Henrichs et al. 2005). Star type Sample Variable Fraction Classa Number O 100 60 60% 1 All β Cep 54 8 15% 1, 2, 3 4, 2, 2 Be 82 25 30% 1, 2, 3 7, 6, 12 other B 152 16 11% 1, 2 13, 3 Bp 14 14 100% 2 All a Class 1 = DAC type; Class 2 = magnetic type; Class 3: Known magnetic θ 1 Ori C β Cep, V2052 Oph β Cep, ω Ori (tbc) ζ Cas intermediate type 1.3.1.2 Different types of UV wind-line variability As variability in UV wind-lines is a reliable indicator of the presence of a magnetic field, ten Kulve (2004) performed an exhaustive study of line variability based on the IUE data archive. This archive spans more than 18 years of observations and contains over 6000 high resolution spectra of more than 600 OB stars, out of which 401 suitable objects could be selected with repeat observations. Table 1.2 summarises the results of this investigation. Three different types of variability are observed, of which two were already known. The DAC-type, with variability at high velocity due to Discrete Absorption Components (DACs), and the magnetic-type, with variability near zero velocity. A new third ’intermediate type’ is characterised by variability at intermediate velocities. Fig. 1.3 gives examples of all three types. Our preliminary interpretation of the existence of three classes is that all three have a magnetic origin, the difference being inclination angle of the star, orientation of the magnetic axis and the degree to which the magnetic field is able to control the flow pattern of the stellar wind (see Chapter 5). Model studies are needed to better understand the nature of these differences. 1.3.1.3 Other indirect indicators for magnetic fields In addition to the cyclical wind variability in the UV wind lines, several other phenomena are thought to be indicative of the presence of surface magnetic fields. Examples are cyclic variability in Hα and He II 4686 emission, chemical peculiarity, specific pulsation behaviour, anomalous X-ray emission, and non-thermal emission in the radio region. The optical emission line variability is related to the magnetically dominated outflow close to the star (e.g. Moffat & Michaud 1981; Kaper et al. 1997; Rauw et al. 2001). Chemical peculiarity is a property always connected to magnetism, related to constrained transport of elements. All magnetic B stars appeared to have some abundance anomaly (see Table 1.3) but not as outspoken as the He-peculiar stars. Neiner et al. (2003b) concluded that V2052 Oph was in fact a helium strong star, after the 6 I NTRODUCTION 1 non–variable 0 3 2 1 0 –1500–1000 –500 –1 0 500 1000 1500 Velocity (km s ) (stellar rest frame) σobs/σexp Flux (10–10 erg cm–2s–1Å–1) σobs/σexp Flux (10–09 erg cm–2s–1Å–1) η Tau HD 23630 B7IIIe Wavelength (Å) 19 spectra 1544 1548 1552 2 DAC type 0 3 2 1 0 –1500–1000 –500 0 500 1000 1500 Velocity (km s–1) (stellar rest frame) σobs/σexp Flux (10–10 erg cm–2s–1Å–1) σobs/σexp Flux (10–09 erg cm–2s–1Å–1) 4 6 4 2 magnetic type 0 4 2 0 –1500–1000 –500 0 500 1000 1500 Velocity (km s–1) (stellar rest frame) δ Cen HD 105435 B2IVe Wavelength (Å) 16 spectra 1544 1548 1552 6 8 ϑ CrB HD 138749 B6Vnne Wavelength (Å) 50 spectra 1544 1548 1552 3 QY Car HD 88661 B2IVpne Wavelength (Å) 14 spectra 1544 1548 1552 1556 2 1 Intermediate type 0 4 2 0 –1500–1000 –500 0 500 1000 1500 Velocity (km s–1) (stellar rest frame) Figure 1.3: The different types of wind variability found in the IUE archive. Shown are examples of the C IV line in Be stars of all types: the non-variable type (top left), the magnetic type (top right), the DAC type (bottom left) and the intermediate type (bottom right). magnetic field was found. Abundance anomalies are therefore also good indirect indicators of a magnetic field. Pulsation modes in the presence of magnetic fields are split, which opens the way to astroseismology as illustrated by Shibahashi & Aerts (2000) for β Cep (see also Chapter 6). Narrowness of X-ray emission lines (Waldron & Cassinelli 2001; Cohen et al. 2003; Smith et al. 2004) and hard X-ray variability (Gagné et al. 2005) are also strong indications of magnetic fields in the emission regions. In β Cep the X-ray emission is consistent with model predictions (Babel & Montmerle 1997; Donati et al. 2001), and Cohen et al. (2003) already suggested the presence of a magnetic field in τ Sco before it was detected by Donati et al. (2006b). In case of oblique rotators a rotational modulation of the X-ray intensity is predicted. Finally, synchrotron radio emission is also expected to be produced in the presence of a magnetic field, and has indeed been detected in Ap/Bp stars (Drake et al. 1987). 7 C HAPTER 1 Table 1.3: Abundances in several known magnetic B stars from Morel et al. (2006, β Cep, V2052 Oph and ξ 1 CMa), Neiner et al. (2003a, ζ Cas) Neiner et al. (2003c, ω Ori) and the average abundances for B stars from Gies & Lambert (1992). By definition log [H]=12; [X/Y] is defined as log[(X)/(Y)]; [He/H] for the Sun is 0.085. Solar abundances are from Grevesse & Sauval (1998). Star [He/H] [C/C ] [N/N ] β Cep 0.078±0.028 −0.50±0.10 −0.01±0.13 V2052 Oph 0.118±0.032 −0.31±0.07 0.07±0.17 ζ Cas −0.05±0.09 0.41±0.10 ω Ori 0.00±0.07 0.26±0.10 ξ 1 CMa 0.098±0.017 −0.33±0.11 0.08±0.16 average B star −0.32±0.16 −0.11±0.22 [O/O ] −0.36±0.14 −0.44±0.30 −0.09±0.14 −0.09±0.06 −0.34±0.16 −0.15±0.14 A search for synchrotron emission from O star magnetic candidates is presented in Chapter 9. 1.4 Notes on polarisation† Astronomical objects are studied by the light that they emit. Apart from the intensity and wavelength dependence of this light, that can be studied through photometry and spectroscopy, an important property of the light emitted by such objects is its polarisation. Polarimetry is currently not as popular as photometry or spectroscopy, but in many cases the information contained in the polarisation of the light cannot be obtained in any other way. Before going into the details of how the polarisation of light is used to measure magnetic fields, it may be helpful to describe some of the basics of polarisation, as these are usually not taught in basic astronomy courses. This chapter is not intended to cover all the basics of the characteristics of the polarisation of light. It only intends to point out some of the basic properties of polarisation that are exploited in the following chapters of this thesis. 1.4.1 A photon as a wave A photon can be described as an electromagnetic wave, of which the electric- and magnetic-field wave components vary perpendicularly to the direction of propagation of the wave. The magnetic and electric field vectors are related by ~ r, t) = ~n × E(~ ~ r, t), B(~ (1.2) ~ and E ~ are where ~n is the unit vector in the direction of wave propagation, and B ~ ~ measured in c.g.s. units. As B and E are perpendicular to each other and the di† This Section is based on the books by degl’Innocenti & Landolfi (2004) and Hovenier et al. (2004), see also Mathys (1989). 8 I NTRODUCTION rection of propagation, the description of a photon in terms of the electric or the magnetic field vector is equivalent. If we choose a right-handed coordinate system (x,y,z) with the z-axis pointing in the direction of propagation, a monochromatic electromagnetic wave observed at a fixed position on the z-axis can be described as Ex (t) = E1 cos(ωt − φ1 ), Ey (t) = E2 cos(ωt − φ2 ), (1.3) where E1 and φ1 , and E2 and φ2 are the amplitude and phase of the x- and ycomponents of the observed oscillation of the electric field, respectively, and ω is related to the photon frequency, ν by ω = 2πν. In general the relations in Eq. 1.3 describe an ellipse, which is called the polarisation ellipse. For specific cases of φ1 and φ2 , the oscillation describes either a line or a circle. If we choose our t = 0 such that φ1 = 0, then for [φ2 = 0 mod π] Eq. 1.3 describe a line, as is the case for [E1 = 0 or E2 = 0], and if [φ2 = π/2 mod π] they describe a circle, where angles are measured in radians. 1.4.2 The Stokes parameters I, Q, U and V To fully describe the properties of ray of light at a given frequency, it is not enough to know just the intensity. For a complete description all the polarisation properties of the light also have to be described. To do so Stokes (1852, see also Walker 1954) introduced the four Stokes parameters (I, Q, U , V ). The intensity of the light is given by I, the linear polarisation components are determined by Q and U and the circular polarisation is given by V . In this context it is important to note that the Stokes parameters describe the time averaged properties of the radiation. This is the reason that both Q and U are required to describe the linear polarisation; not only the angle of the linear polarisation, but also the fraction of the light that is polarised has to be described. A monochromatic electromagnetic wave with a constant amplitude and phase is always 100% polarised. The Stokes parameters are defined as follows: Stokes V is the difference between the right- and left-circular polarised flux, Q is the difference in flux between the two orthogonal linear polarisation states and U is the difference in flux between two orthogonal linear polarisation states that make an angle of 45 ◦ with those of Q. This is illustrated in Fig. 1.4. Positive circular polarisation is then defined as clockwise rotation of the electric field vector at a fixed point in space for an observer facing the source, negative circular polarisation is defined as counterclockwise rotation. This is the convention adopted by most optical astronomers, but in the field of radio astronomy the opposite convention is often used. 9 C HAPTER 1 Q= U= V= Figure 1.4: The definition of the Stokes parameters Q, U and V at a fixed point in space, for an observer facing the source. Figure after degl’Innocenti & Landolfi (2004). 1.4.3 Zeeman splitting of spectral lines In quantum mechanics the possible states of an electron within an atom are given by the eigenvectors of the Hamiltonian. These eigenvectors are often defined by the ~ the total angular momentum, and M ~ , the angular momentum quantum numbers J, component along some preferential axis. In the presence of a magnetic field it is useful to choose this axis along the direction of the magnetic field. In the absence of a magnetic field, the possible energy levels within an atom are in general degenerate, i.e. several different eigenvectors correspond to the same energy level (have the same eigenvalue). This degeneracy is related to the different possible ~ The degeneracy of a level with total orientations of the total angular momentum J. angular momentum J~ is given by the possible values of M = −J, −J + 1, ..., +J. In the presence of a magnetic field, the energy of a level will depend on the orientation of J~ and this degeneracy is removed, splitting every level into 2J + 1 sublevels. The energy of these levels is E0 +µ0 gBM , where E0 is the energy in absence of a magnetic field, µ0 is the magnetic permeability, g is the Landé factor of the level, and B is the magnetic field strength. For the spectral lines related to electron state transitions, the simplest case is that of a classic Zeeman triplet, which is also referred to as the normal Zeeman effect. This case applies when one of the two levels involved in the transition has J = 0, or when both levels have the same Landé factor. As the selection rule for electric-dipole transitions is ∆M = −1, 0, 1, this results in a triplet with wavelength separation of 10 I NTRODUCTION ∆λ = λ2 egB λ20 µ0 gB = 0 hc 4πme c2 (1.4) between the components of the triplet (assuming ∆λ λ0 and the levels having the same Landé factor). Here λ0 is the central wavelength of the line without magnetic fields, and h, c, e and me have their usual meaning. The transitions with ∆M = ±1 are called the σ components, and those with ∆M = 0 are called the π components. When observed in emission, π components are linearly polarised parallel to the magnetic axis when observed from a plane normal to the magnetic axis and unpolarised when looking along the magnetic field lines. Both the σ components with ∆M = ±1 are circularly polarised when observed along the magnetic field lines, but their polarisation is opposite (left vs right circularly polarised). When viewed from a plane normal to the magnetic axis both σ components are linearly polarised. In the Stokes V spectrum, the difference between the right- and left-circularly polarised light (see Fig. 1.4) of the σ components is measured. In general the presence of a magnetic field in the line forming region results in a magnetic signature in the Stokes V spectrum, of which the shape depends on the viewing angle (see, e.g., Fig. 6.6). It can be shown that for a classic Zeeman triplet the average magnetic field component along the line of sight is related to the first moment of the Stokes V profile of a spectral line by: R vV (v) dv eλ0 g = hBeff i, (1.5) EW 4πme c where the equivalent width in velocity space is defined Z EW = [1 − I(v)]dv, (1.6) and v is the velocity relative to λ0 (Mathys 1989). In the general case, however, the line patterns are more complicated than that of the classical Zeeman triplet, which may result in deviations in the field determination (Stift & Leone 2003). 1.4.4 The Least-Squares Deconvolution method The circular polarisation signature of a spectral line in the presence of a magnetic field, in principle allows for the determination of the line of sight component of the magnetic field using Eq. 1.5. However, the small amplitude of these signatures makes them hard to measure. For a 1 kG field and a line at 500 nm, the typical separation between the σ components is only a few hundred km s −1 , which results in a signature with an amplitude of the order of 0.1% in a Stokes V /I spectrum. Clearly, very high signal-to-noise spectra are required to enable the measurement of such small signatures. 11 C HAPTER 1 In stars this signature is similar for all lines in the spectrum. To exploit this, Semel (1989, see also Donati et al. 1997) developed a method to combine the Stokes V signatures of all the magnetically sensitive lines in the spectrum into one fictitious high S/N average Stokes V signature. This method is called the Least-Squares Deconvolution method (LSD, see also Chapter 2). Due to the very high signal to noise ratio that can be obtained for this average Stokes V signature, this method is very powerful for detecting magnetic fields. Some of the assumptions underlying this method can, however, result in deviations of the determined field strengths, which are investigated in more detail in Chapter 2. 1.4.5 The design of spectropolarimeters To measure the polarisation properties of radiation received from astronomical objects (galaxies, stars, planets, interstellar and circumstellar material, etc.) optical telescopes are equipped with polarisation analysers. For measuring the Stokes parameters it is always required to determine the difference between two opposite polarisation states (see Fig. 1.4). In principle this would be done most accurately by measuring these two polarisation states on a CCD at the same time and on the same pixels. Unfortunately this is impossible. In practise, either both polarisation states are measured on the same pixels, one after the other, or both polarisation states are recorded simultaneously on different pixels. For the use of a polarisation analyser with a spectrograph the second approach is currently the most widely used. To correct for most of the artifacts resulting from the fact that the two spectra (one for each polarisation state) are recorded on different pixels, observations are usually performed in a sequence where the beams corresponding to the two polarisation states are switched, thus recording the opposite polarisation state also on the same pixels. A common instrumental setup to allow this in optical (and also infrared) instruments is the combination of a half-wave plate (λ/2 plate), quarter-wave plate (λ/4 plate) and a Wollaston prism. In half-wave and quarter-wave plates the propagation of the electromagnetic wave vibrating along one direction (the fast axis) is faster than that of the electromagnetic wave vibrating along the perpendicular direction. As a result one component is delayed by λ/2 or λ/4 relative to the other component. In circular polarisation measurements quarter wave plates are used to convert circular polarisation into linear polarisation. Light that is 100% circularly polarised can be described by two orthogonal electric field components as defined in Eq. 1.3 with a phase difference of φ1 − φ2 = π/2 or φ1 − φ2 = 3π/2 (corresponding to left and right circular polarisation). If one of the components is delayed by λ/4 (or π/2) relative to the other, the phase difference is either 0 or π depending on whether you started with left or right circular polarisation. These describe two orthogonal linear polarisation states. Therefore a quarter wave plates converts the two circular polarisation states into two orthogonal linear polarisation states. To separate these two opposite polarisation states one can use a Wollaston prism, which splits a single beam into two beams corresponding to two opposite linear polarisation states. Note that it is 12 I NTRODUCTION important that the angle between the axes of the quarter wave plate and the Wollaston prism is properly set (e.g. to 45◦ ). By rotating the quarter wave plate over 90◦ , the polarisation states that belong to the split beams after the Wollaston prism are switched, which allows to record the two opposite polarisation states on the same pixels. The analysis of linear polarisation is very similar, using a half-wave plate instead of a quarter-wave plate. With a half-wave plate the angle that switches the two polarisation states is 45◦ and, as both Q and U need to be determined, twice as many measurements are required as compared to circular polarisation. Spectropolarimeters with such a setup are available at observatories such as the Very Large Telescope, William Herschel Telescope, Telescopio Nazionale Galileo, United Kingdom Infra-Red Telescope, Telescope Bernard Lyot and Canada-FranceHawaii Telescope. 1.5 This thesis This thesis covers different topics related to magnetic fields in massive stars. In Chapter 2 we explore the reliability of magnetic field measurements based on the Least-Squares Deconvolution (LSD) method. We conclude that it is a very efficient method to discover new magnetic fields, but that some caution is required when interpreting quantitative magnetic field measurements. In the Chapters 3, 4 and 5 we focus on the magnetic field, Hα emission and UV wind line variability in β Cephei. The first chapter describes the discovery of the magnetic field in this star. In the following chapter we solve the enigma of the origin of the Hα emission from this system, by showing that it does not originate from the slowly rotating primary star, but from its close companion. In the third chapter of this trilogy we model the effect of the magnetic field on the UV wind lines, concluding that X-rays likely play an important role in explaining the observed variability. In Chapter 6 we show that the strong magnetic field that was predicted to be present in ν Eri based on the observed pulsation frequencies is not present. Magnetic field measurements of selected O and B stars are presented in Chapters 7 and 8, from which we conclude that large scale magnetic fields of a few hundred gauss or more are not common among massive stars. 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Stift & H. F. Henrichs Astronomy and Astrophysics, 2006 (submitted) Abstract We address the question whether magnetic field measurements derived from circular spectropolarimetric observations with the help of the Least-Squares Deconvolution (LSD) method are suitable for the determination of stellar magnetic topologies. We attempt to recover the geometric and magnetic input parameters from synthetic Stokes I and V spectra calculated under various assumptions concerning magnetic configuration, rotational velocity, inclination, and field strength. In many of the cases considered, the resulting effective magnetic field strength deviates significantly from the theoretical value, given by the longitudinal field component integrated over the visible hemisphere and weighted with the continuum flux. LSD is a powerful method for qualitatively detecting the presence of very weak stellar magnetic fields, but quantitative results, as for example magnetic topologies, can show systematic deviations up to 50%. ∗ Least Squares Deconvolution 19 C HAPTER 2 2.1 Introduction Magnetic fields of stars can be detected and measured by using the polarimetric properties of spectral line profiles. This was pioneered by (Babcock 1947) who discovered the first magnetic star other than the Sun, viz. 78 Vir (A2p). Babcock used circular spectropolarimetry because of the relatively low sensitivity of the photographic plate and because of the limited resolution of the spectrographs. It can be shown that for weak and moderate magnetic fields, the distance in wavelength between the σred and the σblue components of Zeeman split spectral lines is linearly related to the effective magnetic field Beff of the star, i.e. the line-intensity weighted average over the visible stellar disk of the line-of-sight component of the magnetic field vector. Usually, Beff values obtained from a number of different lines are statistically combined with the aim to improve the precision of the effective field measurement. However, application of this technique is essentially restricted to the measurement of magnetic fields in Ap stars, main sequence stars characterised by relatively low rotational velocities and by the presence of magnetic fields organised on a large scale. Semel (1989) suggested a method for the construction of a fictitious mean Stokes V profile with a very high S/N ratio by combining the signals of a fair number of well chosen spectral lines. This idea underlies the so called “Least-Squares Deconvolution” or LSD method as coded by (Donati et al. 1997). This method, which can detect very weak Stokes V profiles (peak-to-peak amplitudes as low as 0.05 percent), has changed the study of weak stellar magnetic fields and has opened the possibility of considering late-type stars where magnetic fields are so complex that the average value of the longitudinal component is close to zero (Donati et al. 1997); it can also be applied to very fast rotators where the Stokes V profiles are strongly flattened by rotational broadening (Donati et al. 2001). In principle, we would expect no differences between B eff values obtained from the average of the individual lines on the one hand, and from the average line profile on the other hand. However, it is not straightforward to assign proper scales and weights to the Stokes profiles of individual spectral lines used in LSD that would lead to the definition of the perfect fictitious average line. In general, a magnetic field affects the various individual spectral lines in quite different ways; so many simplifying assumptions enter the LSD approach that one may wonder how accurately the true field configuration can be recovered with this method. The aim of this paper is to assess the effects of the assumptions underlying the LSD approach and to quantify the capability of LSD to measure the “true” effective magnetic field of a star. Our analysis is based on the application of this method to a series of synthetic polarised spectra computed with the COSSAM code (Stift 2000) for a considerable number of magnetic dipole configurations, rotational velocities and inclinations between rotational axis and line-of-sight. First, in Sect. 2.2 we present details of the calculation of these synthetic spectra. In Sect. 2.3, measuring the stellar magnetic fields with Babcock’s classical approach, we investigate the question 20 O N THE RELIABILITY OF THE LSD METHOD of how well this approach is suited for recovering stellar geometries. Sect. 2.4 starts with a close look at the LSD method and its underlying assumptions; a cautionary note concerns the often practised continuum normalisation. Finally, the results of the measurements of effective magnetic field from the synthetic spectra, employing the methods discussed before, are given in Sect. 2.5, and the conclusions are presented in Sect. 2.6. 2.2 Synthetic spectra Synthetic spectra have been computed with COSSAM (Codice per la Sintesi Spettrale nelle Atmosfere Magnetiche, Stift 2000), an LTE Stokes code with full component by component opacity sampling (CoCoS) that solves the equation of polarised radiative transfer in a plane-parallel atmosphere (for further details and a comparison with other Stokes codes see also Wade et al. 2001). The atmosphere adopted is characterised by Teff = 26000 K, log g = 3.89, a He abundance of 10% with respect to hydrogen, and zero microturbulence. Zeeman splittings and relative Zeeman subcomponent strengths are computed from the Landé factors and J values provided by the VALD spectral line database (Piskunov et al. 1995). Whenever Land é factors are not listed in VALD they are either calculated from spectroscopic term designations under the assumption of LS-coupling or set to unity (i.e. a classical Zeeman triplet is assumed). Magneto-optical effects are correctly considered. Wavelength- and depthdependent continuous opacities are interpolated in a table established with ATLAS9 (Kurucz 1993). In order to closely match realistic observational conditions, we computed a series of spectra in the 4200–5820 Å range with 0.025 Å step size. For the magnetic field topology we assumed a centred dipole and we tried to cover a relevant part of the parameter domain. The inclination of the rotation axis towards the line-ofsight takes the values i = 10, 30, 70◦ ; the tilt of the dipole axis with respect to the rotation axis (the obliquity) is β = 20, 40, 80◦ . The polar strength of the dipolar field is Bp = 100, 500, 2000, 10000 G. Three different rotational phases are considered, viz. φ = 0.00, 0.25, 0.50. Finally, the projected rotational velocity is assumed to be ve sin i = 10, 50 and 90 km s−1 . To better simulate the application of the LSD method to real échelle spectra, we have converted our synthetic spectra from a constant wavelength step to constant resolving power with R = λ/∆λ = 30 000, 60 000, 90 000. 2.3 The classical method to measure Beff Babcock’s method to derive the effective magnetic field is based on measuring the average distance in wavelength between the σred and the σblue Zeeman components of spectral lines. This is called the centre of gravity method (COG). It was shown by Mathys (1989) that this is equivalent to the determination of the first order moment 21 C HAPTER 2 of the Stokes V line profile (valid for unblended spectral lines): Z 1 Vc − V λ (1) RV = (λ − λI ) dλ W FI c (2.1) which is related to the effective magnetic field Beff by (1) RV = 4.67 × 10−13 geff λ2 Beff (2.2) where W is the equivalent width, Vλ the flux in Stokes V across the spectral line, Vc the Stokes V flux in the neighbouring continuum, FIc the unpolarised continuum flux, λI the wavelength of the centre of gravity of the Stokes I flux profile and g eff the effective Landé factor (the weighted mean displacement of the σ components). The wavelength λ is given in Å and the field strength in Gauss. Equation (2.2) is strictly valid only in the weak line limit, as it implicitly contains the assumptions of a Milne-Eddington solution of the transfer equation for polarised light (Mathys 1989). In order to evaluate how far measurements of the effective magnetic field can deviate from the theoretical value, Leone & Catanzaro (2004) computed the Stokes I and V profiles of a fictitious spectral line with the help of COSSAM, adopting the same 20 different Zeeman patterns as in Stift & Leone (2003). They assumed a uniform magnetic field of 1 and 5 kG respectively, inclined by an angle γ = 0, 35, 70◦ with respect to the line-of-sight, and adopted logarithmic abundances of 6.5, 8.0 and 9.5 (with the hydrogen abundance equal to 12). Effective magnetic fields measured by using the above relation were, as expected, very close to the input value for weak lines or small values of the angle γ. The standard deviation of the measured effective magnetic field, using a random sample of transitions, was of the order of 7%. For strong lines and large values of the angle γ, effective fields were found to be under-estimated by up to 23%. Before making a comparison between the magnetic input values of our simulations and the effective fields determined with the LSD method from the synthetic spectra, we have carried out a line by line measurement of the effective magnetic field, using Eq. (2.2). Since we want to estimate the errors due to the assumptions behind this equation, no noise has been added to the synthetic spectra and no convolution for the instrumental broadening has been performed. 2.3.1 Recovering the geometry To investigate the capability of recovering the magnetic field geometry from the measured effective field, we have applied the classical relation between obliquity and inclination (Preston 1971): 1−r , (2.3) tan β tan i = 1+r where r is the ratio between the minimum and maximum measured value of the effective magnetic field, and also the Schwarzschild (1950) relation to recover the polar 22 O N THE RELIABILITY OF THE LSD METHOD Table 2.1: Magnetic geometries recovered from effective magnetic field measurements (employing 3 different methods) of noise-free synthetic COSSAM I and V spectra, computed for a centred magnetic dipole. The input values (i is the angle between the rotation axis and the line of sight, β the obliquity angle between dipole axis and rotational axis, and Bp the polar field strength) have been recovered using Eqs. (2.3) and (2.4), due to Preston (1971) and Schwarzschild (1950) respectively. The LSD method has been applied with and without continuum normalisation of the fictitious average line, for a resolution of R=90000. The magnetic field values were measured from synthetic spectra calculated for 3 different values of the projected rotational velocity, viz. 10, 50, and 90 km s −1 . Models for i = 10◦ and ve sin i = 90 km s−1 have not been calculated as this would imply supercritical rotation. Input COG (Eq. 2.2) 10 i = 10◦ β Bp [G] 20 100 20 500 20 2000 20 10000 40 100 40 500 40 2000 40 10000 80 100 80 500 80 2000 80 10000 i = 30◦ 20 100 20 500 20 2000 20 10000 40 100 40 500 40 2000 40 10000 80 100 80 500 80 2000 80 10000 i = 70◦ 20 100 20 500 20 2000 20 10000 40 100 40 500 40 2000 40 10000 80 100 80 500 80 2000 80 10000 LSD ve sin i [km s−1 ] 50 90 β Bp [G] 19.9 99 20.0 497 20.0 1987 20.0 9936 40.3 100 40.0 497 40.0 1988 40.0 9938 80.0 100 80.0 497 80.0 1988 80.0 9941 β Bp [G] β Bp [G] 19.4 135 19.6 124 19.0 626 19.0 577 20.2 2268 20.2 2095 17.7 9571 17.7 8900 39.4 135 39.2 124 35.5 604 35.4 557 37.5 2212 37.5 2043 36.3 9443 36.4 8788 80.2 136 80.2 125 80.0 666 80.0 613 80.0 2433 80.0 2246 80.0 10517 80.0 9760 20.1 20.0 20.0 20.0 40.1 40.0 40.0 40.0 80.0 80.0 80.0 80.0 97 486 1946 9728 97 486 1946 9730 97 487 1947 9733 19.9 17.8 18.0 18.2 40.3 38.5 38.3 38.5 80.3 80.1 80.5 80.5 136 20.0 623 17.9 2224 18.0 9754 18.3 135 40.2 614 38.5 2202 38.3 9675 38.5 135 80.3 655 80.1 2341 80.5 10217 80.5 122 20.7 560 20.0 2001 19.8 8855 17.9 121 39.4 552 40.1 1982 40.1 8787 38.2 121 80.0 588 80.1 2106 79.9 9260 80.4 104 532 2138 9739 107 532 2139 9612 106 532 2136 10257 20.8 20.0 19.9 18.0 39.5 40.1 40.2 38.3 79.9 80.1 79.9 80.4 81 20.2 410 20.4 1652 21.5 7685 18.8 83 37.6 410 39.2 1653 41.1 7590 39.7 82 79.3 410 79.9 1649 79.7 8070 79.7 84 20.3 409 20.4 1711 21.5 9825 18.9 79 37.5 406 39.2 1724 41.1 9797 39.8 81 79.4 411 79.9 1645 79.7 10047 79.7 57 277 1159 6753 53 274 1168 6738 55 278 1114 6889 20.0 20.0 20.0 20.0 40.0 40.0 40.1 40.1 79.9 80.1 80.0 80.0 97 486 1943 9715 97 486 1944 9720 97 486 1946 9730 19.7 20.0 20.0 20.0 39.8 41.5 42.0 41.3 79.9 81.0 80.7 81.5 135 19.7 653 20.0 2314 20.0 10102 20.0 135 39.8 617 41.5 2189 42.0 9810 41.3 135 79.7 621 81.1 2211 80.7 9771 81.5 122 20.2 588 20.1 2082 20.0 9155 20.0 121 39.0 555 40.3 1970 39.4 8902 41.9 121 80.0 558 79.9 1990 81.8 8872 80.9 105 530 2143 10146 109 530 2196 9596 107 530 2148 9707 20.3 20.1 20.0 20.0 38.8 40.3 39.4 41.8 80.1 79.9 81.8 80.8 80 20.0 409 19.8 1655 20.0 7989 20.0 85 37.4 408 39.4 1696 39.2 7574 40.0 82 81.0 409 80.4 1660 78.8 7661 81.4 80 20.0 416 19.8 1655 20.0 10096 20.0 88 37.2 414 39.4 1706 39.1 9932 39.9 83 80.7 412 80.3 1715 78.8 9825 81.4 54 281 1120 6926 59 280 1156 6829 56 279 1161 6754 23 β Bp [G] LSD(no cont. norm.) ve sin i [km s−1 ] 10 50 90 β Bp [G] β Bp [G] 19.5 86 18.9 80 20.0 425 20.1 385 18.6 1730 23.2 1665 18.0 7723 17.8 9522 42.0 89 39.2 77 40.4 428 40.7 385 41.6 1780 43.3 1664 35.7 7568 39.9 9744 80.0 89 81.1 86 79.7 417 80.1 386 80.1 1718 80.0 1526 80.0 8533 80.0 9687 β Bp [G] C HAPTER 2 field strength, assuming a linear limb-darkening coefficient of 0.37 (Claret 2004), applicable to a B1 star like β Cep: Beff (min, max) = 0.29Bp cos(β ± i) (2.4) Table 2.1 lists the magnetic geometries determined from B eff measurements obtained with the classical line by line method. Inspection of the numbers shows that the obliquity and dipole strength are correctly determined, with errors smaller than about 3%. 2.4 The Least-Squares Deconvolution method 2.4.1 Basics Least-Squares Deconvolution (LSD) is a method that combines the weak Stokes V signals from a large number of magnetically sensitive lines in a spectrum. The original suggestion to improve the S/N ratio of a Stokes V profile by taking the average of many spectral lines was made by Semel (1989). This idea was for the first time applied to stellar spectra by Semel & Li (1996) and by Carter et al. (1996). The more sophisticated LSD method, developed by Donati et al. (1997) constitutes an improvement of Semel’s approach and is currently widely used for the detection of magnetic fields and for the determination of field strengths. In order to calculate the average Stokes V line profile, it is assumed that all lines exhibit the same shape and that the Stokes V profile is related to the local Stokes I profile by ∂Iloc (v) (2.5) Vloc (v) ∝ geff λ ∂v with geff the effective Landé factor. Because of the identical shapes of all intensity profiles, the individual Stokes V profiles – after integration over the visible stellar disk, and taking rotation into account – can be described by V (v) = geff λ0 d Z(v) (2.6) where d denotes the central line depth, λ0 is the central wavelength of the intensity profile, and Z(v) the average Stokes V profile, the mean Zeeman signature. Defining a line pattern function X geff,i λ0,i di δ(v − vi ), (2.7) M (v) ≡ i the circularly polarised spectrum can be described by the convolution V = M ∗ Z. (2.8) From the Stokes V spectrum the average Zeeman pattern Z can be recovered by adopting the appropriate line pattern M and by employing a deconvolution scheme that establishes a least-squares solution for Z. 24 O N THE RELIABILITY OF THE LSD METHOD 2.4.2 Underlying assumptions LSD is certainly a very powerful method, but is based on several simplifying assumptions that in general are not met in real spectra: 1. 2. 3. 4. the Stokes V profiles are proportional to the derivative of the Stokes I profile, all lines exhibit the same shape, all lines show the same Zeeman pattern, line intensities add up linearly in the case of strong blends (but a blend can at most become completely dark). The first assumption is strictly valid only in the weak field regime, the second is certainly not true for strong lines. We shall discuss the third in the following subsection. In hot stars, were we count only up to 100 − 200 lines, the fourth assumption is not overly restrictive. 2.4.3 Zeeman patterns The LSD method assumes that all line shapes are identical and that the Stokes I profile simply scales with central depth. Moreover, Stokes V is assumed to be proportional to the derivative of Stokes I with respect to the velocity. The contribution of each spectral line to the average LSD profile is weighted by the product of effective Landé factor, wavelength and depth. To verify how realistic the assumption of identical Zeeman patterns for all spectral lines is, we have computed the Stokes V and I profiles for 2 neutral oxygen lines at 4705.343 and 4673.732 Å, assuming a 500 G magnetic field inclined by 70◦ towards the line-of-sight. Not unexpectedly, we find quite significant differences between the V /I profiles (Fig. 2.1). 2.4.4 Continuum determination The LSD method can include thousands of spectral lines, many of which can be severely blended. Donati et al. (1997) for example used around 2000 spectral lines to measure the magnetic field of late-type stars. When the number of spectral lines is increased, a clear advantage appears: the coherent signal within spectral lines increases and the incoherent photon noise of the adjacent continuum decreases. However, as noted by Semel (1995), incoherent addition of blended lines results in a reduced continuum. Examination of the published literature reveals that LSD profiles have invariably been normalised. We shall show below how such a normalisation or the lack thereof affects the effective magnetic field measurements. 2.5 Measurements of Beff with the LSD method In order to quantitatively investigate the reliability of the LSD method, we have applied it to synthetic Stokes I and V spectra, and recovered the magnetic geometry 25 C HAPTER 2 1 0.5 0 -0.5 -1 0 Figure 2.1: Stokes profiles V /I for the lines O I 4705.343 Å (solid line) and O I 4673.732 Å (dashed line), computed for a 500 G field seen under an angle of 70o . Scaling of the profiles helps to clearly reveal the dissimilar shapes due to the different Zeeman patterns (shown above). As usual, π components are displayed above the horizontal line, σ components below. The dots represent the positions of the components of a simple Zeeman triplet. from the effective field measurements. The number of unblended lines identified in the spectra is 49. In a first approach, the synthetic spectra were used without added noise; the results are reported in Table 2.1. We note that the angles β between rotational axis and dipole axis are recovered to within 10%. Effective field strengths are generally over-estimated by between 20% and 30% in the case of relatively weak fields (Bp ≤ 2000 G). For strong fields (Bp ∼ 10000 G) they tend to be under-estimated by up to about 10%. The problem of the continuum normalisation of the fictitious average line profile produced by the LSD method deserves close attention. In fact, blending will reduce the continuum of the fictitious line (Semel 1995) resulting in a smaller equivalent width, and by normalising the continuum we would expect to over-estimate the effective field based on Eq. 2.1. However, as it turns out, we accurately recover β, but usually under-estimate the polar field values. Noise has been added to our spectra to investigate real life cases and leads to results that are not easy to understand. In Fig. 2.2 we show the results for spectra computed with a resolution of R = 90 000 for a centred magnetic dipole seen at 3 different rotational phases, viz. 0.00, 0.25. 0.50 and the following parameter values: i = 30◦ , β = 20◦ , v sin i = 10, 50 and 90 km s−1 , Bp = 0.5 and 2.0 kG. The effective field LSD Beff determined with the help of LSD is then compared to the theoretical effective magnetic field value Beff , which is defined as the integral over the visible hemisphere 26 O N THE RELIABILITY OF THE LSD METHOD Figure 2.2: For a centred magnetic dipole seen at three different rotational phases (φ = 0.00, 0.25, 0.50 from top to bottom) and with 2 different values of the polar field strength (top 3×3 plot: 500 G, bottom 3×3 plot: 2000 G) we plot the relative differences between the theoretical value B eff of the effective field LSD (defined in Sect. 2.5) and the field Beff measured with the LSD method as a function of the signal-tonoise ratio. Triangles represent the LSD result without final continuum normalisation of the fictitious average line. 27 C HAPTER 2 of the longitudinal field component, weighted by the continuum flux. For the stellar parameters adopted here and the simulated observational condiLSD tions, we find that the differences between Beff and Beff can become quite large. Even under excellent observational conditions, with S/N= 900, the relative differLSD ence ∆ = (Beff − Beff )/Beff can be as large as 0.6. Contrary to our expectations, the values of ∆ do not decrease for weak fields. The Bp values recovered depend little on the geometry (i and β) and thus seem to be mainly related to the process of combining spectral lines, that have different Stokes V signatures. Table 2.2 lists the LSD results for R = 90 000 and S/N = 900. We note that even in this favourable case of very high-quality observations, errors – particularly in the β values – can become quite large and the results concerning magnetic geometries therefore unreliable. There is no clear improvement in the LSD results when the continuum is not normalised. 2.6 Conclusions A considerable number of synthetic Stokes spectra have been computed with the COSSAM code for various dipolar magnetic geometries and stellar rotational velocities. The spectra have subsequently been converted from constant wavelength step to constant resolving power (corresponding to typical échelle observations), and noise has been added. None of the simplifying assumptions underlying LSD (see Subsect. 2.4.2) enter COSSAM and Eq. (2.2) applied to these spectra usually yields effective field values in reasonably close agreement with the theoretical values. The very few spectral lines subject to the partial Paschen-Back effect can easily be excluded from or altogether neglected in the analysis. COSSAM thus appears an appropriate tool for testing the reliability of stellar magnetic modelling based on LSD measurements. If we compare the results of the COG method using Eq. 2.2 to those obtained with the LSD method, we have to conclude that the simplifying assumptions necessary to build the fictitious high signal-to-noise Stokes I and V signatures result in significant deviations, typically 20-30% in the idealised case of noise-free spectra. In many real life cases, even with noise at the 0.1% level, the magnetic geometries recovered from LSD measurements show large deviations. We conclude that the LSD method is a powerful tool to enhance the S/N ratio of some average polarisation signal that would otherwise remain undetectable, but that it is in general less reliable for the modelling of stellar magnetic topologies. Magnetic geometries derived from LSD measurements have to be treated with caution, even when they are based on extremely high S/N ratio spectra. Acknowledgements. RSS and HFH thankfully acknowledge the generous hospitality of the Osservatorio Astrofisico di Catania during their visit. MJS is grateful for support by the Austrian Science Fund (FWF), project P16003-N05 ”Radiation driven diffusion in magnetic stellar atmospheres”. 28 O N THE RELIABILITY OF THE LSD METHOD Table 2.2: Magnetic geometries recovered from LSD effective magnetic field measurements of synthetic COSSAM I and V spectra, computed for a centred magnetic dipole and sampled with a spectral resolution of R = 90 000 and S/N = 900, i.e. similar to very high-quality observations. The LSD method has been applied with and without continuum normalisation of the fictitious average line. Models for i = 10◦ and ve sin i = 90 km s−1 have not been calculated as this would imply supercritical rotation. LSD Input i = 10◦ β Bp [G] 20 100 20 500 20 2000 20 10000 40 100 40 500 40 2000 40 10000 80 100 80 500 80 2000 80 10000 i = 30◦ 20 100 20 500 20 2000 20 10000 40 100 40 500 40 2000 40 10000 80 100 80 500 80 2000 80 10000 i = 70◦ 20 100 20 500 20 2000 20 10000 40 100 40 500 40 2000 40 10000 80 100 80 500 80 2000 80 10000 10 β 61.4 18.4 13.4 19.3 69.5 44.5 41.5 39.3 13.2 64.9 79.6 80.5 ve sin i [km s−1 ] 50 Bp [G] 486 716 2760 12600 473 712 2817 12622 247 445 2795 13582 β Bp [G] 61.3 359 18.3 531 13.3 2050 19.5 9548 69.5 351 44.5 528 41.6 2094 39.5 9562 13.2 183 64.9 331 79.6 2075 80.5 10238 90 β Bp [G] LSD (without continuum normalisation) ve sin i [km s−1 ] 10 50 90 β Bp [G] β Bp [G] 70.6 359 13.4 509 40.8 414 77.4 659 23.7 1635 6.4 1358 19.3 7207 13.5 7665 81.3 426 14.2 282 33.6 562 32.4 442 48.0 1654 62.7 2753 39.2 7185 36.5 7380 12.2 173 57.5 503 76.2 662 89.2 1426 81.8 1851 69.5 896 80.0 7257 79.3 7639 β Bp [G] 32.3 79 32.5 22.0 776 22.1 20.5 2780 20.5 19.4 12396 19.6 7.7 132 7.7 49.6 572 49.5 39.4 2732 39.4 39.4 12342 39.5 63.7 112 63.8 72.7 658 72.7 80.5 2892 80.5 80.5 12642 80.4 56 548 1968 8993 93 404 1934 8959 79 465 2046 9130 36.8 116 31.4 511 18.7 2279 20.4 10658 70.1 53 21.4 625 41.1 2114 38.8 10710 77.4 66 83.1 716 81.1 1980 80.8 10888 36.8 31.4 18.7 20.6 70.4 21.5 41.1 39.0 77.4 83.1 81.1 80.8 71 313 1397 6740 33 382 1297 6780 40 438 1213 6849 28.2 54.0 26.6 14.0 15.3 13.4 32.0 37.7 69.0 12.1 77.4 78.0 256 648 1572 7750 440 420 1239 7617 101 205 1649 7779 28.2 54.0 26.6 14.4 15.2 13.3 32.0 37.9 69.1 12.1 77.4 77.9 137 348 848 4327 236 225 667 4263 54 110 887 4318 76.9 125 76.8 29.2 569 29.3 22.1 2686 22.1 19.9 12641 19.9 32.3 123 32.1 41.6 671 41.6 41.6 2800 41.6 41.2 12213 41.1 70.4 159 70.4 66.7 705 66.7 78.2 2734 78.1 79.9 12338 79.8 88 402 1901 9136 87 474 1982 8858 112 498 1936 8949 11.7 223 75.1 64 21.8 2228 20.2 11087 22.1 292 72.7 485 43.0 1989 40.1 10648 69.6 126 90.0 629 75.5 2348 79.2 10614 11.6 75.2 21.8 20.2 22.0 72.6 43.0 40.0 69.7 0.0 75.5 79.0 137 39 1365 6979 178 297 1219 6733 77 1055 1439 6711 13.6 34.8 25.2 21.1 4.9 48.4 21.8 41.7 4.7 50.5 5.1 81.1 71 142 1071 7785 467 213 1433 7729 294 72 1644 7592 13.1 35.0 25.3 21.1 5.0 48.6 21.8 41.5 4.7 50.5 5.2 80.8 38 76 576 4329 251 114 771 4313 158 39 885 4243 29 C HAPTER 2 Bibliography Babcock, H. W. 1947, ApJ, 105, 105 Carter, B., Brown, S., Donati, J.-F., Rees, D., & Semel, M. 1996, Publications of the Astronomical Society of Australia, 13, 150 Claret, A. 2004, A&A, 428, 1001 Donati, J.-F., Semel, M., Carter, B. D., Rees, D. E., & Collier Cameron, A. 1997, MNRAS, 291, 658 Donati, J.-F., Wade, G. A., Babel, J., Henrichs, H. F., de Jong, J. A., & Harries, T. J. 2001, MNRAS, 326, 1265 Kurucz, R. 1993, CDROM Model Distribution, Smithsonian Astrophys. Obs. Leone, F. & Catanzaro, G. 2004, A&A, 425, 271 Mathys, G. 1989, Fundamentals of Cosmic Physics, 13, 143 Piskunov, N. E., Kupka, F., Ryabchikova, T. A., Weiss, W. W., & Jeffery, C. S. 1995, A&AS, 112, 525 Preston, G. W. 1971, PASP, 83, 571 Schwarzschild, M. 1950, ApJ, 112, 222 Semel, M. 1989, A&A, 225, 456 Semel, M. 1995, in ASP Conf. Ser. 71: IAU Colloq. 149: Tridimensional Optical Spectroscopic Methods in Astrophysics, ed. G. Comte & M. Marcelin, 340 Semel, M. & Li, J. 1996, Sol. Phys., 164, 417 Stift, M. J. 2000, A Peculiar Newsletter, 33, 27 Stift, M. J. & Leone, F. 2003, A&A, 398, 411 Wade, G. A., Bagnulo, S., Kochukhov, O., Landstreet, J. D., Piskunov, N., & Stift, M. J. 2001, A&A, 374, 265 30 Het moet nu maar eens uit zijn met dat gepraat over mijn sufheid. Ik ben niet traag, maar ik denk dieper, dat is het. Heer Bommel C HAPTER 3 D ISCOVERY OF THE MAGNETIC FIELD IN THE PULSATING B STAR β C EPHEI ∗ H. F. Henrichs, J. A. de Jong, E. Verdugo, R. S. Schnerr, C. Neiner, J.-F. Donati, C. Catala, S. L. S. Shorlin, G. A. Wade, P. M. Veen, J. S. Nichols, A. Talavera, G. M. Hill, L. Kaper, A. M. Tijani, V. C. Geers, K. Wiersema, B. Plaggenborg, K. L. J. Rygl Astronomy and Astrophysics, (to be submitted) Abstract The 12 day periodicity and the type of variations in the UV stellar wind lines of β Cephei are very similar to what is observed in magnetic He-peculiar B stars. The presence of a magnetic field in the slowly rotating B1 IV star β Cep had been predicted. We present results of magnetic field measurements of β Cep from the discovery of its magnetic field in 1998 to 2005, and make a comparison with the wind variability in UV spectral lines. From a series of 124 time-resolved circular polarisation spectra obtained with the MuSiCoS echelle spectropolarimeter at the 2m Telescope Bernard Lyot, we show that β Cep hosts a weak magnetic field whose line-of-sight component varies sinusoidally with an amplitude of 93±4 G around an average value of 1±3 G. From the variability of UV stellar wind lines we derive a period of 12.00075(11) days, which is the rotation period of the star and compatible with the modulation of the magnetic field. Phases of maximum and minimum longitudinal field are found to match those of maximum emission in the UV wind lines. This strongly supports an oblique magnetic-rotator model for this star, sharing some similarities with helium peculiar stars. We discuss the magnetic behaviour as a function of pulsation behaviour and UV line variability. We also analyse the short- and long-term radial velocity variations, due to the pulsations and 90-year binary motion, respectively. This is the first confirmed detection of a dipolar magnetic field in an upper main-sequence pulsating star. The wind emission originates in the magnetic equator, with maximum emission occurring when the magnetic northpole points to the Earth. The observed radial velocities are in agreement with the predicted values for a ∼90-year period around its close binary companion. ∗ Based on observations obtained using the MuSiCoS spectropolarimeter at the Observatoire du Pic du Midi, and by the International Ultraviolet Explorer, collected at NASA Goddard Space Flight Center and Villafranca Satellite Tracking Station of the European Space Agency. 33 C HAPTER 3 3.1 Introduction The star β Cep (HR 8238, HIP 106032, HD 205021) has been classified as spectral type B1 III by Lesh (1968), but earlier references give also B2 III or B1 IV, whereas Morel et al. (2006) assigned a revised spectral type of B1Vevar. The Be status of this star has been dismissed by Schnerr et al. (2006) who unambiguously demonstrated by using spectroastrometry that the intermittent Hα emission often encountered in spectra of β Cep in fact originated from the 3.4 magnitude fainter very close companion star, classified as B6-8, which is normally unresolved except by speckle techniques. This companion was discovered with the 200-inch Hale telescope by Gezari et al. (1972) and its orbit with an approximate period of 90 years was determined by Pigulski & Boratyn (1992). The star β Cephei is the prototype of the β Cephei class of pulsating stars (Frost & Adams 1903). Its multiperiodic photometric and spectroscopic lineprofile variability have been studied extensively (Heynderickx et al. 1994; Telting et al. 1997; Shibahashi & Aerts 2000). In addition to the main pulsation period of 4h 34m , the star exhibits a very significant period of 12 d in the equivalent width of the ultraviolet resonance lines. At its discovery by Fischel & Sparks (1972) with the OAO-2 satellite there was still an ambiguity between 6 and 12 days, but later investigations with IUE data (Henrichs et al. 1993, 1998) left no doubt that the two minima in equivalent width of the C IV stellar wind lines, which are separated by 6 d, are unequal, and that the real period is 12 d. Henrichs et al. (1993) proposed that the UV periodicity arises from the 12 d rotational period of the star and suggested that the stellar wind is modulated by an oblique dipolar magnetic field at the surface. Support for this hypothesis was given by the striking similarity between the UVline behaviour of β Cep and of well-known chemically peculiar magnetic B stars, for example the B2 V helium-strong star HD 184927 (Barker et al. 1982; Wade et al. 1997). There is a reported (but not confirmed) average magnetic field strength of B = (810 ± 170) G for β Cep itself by Rudy & Kemp (1978). A rotational period of 12 days corresponds well with an adopted radius between 6 and 10 solar radii, given the reported values of 20 – 43 km s−1 for vsini. To verify this hypothesis Henrichs et al. (1993) presented new magnetic field measurements obtained by one of us (GH) with the University of Western Ontario photoelectric Pockels cell polarimeter and 1.2m telescope, simultaneously with UV spectroscopy with the IUE satellite. The technique to measure the magnetic field was differential circular polarimetry in the Hβ line (Landstreet 1982, and references therein). The 12 day UV period in the equivalent width of the stellar wind lines of C IV, Si III, Si IV and N V was confirmed, but the values for the magnetic field with 1σ error bars of about 150 G, comparable to the measured field strength, were much lower than the value reported by Rudy & Kemp (1978). Additional magnetic measurements with the same instrumentation by G. Hill (see Fig. 3.1) could not confirm the 12 d period, which was unexplained. It also remained puzzling why these new magnetic field measurements showed a much lower field than in 1987. The suggestion was put forward that perhaps the new Be phase of the star, discovered in July 34 D ISCOVERY OF THE MAGNETIC FIELD IN THE PULSATING B STAR β C EPHEI 1200 G. Hill, G. Wade, UWO, Hβ β Cep B1 IV October 1991 – October 1995 1000 P = 12.00075 days (fixed) 800 600 Blong(G) 400 200 0 –200 –400 –600 –800 –1000 –1200 0 0.2 0.4 0.6 Rotational Phase 0.8 1 Figure 3.1: Early magnetic measurements of β Cep obtained with the University of Western Ontario photoelectric Pockels cell polarimeter and 1.2m telescope. Typical exposure times were between 1 and 3.5 hours. The dashed curve is the same as in Fig. 3.4. 1990 by Mathias et al. (1991), (see also Kaper et al. 1992; Kaper & Mathias 1995), might have been related to the decrease in magnetic field strength, but this could not be tested, and which is now entirely obsolete by the discovery by Schnerr et al. (2006) that the emission stems from the binary companion. A possible explanation of the discordance between the magnetic field measurements from the Hβ line and those given below might be that Hβ may have been partially filled in with emission, as Hα was in emission during the time of observations. These considerations motivated us to undertake new magnetic measurements of β Cep with the much more sensitive MuSiCoS polarimeter at the Pic du Midi observatory in France. Using this instrument has the clear advantage that all available (mostly metallic) lines can be selected in the spectrum, rather than just one Balmer line, which may be contaminated with some emission. The present paper presents and discusses the discovery measurements, and analyzes the correlation of magnetic, pulsation and UV behaviour. The magnetic field of β Cep was discovered on December 13th, 1998, followed by 22 observations in January and June/July 1999, such that the rotational period was sufficiently well covered, allowing a first assessment. In an earlier stage of writing the current paper we decided to separately publish the model calculations based on these first 23 measurements (Donati et al. 2001), which would take much less time to complete in view of the extended data analysis and difficult interpretation of the odd behaviour of the variable Hα emission to follow. In that paper we also included a discussion of the stellar parameters, which we have summarized in Table 3.1. The model calculations were constrained by the observed X-ray emission as observed by Berghöfer et al. (1996). Donati et al. (2001) also devote a discussion to possible implications of the magnetic field of β Cep for understanding the Be phenomenon, which appears now academic. As the variabil35 C HAPTER 3 Table 3.1: Adopted stellar parameters for β Cep. Spectral Type V dHipparcos (pc) MV Mbol log(L/L ) Teff log g (cm s−2 ) R/R M/M vsini (km s−1 ) Prot (d) B1 IV 3.2±0.1 182±17 −5.8±0.2 −5.57±0.49 4.12±0.20 26 000 K 3.7 6.5±1.2 12 27±4 12.000752 ±0.000107 ity of the Hα line stems from the companion of β Cep we do not discuss this aspect in the current paper. In Section 3.2 we describe the experimental setup and the observations. Section 3.3 summarizes the data reduction and the results. In Section 3.4 we derive the system velocity and compare the known periodicities in β Cep with the magnetic measurements. In the last section we give our conclusions and discuss the implications of the current measurements. 3.2 Experimental setup and observations We obtained circular polarisation (Stokes V ) and total intensity (Stokes I) of β Cep, using the MuSiCoS spectropolarimeter mounted on the 2 m T élescope Bernard Lyot (TBL) at the Observatoire du Pic du Midi. The strategy of the observations was threefold: (1) to cover the known 12 d period of the UV lines, (2) to have reasonable coverage during one pulsational period of 4.6 h, and (3) to study the behaviour at a half-year timescale. The journal of observations is given in Table 3.2. The setup consisted of the MuSiCoS fiber-fed cross dispersed échelle spectrograph (Baudrand & Bohm 1992; Catala et al. 1993) with a dedicated polarimetric unit (described by Donati et al. 1999) mounted at the Cassegrain focus. The light passes through a rotatable quarter wave plate, converting the circular polarisation into linear, after which the beam is split into two beams with a linear polarisation along and perpendicular to the instrumental reference azimuth, respectively. Two fibers transport the light to the spectrograph, where both orthogonal polarisation states are simultaneously recorded. The spectral coverage in one exposure is from 450 to 660 nm with a resolving power of about 35000. The Site CCD detector with 1024×1024 of 24µ pixels was used, which has a quantum efficiency exceeding 50% in the U band. 36 D ISCOVERY OF THE MAGNETIC FIELD IN THE PULSATING B STAR β C EPHEI Table 3.2: Journal of observations and results of magnetic measurements of MuSiCoS spectropolarimetry of β Cep at TBL at the Pic du Midi, 1998 – 2000. The Barycentric Julian date is given at the center of the exposure time (texp ). Column 5 lists the quality of the Stokes V spectra, expressed as the S/N per 4.5 km s−1 around 550 nm in the raw spectrum, and the relative rms noise level NLSD (per 4.5 km s−1 velocity bin) in the Least-Squares Deconvolved Stokes V spectra (column 8). The phase in the radial velocity curve (with phase 0 defined at maximum) has been calculated with the ephemeris given by Pigulski & Boratyn (1992) in column 7. The UV (rotational) phase in column 8 has been derived from Eq. 3.3. The measured radial velocity (accuracy: 2.5 km s −1 ) is given in column 9, whereas the velocity shift, measured at minimum flux, used before calculating the magnetic field is given in column 10. Columns 11 and 12 give the magnetic field values with their 1-σ uncertainties. The last two columns give the computed magnetic values of the diagnostic null (or N ) spectrum, also with their 1-σ uncertainties. No. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 Date 1998 Dec. 1998 Dec. 1998 Dec. 1998 Dec. 1998 Dec. 1998 Dec. 1998 Dec. 1998 Dec. 1998 Dec. 1998 Dec. 1998 Dec. 1999 Jan. 1999 Jan. 1999 Jan. 1999 Jan. 1999 June 1999 June 1999 June 1999 July 1999 July 1999 July 1999 July 1999 July 2000 June 2000 June 2000 June 2000 June 2000 June 2000 June 2000 June 2000 July 2000 July 2000 July 2000 July 2000 July 2000 July 2000 July 2000 July HJD texp S/N −2451100 min pxl−1 13 61.340 20 290 14 62.337 40 310 15 63.335 40 1160 16 64.345 40 450 17 65.246 20 920 17 65.342 30 1050 18 66.256 40 740 18 66.290 30 770 18 66.314 30 950 18 66.338 30 940 18 66.368 27 910 13 92.256 40 760 15 94.256 20 500 24 103.263 20 660 25 104.271 24 530 30 259.504 40 690 30 259.545 60 640 30 260.492 40 670 1 260.527 50 770 3 262.512 60 830 3 263.486 60 680 6 266.467 40 760 7 267.417 60 790 17 612.632 40 890 21 616.592 48 930 26 621.569 40 980 26 621.600 40 980 28 623.641 28 640 29 624.635 40 910 30 625.643 40 800 5 630.614 20 530 5 630.631 20 540 5 630.648 20 500 6 631.615 20 490 6 631.651 20 380 7 632.667 20 500 8 634.464 28 680 13 638.62 20 450 NLSD % 0.042 0.038 0.010 0.025 0.012 0.010 0.016 0.015 0.011 0.010 0.011 0.015 0.023 0.017 0.021 0.017 0.016 0.016 0.014 0.013 0.014 0.011 0.009 0.014 0.014 0.013 0.013 0.021 0.014 0.017 0.025 0.025 0.028 0.028 0.035 0.026 0.018 0.029 Puls. Phase 0.092 0.331 0.567 0.870 0.601 0.103 0.904 0.080 0.207 0.334 0.489 0.397 0.893 0.180 0.474 0.406 0.622 0.590 0.774 0.197 0.312 0.960 0.950 0.241 0.030 0.158 0.320 0.035 0.253 0.545 0.642 0.731 0.820 0.897 0.086 0.419 0.853 0.677 37 UV Vrad Vmin Phase km s−1 0.600 −23.8 −24.2 0.683 −4.9 −0.6 0.766 −14.1 −13.2 0.851 −34.5 −38.9 0.926 −16.3 −16.3 0.934 −23.0 −24.4 0.010 −35.0 −39.7 0.013 −23.4 −25.0 0.015 −12.3 −9.8 0.017 −3.4 1.1 0.019 −7.1 −3.3 0.176 −4.7 0.2 0.343 −34.9 −40.5 0.094 −13.8 −12.2 0.178 −5.5 −0.9 0.113 −2.6 1.8 0.116 −21.5 −21.8 0.195 −17.6 −16.2 0.198 −31.3 −33.6 0.363 −8.4 −8.6 0.445 −1.4 2.0 0.693 −28.1 −29.7 0.772 −27.7 −30.7 0.538 7.9 3.2 0.868 −20.7 −16.7 0.283 −0.7 −3.4 0.286 7.0 3.6 0.456 −18.0 −15.5 0.539 4.4 0.3 0.623 −8.6 −10.2 0.037 −21.9 −19.8 0.038 −30.0 −26.0 0.040 −33.1 −28.3 0.120 −29.7 −26.7 0.123 −9.9 −10.6 0.208 6.6 1.7 0.358 −34.2 −28.2 0.690 −23.5 −22.4 Bl σ(Bl ) Nl σ(Nl ) G G G G −118 63 20 63 −107 59 32 59 28 15 12 15 73 38 21 38 78 18 10 17 76 14 −20 14 103 23 −24 23 78 22 −42 22 88 16 −14 16 117 15 −9 15 100 17 17 16 29 23 −2 22 −122 34 13 34 90 26 −0 26 97 31 12 31 31 25 −8 25 43 25 40 25 43 24 −8 24 2 21 −10 21 −54 20 8 19 −71 21 −34 20 −42 16 −37 16 −5 13 −27 13 −69 20 −2 17 94 21 27 19 31 18 −18 16 19 19 8 15 −4 31 −7 29 −35 21 15 18 −59 26 −23 21 137 37 −10 34 84 38 54 36 16 40 −16 38 70 40 1 38 107 50 −60 49 100 38 6 37 −41 26 11 24 −130 46 11 43 C HAPTER 3 Table 3.2: continued. No. 16 17 18 19 20 21 1 2 3 4 5 6 7 8 9 10 11 13 14 15 16 17 19 20 21 22 23 24 25 26 27 28 29 30 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 Date 2000 July 2000 July 2000 July 2000 July 2000 July 2000 July 2001 June 2001 June 2001 June 2001 June 2001 June 2001 June 2001 June 2001 June 2001 June 2001 June 2001 June 2001 June 2001 June 2001 June 2001 June 2001 June 2001 June 2001 June 2001 June 2001 June 2001 June 2001 June 2001 June 2001 June 2001 July 2001 July 2001 July 2001 July 2002 June 2002 June 2002 June 2002 June 2002 June 2002 June 2002 June 2002 June 2002 June 2002 June 2002 June 2002 June 2002 June 2002 June 2002 June 2002 June 2002 June HJD texp S/N −2451100 min pxl−1 13 638.638 20 460 17 642.581 20 600 17 642.598 20 670 17 642.615 20 630 17 642.631 20 580 17 642.648 20 630 20 980.602 20 580 20 980.619 20 590 20 980.637 20 590 21 981.612 20 730 21 981.630 20 600 21 981.656 16 480 22 982.626 20 740 22 982.643 20 660 23 983.628 20 240 24 984.554 20 650 24 984.571 20 710 25 985.523 20 610 25 985.540 20 630 26 986.541 20 600 26 986.562 20 300 27 987.485 20 270 27 987.502 20 410 27 987.520 20 400 29 989.531 20 570 29 989.548 20 540 30 990.533 20 690 30 990.553 20 670 1 991.573 20 560 1 991.591 20 640 2 992.535 20 620 2 992.554 20 560 3 993.539 20 730 3 993.557 20 750 11 1336.517 20 570 12 1337.521 20 520 13 1338.537 28 450 14 1339.547 28 530 15 1340.511 20 400 16 1341.529 20 540 17 1342.508 20 510 17 1343.444 28 710 17 1343.465 28 740 18 1344.463 28 570 18 1344.484 28 700 21 1346.524 20 490 21 1346.540 20 510 22 1348.497 20 690 24 1350.438 28 710 26 1351.531 28 710 27 1352.556 28 300 NLSD % 0.028 0.021 0.020 0.021 0.023 0.020 0.020 0.020 0.019 0.015 0.018 0.026 0.016 0.017 0.055 0.018 0.017 0.020 0.019 0.021 0.042 0.047 0.030 0.030 0.020 0.023 0.017 0.017 0.020 0.018 0.019 0.022 0.017 0.016 0.021 0.026 0.028 0.025 0.032 0.024 0.024 0.018 0.017 0.021 0.018 0.027 0.025 0.018 0.017 0.018 0.043 Puls. Phase 0.766 0.465 0.555 0.644 0.728 0.817 0.991 0.080 0.175 0.293 0.388 0.524 0.617 0.706 0.877 0.739 0.828 0.826 0.915 0.170 0.280 0.126 0.215 0.310 0.867 0.956 0.128 0.233 0.588 0.682 0.638 0.738 0.909 0.003 0.457 0.728 0.062 0.364 0.425 0.769 0.908 0.822 0.932 0.172 0.282 0.991 0.075 0.349 0.539 0.277 0.658 38 UV Vrad Vmin Phase km s−1 0.705 −30.1 −27.9 0.034 −2.7 −5.1 0.035 −13.3 −13.4 0.037 −23.6 −21.3 0.038 −31.3 −27.3 0.040 −32.2 −27.9 0.201 −14.1 −12.9 0.202 −5.2 −1.8 0.203 2.8 7.7 0.285 7.1 10.9 0.286 3.6 6.5 0.288 −2.2 −0.3 0.369 −15.9 −20.1 0.371 −22.2 −27.8 0.453 −24.6 −30.3 0.530 −25.7 −29.6 0.531 −25.9 −30.2 0.611 −26.1 −29.9 0.612 −21.3 −23.4 0.695 3.2 8.5 0.697 9.2 15.1 0.774 0.5 2.8 0.776 5.8 9.1 0.777 7.7 11.5 0.945 −23.7 −28.4 0.946 −17.4 −21.0 0.028 −2.2 −0.8 0.030 5.5 9.4 0.115 −13.4 −13.7 0.116 −22.1 −24.3 0.195 −20.0 −21.4 0.197 −25.9 −29.0 0.279 −21.1 −24.4 0.280 −13.1 −14.2 0.858 3.4 5.3 0.942 −23.3 −28.4 0.027 −6.6 −7.3 0.111 7.7 12.5 0.191 3.6 7.8 0.276 −24.8 −30.0 0.358 −21.9 −26.8 0.436 −24.8 −30.0 0.437 −19.8 −23.9 0.520 3.1 7.0 0.522 9.9 15.9 0.692 −15.6 −15.1 0.694 −7.4 −4.2 0.857 6.2 9.5 0.018 −8.9 −7.9 0.109 7.2 13.0 0.195 −22.3 −24.1 Bl σ(Bl ) Nl σ(Nl ) G G G G −20 43 −11 39 93 31 −35 30 66 30 8 28 136 31 9 30 164 34 8 33 94 30 −26 29 46 30 −37 29 53 30 21 29 9 29 50 29 −33 22 −11 21 14 27 −2 27 2 40 −27 39 −54 24 17 23 −114 27 29 26 −144 85 87 85 −136 28 −4 26 −101 26 4 25 −97 31 −5 29 −57 29 10 27 −10 32 31 29 −12 64 41 62 127 71 59 71 46 45 −16 44 −18 46 15 47 106 31 −40 30 85 34 24 34 85 26 −24 26 97 26 −22 25 74 31 −14 30 136 28 21 28 23 30 −28 29 83 34 −49 33 −9 26 18 25 −21 24 16 23 98 31 −22 31 51 37 35 37 108 39 1 39 99 36 6 34 19 45 58 44 −75 34 −31 34 −84 34 −1 33 −62 25 −2 24 −93 24 −12 24 −62 29 10 29 −133 26 −5 26 −88 38 37 37 −19 35 24 35 79 26 −18 26 86 25 −37 24 69 26 −12 25 −38 61 31 60 D ISCOVERY OF THE MAGNETIC FIELD IN THE PULSATING B STAR β C EPHEI Table 3.2: continued. No. 18 1 2 3 4 5 6 7 8 9 10 11 12 1 2 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 1 2 Date HJD texp S/N −2451100 min pxl−1 2002 June 27 1352.578 28 540 2003 June 7 1697.613 27 580 2003 June 9 1700.499 27 440 2003 June 12 1702.545 28 430 2003 June 14 1704.575 20 550 2003 June 17 1707.647 20 590 2003 June 18 1709.449 24 640 2003 June 18 1709.469 24 730 2003 June 20 1711.455 32 510 2003 July 8 1728.553 28 550 2003 July 26 1746.557 40 460 2003 July 30 1751.504 40 730 2003 Aug. 6 1757.536 40 830 2004 Jun 2 2058.564 35 830 2004 Jun 8 2064.510 35 910 2004 July 12 2098.508 35 600 2004 July 15 2101.505 35 910 2004 July 20 2106.571 35 570 2004 July 25 2111.532 35 700 2004 July 26 2112.575 35 730 2004 July 27 2114.500 35 870 2004 July 30 2116.502 35 750 2004 July 30 2117.446 35 790 2004 Aug 7 2124.507 35 310 2004 Aug 10 2128.459 35 640 2004 Aug 12 2130.491 35 880 2004 Aug 14 2132.457 35 700 2004 Aug 24 2142.409 35 590 2004 Nov 17 2227.271 47 900 2004 Nov 21 2231.258 47 920 2004 Nov 23 2233.272 47 970 2004 Nov 25 2235.302 47 980 2004 Nov 27 2237.289 47 750 2005 Jul 15 2466.629 20 710 2005 Jul 15 2466.645 20 750 NLSD % 0.025 0.022 0.027 0.032 0.021 0.021 0.018 0.017 0.026 0.023 0.026 0.016 0.013 0.018 0.024 0.024 0.017 0.026 0.020 0.019 0.017 0.021 0.018 0.052 0.021 0.017 0.020 0.024 0.016 0.016 0.016 0.016 0.019 0.020 0.019 Puls. Phase 0.773 0.119 0.270 0.014 0.671 0.798 0.258 0.361 0.787 0.550 0.065 0.033 0.700 0.024 0.238 0.721 0.455 0.050 0.095 0.571 0.673 0.183 0.138 0.210 0.954 0.622 0.946 0.191 0.694 0.627 0.198 0.854 0.285 0.262 0.349 UV Vrad Vmin Phase km s−1 0.197 −28.0 −30.0 0.948 −0.3 0.5 0.188 10.9 16.0 0.359 −12.6 −15.7 0.528 −18.0 −20.3 0.784 −23.9 −29.3 0.934 8.5 12.7 0.936 8.9 13.4 0.101 −26.1 −29.6 0.526 −11.4 −11.4 0.026 −15.6 −16.9 0.438 −17.6 −20.1 0.941 −32.3 −36.4 0.016 −19.6 −16.9 0.512 7.5 2.1 0.345 −23.0 −18.2 0.594 11.9 7.2 0.017 −10.3 −8.5 0.430 −3.7 −3.3 0.517 −5.5 −5.7 0.677 −14.8 −13.6 0.844 7.9 5.1 0.923 3.7 2.0 0.511 14.3 10.0 0.840 −21.6 −17.3 0.010 −12.4 −10.9 0.174 −17.9 −17.1 0.003 9.4 6.2 0.074 −16.2 −13.9 0.406 −8.0 −5.0 0.574 14.1 10.8 0.743 −20.9 −17.3 0.909 21.3 17.3 0.019 12.0 8.7 0.021 17.4 12.8 Bl σ(Bl ) Nl σ(Nl ) G G G G 59 34 8 35 59 31 −7 30 39 39 41 38 −65 45 58 43 −41 32 −40 32 23 30 22 30 102 26 29 26 96 24 −8 24 10 37 22 36 −72 34 47 33 87 37 −11 36 −117 23 −11 23 96 19 −9 19 95 24 21 24 −107 27 −7 22 −47 35 −34 33 −120 25 −15 22 66 39 6 37 −103 29 −8 26 −141 29 −31 26 −80 25 −49 22 59 31 −9 27 118 26 35 24 −56 76 40 72 4 30 −9 27 36 25 −15 22 10 29 −11 27 32 36 34 34 80 24 −6 22 −95 24 2 22 −61 23 10 21 −36 23 −15 20 108 29 −20 27 113 30 10 28 66 28 35 26 A complete Stokes V measurement consists of four subsequent subexposures between which the quarter wave plate is rotated such that a sequence is obtained with -45/45/45/-45 degrees angle (called the q1-q3-q3-q1 sequence), such that the two beams are exchanged throughout the whole instrument. With such a sequence all systematic spurious circular polarisation signals down to 0.002% rms can be suppressed (Donati et al. 1997, 1999; Wade et al. 2000). At the beginning and at the end of each night we took 15 flatfield exposures, whereas wavelength calibrations with a Th-Ar lamp were taken several times per night, in addition to the usual bias frames and polarisation check exposures. For the reduction we used the flatfield series nearest in time to the observations. 39 C HAPTER 3 3.3 Data reduction and results The data reduction was done with the dedicated ESpRIT reduction package, described by Donati et al. (1997). With this package the geometry of the orders on the CCD is first determined, and after an automatic wavelength calibration on the Th-Ar frames, a rigorous optimal extraction of the orders is performed. The method we used to calculate the magnetic field strenght includes a least-squares deconvolution (LSD) to calculate a normalised average Stokes I line profile and corresponding Stokes V line profiles using as many as possible spectral lines. The presence of a magnetic field will result in a typical Zeeman signature in the average Stokes V profile, from which the effective longitudinal component (B` ) of the stellar magnetic field can be determined by taking the first-order moment using the well-known relation (Mathys 1989; Donati et al. 1997): R vV (v)dv 11 R , (3.1) B` = (−2.14 × 10 G) λgc [1 − I(v)]dv where λ, in nm, is the mean wavelength, c is the velocity of light in cm s −1 (the same units as the velocity v), and g is the mean value of the Land é factors of all lines used to construct the LSD profile. We used λ = 512.5 nm and g = 1.234. The noise in the LSD spectra was measured and given in Table 3.2, along with the signal to noise ratio obtained in the raw data. The profiles were normalised outside the regions [−120, 120] km s−1 . Three important effects appeared decisive for the final outcome of the magnetic results. The absolute values of B` are impacted by fringes, which are present in many spectra, the selection of spectral lines for the LSD analysis, and the limits of integration in Eq. 3.1, which we discuss in turn. 3.3.1 Correction for fringes Many Stokes V spectra appeared to be strongly affected by interference fringes created by the quarter-wave plate. These fringes could induce a spurious Zeeman detection which could modify the value of the measured longitudinal magnetic field. We have eliminated the fringes from the spectra using a Stokes V spectrum of Vega, which was taken during the 1999 June run and which carries no detectable Zeeman signature. This template spectrum is smoothed with a running 20-points mean in order to remove any possible features which could modify the β Cep Stokes V spectra during the correction process. In this way we assure that only the (sine-wave like) fringe pattern remains. The spectra to be corrected are then divided by the template. The method is illustrated in Fig. 3.2 showing an overplot of the smoothed Vega spectrum and the Stokes V spectrum nr. 22 (1999) of β Cep, together with the resulting spectrum. After application of this procedure the error bars improved with typically 10% to 20%, whereas in some cases the resulting magnetic values shifted dramatically by more than 50 G, which showed the imperative necessity to correct for the 40 V/I V/I D ISCOVERY OF THE MAGNETIC FIELD IN THE PULSATING B STAR β C EPHEI Figure 3.2: Top: Overplot of a smoothed Stokes V spectrum of Vega (dashed line) and a Stokes V spectrum of β Cep (1999, nr. 22), both containing a strong spurious modulation caused by fringing on the CCD. Bottom: Stokes V spectrum of β Cep after removal of the fringes. fringes. Table 3.3 gives numerical examples, including the cumulative effects of the selected line list, discussed below. We could not apply the fringe correction to the dataset obtained in June 2000 because no suitable spectrum of Vega or a similar star was available. 3.3.2 Effect of the spectral line list The profiles of 125 relatively weak lines, selected with a table appropriate for early B stars, were combined by means of the LSD method described above in the interval [−243, 243] km s−1 . Many of these lines are blends of multiplets, leaving effectively 77 distinct lines. The selection of lines included in the construction of the LSD profiles appear to have a systematic influence upon the absolute value of the magnetic field. The removal of blends from the list resulted in a larger absolute signal. We also investigated the effect of using measured instead of theoretically calculated line depths. The smallest error bar, and likely resulting in the most reliable value for B` , is obtained when fringe correction is applied, strong blends are excluded and measured line depths are used, as illustrated in Table 3.3. 3.3.3 Limits of integration Applying Eq. 3.1 to calculate B` involves taking the first moment, which implies measuring the asymmetry with respect to the center of the profile. A shift in the radial velocity scale will therefore affect the value of the magnetic field and a proper correction is essential. Because the radial velocity amplitude as a consequence of the pulsation of β Cep is considerable, we shifted the minima of the I profiles (at v min , determined by a parabola fit to the points near the minimum intensity) to zero velocity before calculating the longitudinal field strength. The profiles are often asymmetric, implying that the minimum flux does not occur at the radial velocity (v rad ) of the 41 C HAPTER 3 Table 3.3: Illustrative sample calculations of magnetic-field strength without and with fringe correction and with different selections of spectral lines and weights (line depths) used for the construction of the LSD Stokes V profile. Integration limits of vlimit = 40 km s−1 have been used. Symbols have the same meaning as in Table 3.2. Fringe Bl σ(Bl ) NLSD Nl σ(Nl ) correction G G % G G With all available lines with theoretical depths: 2003 #12 no 102.9 14.2 0.014 −19.6 12.7 2003 #12 yes 88.5 13.0 0.013 −19.6 12.7 2004 #1 no 85.9 16.5 0.017 −8.5 15.0 2004 #2 no −94.4 22.6 0.022 21.9 14.1 Without He blends at 587.5 and 471.3 nm: 2003 #12 no 136.1 15.5 0.015 −14.8 13.8 2003 #12 yes 97.9 14.1 0.013 −14.8 13.8 2004 #1 no 109.1 17.6 0.018 −1.0 15.9 2004 #2 no −114.9 24.5 0.024 29.5 15.2 Without He blends at 587.5 and 471.3 nm with measured linedepths (except blends): 2004 #1 no 93.8 18.5 0.020 −0.8 16.7 2004 #2 no −107.9 25.5 0.027 32.0 15.8 With measured linedepths and without all strong blends: 2004 #1 no 98.8 14.2 0.021 −5.7 12.8 2004 #2 no −89.4 19.3 0.028 23.5 12.1 Spectrum star, which was measured using the first moment of the profile with respect to the barycentric restframe, normalised by the equivalent width (we followed Schrijvers et al. 1997). The measured values of vmin and vrad are included in Table 3.2. We approximated the integral in Eq. 3.1 by a simple summation in a range between ±vlimit and computed the uncertainties as follows: σB` = |B` | s ( P P σ Ii 2 1 − Ii ) 2 + σ vi 2 σ V i 2 P 2 ( vi V i ) P (3.2) The limits of the integral in Eq. 3.1 were carefully determined in order to minimize the uncertainties. We first computed the B` values for 17 different limits between 10 and 90 km s−1 . The full Zeeman signature is obtained when the maximum value for B` is reached. We adopted the average optimum value of several test cases, which was at vlimit = 54 km s−1 . We have also investigated the effect of the asymmetry of the lines (due to the pulsation) by varying the reference center. We find that displacement of more than ±18 km s−1 gives significant lower values for the field strength, but within this range the 42 D ISCOVERY OF THE MAGNETIC FIELD IN THE PULSATING B STAR β C EPHEI 0.001 TBL03, 1998 December 15 LSD profiles of β Cep B = 28 ± 15 G V/IC 0.0005 0 –0.0005 –0.001 I/IC 1 S/N = 1160 0.95 0.9 –150 0.001 –100 –50 TBL10, 1998 December 18 0 Velocity (km/s) 50 0 Velocity (km/s) 50 0 Velocity (km/s) 50 0 Velocity (km/s) 50 100 150 B = 117 ± 15 G V/IC 0.0005 0 –0.0005 –0.001 I/IC 1 S/N = 940 0.95 0.9 –150 0.001 –100 –50 TBL13, 1999 January 15 100 150 B = –122 ± 34 G V/IC 0.0005 0 –0.0005 –0.001 I/IC 1 S/N = 500 0.95 0.9 –150 0.001 –100 –50 TBL21, 1999 July 3 100 150 B = –71 ± 21 G V/Ic 0.0005 0 –0.0005 –0.001 1 I/Ic S/N = 680 0.95 0.9 –150 –100 –50 100 150 Figure 3.3: Representative LSD Stokes unpolarised I (lower panel) and circularly polarised V (upper panel) profiles of β Cep from top to bottom on 15 and 18 December 1998, 15 January and 3 July 1999. The signal to noise ratio (S/N) per velocity bin in the raw data is indicated. Note the clear Zeeman signatures at the zero, positive and negative fields, respectively. The two lower figures illustrate negative fields at almost opposite pulsation phases. In Section 4 we show that the pulsation phase does not influence the magnetic field determination. 43 C HAPTER 3 β Cep B1 IV TBL, MuSiCoS Polarimeter January 1999 June – July 1999 Blong (G) December 1998 150 150 100 100 50 50 0 0 –50 –50 –100 –100 –150 –150 –200 5 10 15 20 45 50 HJD – 2451150 55 210 215 220 –200 Figure 3.4: The longitudinal component of the averaged surface magnetic field of β Cep in December 1998, January, June and July 1999. The dashed curve is a best fit to the magnetic data of a sinusoid with a fixed period of 12.00075 d, as derived from UV data. determined values as well as the error bars remain constant within 4%. For typical examples of Zeeman LSD profiles (Stokes I and V spectrum in velocity space), see Fig. 3.3 for a zero, positive and negative field, respectively, the latter at two different pulsation phases of the star (see also below). We also calculated diagnostic null (or N ) spectra, associated with each Stokes V spectrum, by using subexposures with identical waveplate orientations. This should provide an accurate indication of the noise, and should not give a detectable signal. Upon examination of the N profiles we find that the measured magnetic fields are in most cases consistent with zero, in spite of some spurious signals which are not related to the V profiles. The variable asymmetry in the line profiles has therefore a minor effect on the magnetic field measurements. In Table 3.2 we collected the final results of our calculations, including the calculated values of the N spectra. In Fig. 3.4 the measured values for the first year of observations are plotted as a function of time. We overplotted the best-fit sine function with parameters derived below. 3.4 Period analysis The two main periodicities in β Cep are 4 h 34 m of the radial pulsation mode, studied since 1902, and 12 d in the absorption in the UV wind lines, known since 1972. We investigate whether the observed magnetic variability is related to these periods. 44 D ISCOVERY OF THE MAGNETIC FIELD IN THE PULSATING B STAR β C EPHEI 3.4.1 UV stellar wind period From IUE spectra it is known that the UV stellar wind lines of C IV, Si IV and N V show a very clear 12 day periodicity. In Figs. 3.5, 3.6 and 3.7 we show the behaviour of these doublet UV profiles, along with the significance of variability, where we used a noise model for the high-resolution IUE spectra according to Henrichs et al. (1994) with parameters A = 18, representing the average signal to noise ratio, and B = 2 × 10−9 erg cm−2 s−1 Å−1 , representing the avarage flux level. Note that the outflow velocity exceeds −600 km s−1 . We also note that this type of variability is very unlike what is observed in O stars (e.g. Kaper et al. 1996), but is very similar to profile variations of other magnetic B stars. We measured the equivalent- width (EW) of this line in the velocity range [−700, 800] km s−1 after normalising 81 out of 88 available IUE spectra between 1978 and 1995 to the same continuum around the C IV line and dividing each spectrum by the average of the normalised spectra. The error bars are calculated following Chalabaev & Maillard (1983). The resulting EW values are plotted as a function of phase in Fig. 3.9 (upper panel). The same procedure was carried out for the lines of Si IV (middle panel) and N V (lower panel), where we used 70 spectra with the highest quality and integrated over the intervals [-600, 2500] and [-600, 1200] km s−1 , respectively. We used a superposition of two sine waves to fit the data. The result is obtained with a least-square method which uses weights equal to 1/σ 2 (with 1σ the individual error bars) assigned to each datapoint. With user-supplied initial starting values for the free parameters a steepest descent technique then searched for the lowest mimimum of the χ2 . The variance matrix provides the formal errors in the parameters as in the following function: f (t) = a + b(sin(2π(t/P + d))) + e(sin(2π(t/(P/2) + f ))). The results of the best solution, with a reduced χ2 = 0.53, are: a = 2.41 ± 0.03, b = 0.60±0.05, d = 0.308±0.009, e = 1.77±0.04, and f = 0.84±0.01 and a period P = 12.00075 ± 0.00011 d. The very high precision of less than 10 sec in the period is due to extended coverage over almost 500 cycles. All doublet profiles of C IV, Si IV and N V and are modulated with this same period, which is identified with the rotation period of the star. With this analytic description the epoch of minimum in EW could be derived mathematically. We derived the ephemeris for the deepest minimum (i.e. maximum emission), which we define as the zero phase of the rotation. We find T (EWmin ) = HJD 2449762.050 ± 0.063 + n × (12.00075 ± 0.00011) (3.3) with n the number of cycles. The reference date HJD 2449762.050 is in the middle of the IUE observations. 3.4.2 Magnetic properties We fitted a cosine function of the following form to the 124 B` datapoints with the 1/σ 2 error bars as weights: 45 σobs/σexp Normalized Flux (10–09 erg cm–2s–1Å–1) C HAPTER 3 IUE C IV 1542 β Cep B1 IV Wavelength (Å) 1548 1551 1545 81 spectra 1554 4 3 2 1 0 8 6 4 2 0 –1000 –500 0 500 Velocity (km s–1) (stellar rest frame) 1000 1500 Figure 3.5: Representative C IV profiles from IUE spectra showing the typical variation over a 12 day cycle, very similar to the type of variation observed in other magnetic B stars, but unlike the variations observed in O stars. The two doublet rest wavelengths are indicated. Flux (10–09 erg cm–2s–1Å–1) IUE β Cep Si IV 1388 Wavelength (Å) 1396 1400 1392 1404 71 spectra 6 4 2 σobs/σexp 0 4 2 0 –1500 –1000 –500 0 500 1000 1500 Velocity (km s–1) (stellar rest frame) 2000 2500 3000 Figure 3.6: Similar to Fig. 3.5, but for Si IV. IUE β Cep N V 1234 1236 Wavelength (Å) 1238 1240 70 spectra 1244 1242 Flux (10–09 erg cm–2s–1Å–1) 10 8 6 4 2 σobs/σexp 0 4 2 0 –1500 –1000 –500 0 500 Velocity (km s–1) (stellar rest frame) 1000 Figure 3.7: Similar to Fig. 3.5, but for N V. 46 1500 D ISCOVERY OF THE MAGNETIC FIELD IN THE PULSATING B STAR β C EPHEI Blong(G) EW(C IV) [–700, 800]km/s β Cep B1 IV P = 12.00075(11) d, Tmin = 2449762.05(6) 4 3 2 1 0 150 100 50 0 –50 –100 –150 –200 –250 –1 IUE 1978–1995, 81 spectra TBL 1998–1999, 23 spectra –0.8 –0.6 –0.4 –0.2 0 0.2 UV phase 0.4 0.6 0.8 1 Figure 3.8: Upper panel: equivalent width of the C IV stellar wind line measured in IUE spectra taken during 16 years as a function of phase calculated with Eq. 3.3. The deepest minimum, defined as phase 0, corresponds to the maximum emission. Lower panel: magnetic data as a function of the UV phase. The dashed sine curve has the same parameters as in Fig. 3.4. Note that there is no significant difference in zero phase between the UV and magnetic data and that the field crosses zero at the EW maxima. t + φ)) (3.4) 12.00075 in which t was taken relative to the first observation. The fitted values are B 0 = 0.9± 3.0 G, Bmax = 94 ± 4 G, and φ = 0.4799 ± 0.0070 with a reduced χ2 = 1.3. The quoted 1-σ errors on the parameters are obtained with the same method as described above. With the derived phase we find for the ephemeris of the maximum value of the field strength: B` (t) = B0 + Bmax cos(2π( T (Bmax ) = HJD 2452366.30 ± 0.10 + N × 12.00075 (3.5) The reference date HJD 2452366.30 is given at the middle of the magnetic measurements, which extend over 200 cycles. In Fig. 3.4 we have drawn a sine wave with this period and phase through the magnetic measurements. Fig. 3.10 shows all 124 datapoints folded with the rotational period and an overplot of the best-fit cosine curve. A comparison with the phase of the UV data (Eq. 3.3) shows that a deep EW minimum is predicted at HJD 2452366.21 ± 0.04, which is, within the uncertainties, identical to the phase of maximum (positive) magnetic field. In Fig. 3.8 (lower panel) we have drawn a sine wave with the same parameters as used in Fig. 3.4 through the values of the magnetic field strength, and phased with the UV period. It is clear 47 C HAPTER 3 EW(Si IV) [–600, 2500]km/s EW(C IV) [–700, 800]km/s 5 IUE β Cep B1 IV P = 12.00075(11) d, Tmin = 2449762.05(6) 4 3 2 1 0 6 5 4 3 EW(N V) [–600, 1200]km/s 2 1 0 –1 –1 –0.8 –0.6 –0.4 –0.2 0 0.2 UV phase 0.4 0.6 0.8 1 Figure 3.9: Equivalent width variations of the stellar wind lines of C IV (top) Si IV (middle) and N V (bottom) measured in IUE spectra taken during 16 years as a function of phase calculated with Eq. 3.3. from the figure that the phase of minima of the stellar wind absorption (i.e. maximum emission) coincides very well with the extremes of the magnetic field, and that the maximum wind absorption coincides with field strength zero. It is interesting to note that B0 = 0.5 ± 3.0 G implies that the asymmetry with respect to zero must be very small. The fact that the second EW minimum is shallower will put constraints on the geometry of the field (see below). It is clear, however, that more magnetic data are needed to confirm any absence of asymmetry. We have fitted a simple cosine curve through the magnetic data. In Fig. 3.11 the residuals with the fit are displayed. No obvious discrepancies are emerging with the limited accuracy of the present data. The highest point in the figure is from July 2000, for which no fringe correction could be applied, wich have likely caused a unknown systematic shift. 48 D ISCOVERY OF THE MAGNETIC FIELD IN THE PULSATING B STAR β C EPHEI TBL, β Cep B1 IV, magnetic data 1998 – 2005 124 datapoints 200 150 100 Blong (G) 50 0 –50 –100 –150 –200 –250 Bav = (0.9 +/– 3) G Bmax = (94 +/– 4) G –1 –0.8 –0.6 –0.4 –0.2 0 0.2 Phase (12.00075 d) 0.4 0.6 0.8 1 Figure 3.10: Overplot of all magnetic data folded with the rotational period of 12.00075 d. The drawn curve is the best-fit cosine with amplitude 93 G and offset 0.5 G. TBL, β Cep B1 IV, residuals magnetic data 1998 – 2005 124 datapoints 200 150 Blong (G) (O – C) 100 50 0 –50 –100 –150 –1 –0.8 –0.6 –0.4 –0.2 0 0.2 Phase (12.00075 d) 0.4 0.6 0.8 1 Figure 3.11: Overplot of residuals (O - C) of all magnetic data folded with the rotational period. 3.4.3 Pulsation period and system velocity The measured radial velocities of the star are given in column 9 in Table 3.2. For the calculation of the phase in heliocentric radial velocity due to the radial mode of the pulsation we used the ephemeris for the expected maximum from Pigulski & Boratyn (1992) with P = 0.1904852 d and Tmax = 2413499.5407 (column 7 in Table 3.2). In Fig. 3.12 we plotted the derived radial velocity together with the magnetic field strength as a function of the calculated pulsation phase for the first 23 measurements covering 7 months in 1998 and 1999. Taking all the data together would not make sense because of the expected systemic velocity of the star in its 90 year orbit, especially because the star was very near its periastron passage (see below). From the figure it is clear that there is no correlation between the pulsation phase and the longitudinal component of the magnetic field, as expected. 49 C HAPTER 3 Each magnetic measurement consists of four subexposures for each of which we determined the radial velocity. (Only the average value per 4 subexposures are given in Table 3.2.) We also included spectra from incomplete sets, which made a total of 477 data points, shown in Fig. 3.13. We divided this dataset into logical subsets, with 150 20 100 10 50 0 0 Blong(G) Vrad (km/s) 30 β Cep December 1998 – July 1999 P = 0.1904852 d, Tmax=2413499.5407 TBL –10 –50 –20 –100 –30 –150 Vrad Blong –40 –50 –0.1 0 0.1 0.2 –200 0.3 0.4 0.5 0.6 0.7 Calculated Pulsation Phase 0.8 0.9 1 1.1 –250 Figure 3.12: Derived radial velocity (filled symbols, scale on the left) and magnetic field strength (open symbols, scale on the right) as a function of pulsation phase. As expected, no correlation between the two quantities is present in the data: at several occasions very different magnetic values are measured at a given pulsation phase. The observed system velocity as well as the difference between the observed and calculated phase of the maximum radial velocity confirm the predicted values for the star in its binary orbit near periastron passage. 20 1998 1999 2000 2001 2002 2003 2004 2005 β Cep TBL 10 vrad (km/s) 0 –10 –20 –30 –40 0 500 1000 1500 HJD – 2451160 2000 2500 Figure 3.13: Radial velocities as measured from all spectra from 1998-2005. 50 D ISCOVERY OF THE MAGNETIC FIELD IN THE PULSATING B STAR β C EPHEI Table 3.4: Results from cosine fits using Eq. 3.6 of radial velocity data of all 477 individual subexposures, subdivided in yearly averages. Av. HJD Coverage Nr γ Phase O−C −2450000 (days) points (km s−1 ) (days) 1998-99 Jan 1182.81 42.9 60 −19.15±0.09 0.6781±0.0012 −0.1292 1999 Jun 1363.46 7.9 34 −17.07±0.19 0.7215±0.0018 −0.1374 2000 Jun 1727.64 30.0 88 −12.43±0.12 0.7480±0.0015 −0.1429 2001 Jun 2086.59 14.0 123 −9.25±0.07 0.7584±0.0010 −0.1445 2002 Jun 2444.55 16.1 72 −6.85±0.08 0.7601±0.0012 −0.1448 2003 Jun-Aug 2827.58 59.9 48 −6.42±0.20 0.7521±0.0025 −0.1433 2004 Jun-Nov 3267.90 138.8 52 −5.05±0.14 0.7499±0.0013 −0.1428 Data set Table 3.5: New orbital parameters with 1 σ errors of the β Cep system, based on radial velocity measurements in this paper. For comparison the values given by Pigulski & Boratyn (1992) are listed. Parameter Porb (yr) K1 (km s−1 ) e ω T0 γ (km s−1 ) This paper 84.5 ± 0.13 8.2 ± 0.5 0.74 ± 0.02 198◦ ± 2◦ 1914.6 (fixed) −7.5 ± 0.4 Pigulski & Boratyn (1992) 91.6 ± 3.7 8.0 ± 0.5 0.65 ± 0.03 194◦ ± 4◦ 1914.6 ± 0.4 −6.6 ± 0.4 a coverage of about 0.5 to 3 weeks each year (see column 3 in Table 3.4). We have performed cosine fits for each subset with the function vrad (t) = γ + A cos(2π((t − t0 )/P + φ)) (3.6) We used the ephemeris and the period P from Pigulski & Boratyn (1992) to derive the phase φ and the delay of the maximum of the radial velocity curve of the pulsation (O − C), which is due to the light time effect. The results are given in Table 3.4. A best fit though the values of the system velocity γ yielded the orbital parameters listed in Table 3.5. We kept T0 , the passage of periastron, constant in this fit. Our orbital parameters agree fairly well with those derived by Pigulski & Boratyn (1992). A fit of a simple cosine function through the radial velocity data with the known Our values of the delays are in good agreement with the expected phase delay caused by the light-time effect in the binary orbit (see Pigulski & Boratyn 1992, their Fig. 1). New speckle interferometric measurements by Balega et al. (2002) yielded a separation of 38±2 mas at the epoch 1998.770 (i.e. just preceding our first observation) at a position angle of 228.6◦ , whereas 8 years earlier the position angle was 49.3◦ (Hartkopf et al. 1992) with separation 50 mas, showing that the companion had actually passed minimum radial velocity before our first observation. The binary period 51 C HAPTER 3 0 β Cep TBL γ (km/s) –10 –20 1996 1998 2000 Year 2002 2004 2006 Figure 3.14: Observed system velocity γ overplotted with the orbital solution from 3.5. is therefore likely a few years shorter than 85 years, based on the previous periastron passage in 1914.6 ± 0.4. This is in agreement with Hadrava & Harmanec (1996) who concluded that periastron passage should be closer to 1996 than to 2006 as predicted by Pigulski & Boratyn (1992). Our orbital solution points to the same conclusion. A better orbital solution can be achieved with a renewed analysis with all available radial velocity data, delays times and speckle measurements. 3.5 Conclusions and discussion We have found unambiguously a varying weak magnetic field in β Cep, consistent with a oblique dipolar magnetic rotator model (rotation period 12 d), in which outflow occurs along the magnetic poles, similar to models by Brown et al. (1985); Shore (1987) and Shore et al. (1987). The UV wind-line emission is at maximum if we are in the magnetic equatorial plane. In these models the C+3 production in the jet-like mass loss is presumably due to the dissipation of shear-generated Alfv én waves near the polar cones. Recent model calculations of the outflow and the resulting UV wind lines are presented by Schnerr et al. (2007). For a dipolar field, the ratio of the values at the magnetic extremes r = B min /Bmax is related to the inclination angle, i, and the angle of the magnetic axis with respect to the rotation axis, β according to r = cos(β + i)/cos(β − i) (Preston 1967). We found above that there is no significant asymmetry between the magnetic extremes, which is consistent with an equator-on inclination angle, and with the magnetic axis perpendicular to the rotation axis. If we adopt an inclination angle of 60 ◦ and a 52 D ISCOVERY OF THE MAGNETIC FIELD IN THE PULSATING B STAR β C EPHEI projected rotational velocity of 27(3) km s−1 (as derived by Telting et al. (1997) from a pulsation mode analysis), the rotation period requires a radius of 7.4 ± 0.8 R , which is in rather good agreement with the well-determined radius of the B1 III star Cen of 5.9+1.2 −0.6 R , based on interferometric and parallax measurements. A detailed discussion of the stellar parameters and a best fit of the angles i and β, based on line fits to I and V , is given by Donati et al. (2001). We emphasize that we have only measured the longitudinal component of the magnetic field, i.e. the component in the line of sight averaged value over the stellar disk. The intensity at the magnetic poles must be stronger. For a perpendicular magnetic rotator the polar field of a dipole is 3.2×B`,max (Schwarzschild 1950), i.e. about 300 G. The fact, however, that the EW curve in the stellar wind lines has two unequal maxima at epochs when the projected field is strongest, suggests that there should be a slight asymmetry present. This could of course be due to a slightly different geometry (off-centered dipole, or higher-order fields) at the two hemispheres, which can easily be hidden in the observed field strength which is the integrated value over the visible surface. We note that a configuration as found here favors magnetic braking as discussed by Donati et al. (2001) who investigated the timescale, since this is strongly model dependent. It is also interesting to note that the mode splitting due to the rotation is clearly present in the pulsation properties (Telting et al. 1997). It would be worth examining whether the presence of magnetic field can also be traced back in the pulsation modes. If so, this will give a strong constraint on the evolutionary status of β Cep. Several other issues are still to be solved. First of all, why does β Cep has a magnetic field? This star does not belong to the helium-peculiar stars (Rachkovskaya 1990), which are known to have strong magnetic fields, see e.g. Bohlender et al. (1987). Gies & Lambert (1992) note that β Cep is N enriched, a property that this star shares with other magnetic B stars, as confirmed by Morel et al. (2006). Enrichment of nitrogen in the atmosphere of a B star is apparently a strong indirect indicator of a surface magnetic field, see Henrichs et al. (2005). The presence of a magnetic field could cause such anomalies by inhibiting mixing. Another point of concern is that we have fitted a simple sine curve through the magnetic data. This is obviously a first approximation, and when more accurate measurements become available, a search for deviations of a sine curve, as is found for most magnetic stars, can be done. Last, it should be noted that the star β Cep appears to be one of the very few stars in its class which shows this type of strong wind variability and in this respect β Cep is an exceptional β Cep star. Acknowledgements. We thank Danny Lennon, Gautier Mathys, Sami Solanki and John Telting, for discussions and constructive comments. The helpful assistance of the observatory staff members at TBL, GSFC and Vilspa is well remembered and greatly acknowledged. 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S. 2000, MNRAS, 313, 851 55 C HAPTER 3 56 Diep in het woud, daar waar de rode draaidennen staan, bevond zich de spelonk waar de gnoom Knar zijn eenvoudige werkplaats had ingericht. Lang, lang geleden had hij het wiel uitgevonden en sindsdien gold hij als de grootste deskundige voor alles wat draait. Meestal kon men hem te midden van vervallen werkstukken voor zijn grot aantreffen, waar hij, onder het genot van oude kanaster, nadacht over alles wat wentelt – en dat is veel. Heer Bommel C HAPTER 4 O N THE Hα EMISSION FROM THE β C EPHEI SYSTEM R. S. Schnerr, H. F. Henrichs, R. D. Oudmaijer & J. H. Telting Astronomy and Astrophysics Letters, 459, L21 (2006) Abstract Be stars, which are characterised by intermittent emission in their hydrogen lines, are known to be fast rotators. This fast rotation is a requirement for the formation of a Keplerian disk, which in turn gives rise to the emission. However, the pulsating, magnetic B1IV star β Cephei is a very slow rotator that still shows Hα emission episodes like in other Be stars, contradicting current theories. We investigate the hypothesis that the Hα emission stems from the spectroscopically unresolved companion of β Cep. Spectra of the two unresolved components have been separated in the 6350-6850Å range with spectro-astrometric techniques, using 11 longslit spectra obtained with ALFOSC at the Nordic Optical Telescope, La Palma. We find that the Hα emission is not related to the primary in β Cep, but is due to its 3.4 magnitudes fainter companion. This companion has been resolved by speckle techniques, but it remains unresolved by traditional spectroscopy. The emission extends from about −400 to +400 km s−1 . The companion star in its 90-year orbit is likely to be a classical Be star with a spectral type around B6-8. By identifying its Be-star companion as the origin of the Hα emission behaviour, the enigma behind the Be status of the slow rotator β Cep has been resolved. 59 C HAPTER 4 4.1 Introduction The well-known pulsating star β Cephei (HD 205021) has been classified as B1IVe. Its Be status was assigned after the star showed prominent emission in Hα. The presence of this emission has been reported from time to time since 1933 (Karpov 1933), but often the emission disappeared or was not noticed. A new Hα emission episode was discovered in 1990 (Mathias et al. 1991; Kaper & Mathias 1995), which decayed in about 10 years. Neiner et al. (2001) found that the emission was back again within several years. A summary of the emission phases until 1995 is given by Pan’ko & Tarasov (1997). This behaviour is typical of Be stars. The enigma is that nearly all Be stars are rapid rotators with equatorial rotation rates of typically ∼70-80% of the critical rotation velocity (e.g. Porter & Rivinius 2003), or perhaps even higher (Townsend et al. 2004). However, β Cep is a very slow rotator with v sin i ≈ 25 km s−1 and has a very welldetermined rotation period of 12.00 days (Henrichs et al. 1993), much longer than the inferred rotation periods of other Be stars. Interestingly, the star was discovered to be an oblique magnetic rotator (Henrichs et al. 2000) with a polar field of ∼360 G (see also Donati et al. 2001), which strongly modulates the outflowing stellar wind with the rotation period. This has been very clearly observed in the UV resonance lines of C IV, Si IV, and N V with the IUE satellite over more than 15 years. This spectral line modulation could be modelled reasonably well as being due to the interaction of the magnetic field with the stellar wind (Schnerr et al. 2006), similar to the rotationally modulated winds of the magnetic Bp stars (e.g. Townsend et al. 2005), which also show Hα emission. The serious problem, however, is that every model so far predicts that this 12-day rotation period of β Cep should also be clearly visible in the Hα emission (probing the outflow near the stellar surface), whereas no sign of any 12-day modulation could be found in more than 300 high-resolution Hα profiles taken over 6 years (Henrichs et al. 2006). This discrepancy seriously hampers our understanding of the Be phenomenon: if β Cep really belongs to the (phenomenologically defined) class of Be stars, rapid rotation would not be required for the explanation of the Be phenomenon, opposed to all existing models. In addition, the origin of the unmodulated Hα emission would remain a mystery. Current modelling efforts would clearly benefit from resolving this critical issue. The aim of this study is to investigate the hypothesis that the source of the Hα emission is not β Cep itself, but its nearby companion, which has been resolved by speckle techniques. This suggestion has already been put forward by Tarasov (see Henrichs et al. 2003), which was at that time, ironically, rejected by one of the current authors. If this close companion were to turn out to be a Be star, this would clearly mean a major step forwards in understanding the β Cep system, and also remove the unfulfillable constraint on Be star models it poses now. 60 O N THE Hα EMISSION FROM THE β C EPHEI SYSTEM 4.1.1 The binary components The star β Cep (V=3.2) has a visual companion (V=7.9) at a distance of 13.4 00 . A second companion was detected using speckle interferometry by Gezari et al. (1972) at a distance of ∼0.2500 , which was later found to have a visual magnitude of V=6.6. The parameters of the close binary orbit have been determined from the variations in the pulsation period due to the light time effect and speckle interferometry by Pigulski & Boratyn (1992, see also Hadrava & Harmanec 1996). When recent, additional speckle measurements (Hartkopf et al. 2001) are taken into account, the current position of the companion is at a distance of about 0.100 from the primary, at a position angle of 42◦ (in the NE) on the sky. From the mass ratio determined from the binary orbit, the companion has an estimated spectral type around B6-8. As the target is very bright and the approximate orbit is known, the technique of spectro-astrometry is particularly well-suited to resolving the question of the origin of the Hα emission. Spectro-astrometry measures the relative spatial position of spectral features from a long-slit spectrum (see Bailey 1998a; Porter et al. 2004, and references therein). If one star in an otherwise unresolved binary has, for example, Hα emission, the photocentre across the line perpendicular to the dispersion direction will shift towards that star. So far the technique has mainly been used to detect close binary companions (e.g. Bailey 1998a; Baines et al. 2006), but also the individual spectra of binaries with a separation down to tens of milliarcseconds (mas) can be obtained. 4.2 Observations and data reduction Longslit spectra of β Cep were obtained with the ALFOSC spectrograph at the Nordic Optical Telescope (NOT) on La Palma. We used grism #17 (2400 l/mm VPH), which gives a dispersion of 0.25 Å/pixel for the ∼6350–6850 Å range. The 1.900 off-centre slit was used to avoid a ghost near Hα. We observed with a typical seeing of ∼1.1 00 , resulting in an effective resolution of R≈4500. The CCD with 2048x2048 pixels gives a spatial resolution of 0.1900 /pixel, thereby giving a good sampling of the spatial profile of the spectrum. A total of 11 spectra were obtained on 28 August 2006, between 5:40 and 5:53 UT (HJD 2453975.74), with exposure times between 2 and 5 sec. The star was positioned at three different locations on the slit, to check for possible instrumental effects. The angle of the slit on the sky was set to 42◦ (NE), which was confirmed by images obtained without the slit, leaving the orientation of the sky unchanged with this instrument. Data were reduced using the IRAF software package. The CCD-frames were corrected for the bias level and divided by a normalised flatfield. Scattered light was subtracted. Wavelength calibration spectra were obtained using an Ne lamp. The resulting two-dimensional spectra were fitted by a Gaussian profile in the spatial direction at each wavelength step with the fitprofs routine, using a 5-point running 61 C HAPTER 4 Figure 4.1: Average Hα profile (full line), the profile of 7 July 2000 and 19 June 2001 (dashed and dotted lines respectively, see Henrichs et al. 2003). During our observations more emission was present than in 2000. average in the dispersion direction (comparable to the spectral resolution). We have checked that similar results were obtained when no correction for scattered light was applied, or when Voigt instead of Gaussian profiles were used. Further consistency checks were carried out by comparing the results for all individual spectra taken at different slit positions. All traces were similar to each other, strongly suggesting that instrumental artifacts are not present. 4.3 Results The average Hα profile is plotted in Fig. 4.1, together with spectra taken in 2000 and 2001 (Henrichs et al. 2003). Although it is not directly clear from the new spectra that emission is present, comparison with the spectrum of July 2000 shows that the emission is currently stronger than it was in 2000. 4.3.1 The source of the Hα emission The spectro-astrometric results for Hα (6563 Å) and the He I line at 6678 Å are shown in Fig. 4.2. It is clear that near Hα the photocentre of the spatial profile of the spectrum shifts towards the companion (in the NE direction). This is due to an increased relative contribution to the flux of the companion, indicating that the companion is the source of the Hα emission. The width of the signature in Hα is from about −400 62 O N THE Hα EMISSION FROM THE β C EPHEI SYSTEM Figure 4.2: Spectro-astrometric observations of Hα (left) and the He I line at 6678 Å (right) of the β Cep system. Shown are the normalised intensity line profile (top) and the position of the photocentre of the spatial profile relative to that of the continuum (bottom). In the plot of the offset of the photocentre the results of all individual spectra are shown (dotted lines) as well as the average (full line). In both the Hα and He I plots a shift of the photocentre towards the companion is visible. However, in Hα the photocentre is offset from about −400 to +400 km s−1 , while in He I the width of the offset is similar to the width of the line. to +400 km s−1 , which is much broader than the width of the absorption line and is typical for a Be star emission line. 4.3.2 The spectra of the individual stars For close binaries with smaller separations than the slit, it is possible to determine the two spectra of the individual, unresolved, binary components with the technique described in Bailey (1998b) and Takami et al. (2003, see also Porter et al. 2004). Using average photocentre shifts, we determined the individual spectra, adopting the measured magnitude difference of 3.4 magnitudes (Hartkopf et al. 2001) and separations of 0.0700 , 0.100 , and 0.1500 , bracketing the estimated separation. The resulting spectra are shown in Fig. 4.3. The results for three possible separations are shown, and apart from the strength of Hα the results are qualitatively similar. The conclusion that the NE component is the source of the Hα emission is confirmed when the spectra are split. We find that the secondary has a doublepeaked emission profile, characteristic of a classical Be star. In the He I line the signal is also in the direction of the companion, but it has the same width as the absorption line in the total intensity spectrum. In the separated spectra it can be seen that this line is present only in the primary and not in the secondary, as expected for its later spectral type. 63 C HAPTER 4 Figure 4.3: The results of the separation of the spectra of the primary and secondary components. We show the normalised intensity line profile (top) and the separated line profiles of the primary (middle) and the secondary (bottom). For the splitting of the spectra we have assumed a separation of 0.07 00 (dashed lines), 0.100 (full line, corresponding to the best estimate of the separation), and 0.1500 (dotted line). A double-peaked Hα emission line with a width of ∼400 km s−1 , typical of a classical Be star, is found in the secondary star. The He I line at 6678 Å is only present in the primary star. 4.4 Conclusions and discussion We have shown that the Hα emission observed from the β Cep system is not related to the slowly rotating primary star, but to the secondary, which is most likely a classical Be star. This explains why the Hα emission is not modulated by the rotation of the primary. This removes the exceptional status of β Cep among the fast rotating Be stars, which therefore no longer contradicts the current models that require rapid rotation for explaining the Be phenomenon. We find that the Hα emission extends from about −400 to +400 km s−1 , in agreement with the results from Hadrava & Harmanec (1996) and Pan’ko & Tarasov (1997). This is independently confirmed by the extent of the variability shown in Fig. 4.1. The large width of the Hα emission suggests a relatively high value for v sin i, which points to a high inclination angle. With the orbital inclination angle of 87 ◦ (Pigulski & Boratyn 1992) and the high inclination angle of β Cep itself (>60 ◦ , Telting et al. 1997; Donati et al. 2001) this means that the spin and orbital angular momentum 64 O N THE Hα EMISSION FROM THE β C EPHEI SYSTEM vectors could well be aligned. An interesting question is how such a binary system with one, presumably spun-down, magnetic B star and a Be star may have evolved. Our result implies that the observed Hα emission is not related to the magnetic field of the primary star. This agrees with models explaining the variability observed in the UV wind-lines as due to the rotation of the magnetic field. New spectro-astrometric observations to obtain a wider spectral coverage are being planned and will allow us to further constrain the v sin i and spectral type of the secondary star. Acknowledgements. Based on observations obtained with the Nordic Optical Telescope, which is operated on the island of La Palma jointly by Denmark, Finland, Iceland, Norway, and Sweden, at the Spanish Observatorio del Roque de los Muchachos of the Instituto de Astrofisica de Canarias. The data presented here were taken using ALFOSC, which is owned by the Instituto de Astrofisica de Andalucia (IAA) and operated at the Nordic Optical Telescope under agreement between IAA and the NBIfAFG of the Astronomical Observatory of Copenhagen. RS and HFH thank F. Leone for useful discussions. Bibliography Bailey, J. 1998a, MNRAS, 301, 161 Bailey, J. A. 1998b, in Proc. SPIE Vol. 3355, p. 932-939, Optical Astronomical Instrumentation, Sandro D’Odorico; Ed., ed. S. D’Odorico, 932–939 Baines, D., Oudmaijer, R. D., Porter, J. M., & Pozzo, M. 2006, MNRAS, 367, 737 Donati, J.-F., Wade, G. A., Babel, J., Henrichs, H. F., de Jong, J. A., & Harries, T. J. 2001, MNRAS, 326, 1265 Gezari, D. Y., Labeyrie, A., & Stachnik, R. V. 1972, ApJ, 173, L1 Hadrava, P. & Harmanec, P. 1996, A&A, 315, L401 Hartkopf, W., Mason, B., Wycoff, G., & McAlister, H. 2001, Fourth Catalog of Interferometric Measurements of Binary Stars, http://www.ad.usno.navy.mil/wds/int4.html Henrichs, H. F., Bauer, F., Hill, G. M., Kaper, L., Nichols-Bohlin, J. S., & Veen, P. 1993, in IAU Colloq. 139: New Perspectives on Stellar Pulsation and Pulsating Variable Stars, ed. J. M. Nemec & J. M. Matthews, 186 Henrichs, H. F., de Jong, J. A., Donati, J.-F., Catala, C., Wade, G. A., Shorlin, S. L. S., Veen, P. M., Nichols, J. S., & Kaper, L. 2000, in ASP Conf. Ser. 214: IAU Colloq. 175: The Be Phenomenon in Early-Type Stars, ed. M. A. Smith, H. F. Henrichs, & J. Fabregat, 324 Henrichs, H. F., de Jong, J. A., Verdugo, E., Schnerr, R. S., Neiner, C., Donati, J.-F., Catala, C., Shorlin, S. L. S., & et al. 2006, in prep. Henrichs, H. F., Neiner, C., & Geers, V. C. 2003, in ASP Conf. Ser., Vol. 305, “Magnetic Fields in O, B and A Stars: Origin and Connection to Pulsation, Rotation and Mass Loss”, ed. L. A. Balona, H. F. Henrichs, & R. Medupe, 301 65 C HAPTER 4 Kaper, L. & Mathias, P. 1995, in ASP Conf. Ser. 83: IAU Colloq. 155: Astrophysical Applications of Stellar Pulsation, ed. R. S. Stobie & P. A. Whitelock, 295 Karpov, B. G. 1933, Lick Observatory Bull., 16, No. 457, 167 Mathias, P., Gillet, D., & Kaper, L. 1991, in Rapid Variability of OB-stars: Nature and Diagnostic Value, ed. D. Baade, 193 Neiner, C., Henrichs, H., Geers, V., & Donati, J.-F. 2001, IAU Circ., 7651, 3 Pan’ko, E. A. & Tarasov, A. E. 1997, Astronomy Letters, 23, 545 Pigulski, A. & Boratyn, D. A. 1992, A&A, 253, 178 Porter, J. M., Oudmaijer, R. D., & Baines, D. 2004, A&A, 428, 327 Porter, J. M. & Rivinius, T. 2003, PASP, 115, 1153 Schnerr, R. S., Owocki, S. P., ud-Doula, A., Henrichs, H. F., & Townsend, R. H. D. 2006, A&A, in prep. Takami, M., Bailey, J., & Chrysostomou, A. 2003, A&A, 397, 675 Telting, J. H., Aerts, C., & Mathias, P. 1997, A&A, 322, 493 Townsend, R. H. D., Owocki, S. P., & Groote, D. 2005, ApJ, 630, L81 Townsend, R. H. D., Owocki, S. P., & Howarth, I. D. 2004, MNRAS, 350, 189 66 C HAPTER 5 N UMERICAL SIMULATIONS OF UV WIND LINE VARIABILITY IN MAGNETIC B STARS : β C EPHEI R. S. Schnerr, S. P. Owocki, A. ud-Doula, H. F. Henrichs & R. H. D. Townsend Astronomy and Astrophysics, (to be submitted) Abstract Winds of many early-type stars studied in the UV by the IUE satellite show cyclic or even periodic variability on a rotational timescale. In recent years a number of such stars were found to have magnetic fields with polar field strengths in the range of 102 -103 Gauss. In an attempt to explain the strictly periodic variability in these stars with relatively weak magnetic fields, we have performed line profile calculations of simple stellar wind models and 2D-MHD simulations. For our simulations we have taken the B1IV star β Cephei as our prototype, as this star has been studied extensively, has a slow rotation rate and has a favourable inclination of the rotation and magnetic field axes. We find that simple models with an enhanced density of absorbing ions in the magnetic equator, qualitatively reproduce the observed variability of the UV wind lines. Such enhancement of density might naturally be expected due to channelling of material towards the magnetic equator by the magnetic field. However, quite surprisingly, we find that less stellar flux is absorbed in the magnetic equator compared to the magnetic poles in the MHD simulations. This is because material in the magnetic equator tends to be either confined to a geometrically thin disk, or have a temperature too high for the ions of typical UV wind lines, resulting from shock heating due to the colliding winds of the two magnetic hemispheres. Although magnetic channelling of the stellar wind is certainly important, we conclude that the inclusion of X-ray ionisation is likely required to explain the observed UV wind line variability. 67 C HAPTER 5 5.1 Introduction The majority of the O stars and a significant fraction of the early B stars exhibit variability in their UV wind lines. In well-studied cases this variability has been found to be either strictly periodic or cyclic, i.e. not phase locked from one year to the next (see for instance Fullerton 2003, for a review). In the chemically peculiar Ap/Bp stars, which have kG magnetic fields, the strictly periodic variability can be explained by the stellar rotation of the magnetic field which modulates the outflow. Pointed out by their strictly periodic UV wind line variability, recently several nonchemically peculiar OB-type stars were also found to posses magnetic fields. These are the B stars β Cep (Henrichs et al. 2000), ζ Cas (Neiner et al. 2003a), V2051 Oph (Neiner et al. 2003b), τ Sco (Donati et al. 2006b) and ξ 1 CMa (Hubrig et al. 2006), and the O star θ 1 Ori C (Donati et al. 2002). The B star ω Ori (Neiner et al. 2003c) and the O star HD 191612 (Donati et al. 2006a) have also been found to posses a magnetic field, but ω Ori was only observed to show cyclic variability over a period of three days, and HD 191612 was pointed out as a magnetic candidate by strong periodic changes in its optical spectrum (Walborn et al. 2004). These stars have weaker large scale fields (102 − 103 G) and stronger winds than the Ap/Bp stars, which are mostly of a later spectral type. The observed strictly periodic variability is most likely related to the presence of these magnetic fields. To characterise the capability of a magnetic field to influence the flow of the wind ud-Doula & Owocki (2002) defined the ‘wind magnetic confinement parameter’ η ∗ = 2 R∗2 /Ṁ v∞ , where Beq is the magnetic field strength at the magnetic equator, R∗ Beq the stellar radius, Ṁ the mass loss rate, and v∞ the terminal velocity of the wind. For the strongly magnetic Ap/Bp stars η∗ is of order 103 or more and the magnetic field completely dominates the wind flow up to several stellar radii from the star. In the case of the OB stars with weaker magnetic fields and stronger stellar winds, η ∗ is of the order of 102 and magnetic fields will still play an important role but no longer completely determine the flow. For early-type stars without a detected magnetic field and for which the variability has been found to be cyclic, i.e. not strictly periodic, the origin of the variability is unexplained. Henrichs et al. (2005) found that three different kinds of variability can be distinguished: the Discrete Absorption Component (DAC) type (absorption at high blue shifted velocities), the magnetic oblique rotator type (absorption around zero velocity) and an intermediate type (absorption at intermediate velocities), and concludes that they are all likely to be related to magnetic fields. The timescales for the DAC- and oblique rotator type are of the order of a few days to weeks, i.e. the rotational timescale, whereas the timescale of the intermediate type remains undetermined because of a lack of time coverage. Stellar pulsations can also cause variability in UV wind lines, but the observed timescales are shorter than the rotational timescale. Using phenomenological models and 2D-MHD simulations, we have investigated whether the presence of the measured 102 − 103 G magnetic fields can explain the 68 N UMERICAL SIMULATIONS OF UV WIND - LINE VARIABILITY: β C EPHEI strictly periodic variability observed in the UV wind lines of B stars. Understanding the origin of such strictly periodic variability could help us to better understand the variability observed in other stars that has not been found to be strictly periodic. Most of the UV wind-line variability of B stars is observed in the lines of Si IV, C IV and N V. At the relevant effective temperatures of up to ∼ 30.000 K, the dominant ionisation stage is always well below these observed lines (Arnaud & Rothenflug 1985). The fact that we do observe lines of these ions is thought to be due to superionisation by X-rays. The precise origin of the X-rays is unknown, but excess X-rays are observed for many OB stars (e.g. Berghöfer et al. 1996). As a test case we have modelled the bright B1IV star β Cep, of which the parameters are known relatively well and which has a favourable geometry with both magnetic poles (almost) crossing the line of sight each rotation period. 5.2 The UV behaviour and magnetic field of β Cep The stellar parameters of the B1IV star β Cep (HD 205021, V=3.2) are summarised in Table 5.1. A clear 6 or 12 day period in its UV lines was reported by Fischel & Sparks (1972). Henrichs et al. (1993) proposed that this 12 day period was the rotational period, which was seen in the wind lines due to a co-rotating magnetic field that affected the wind. This was confirmed by the discovery of the magnetic field by Henrichs et al. (2000, see also Donati et al. 2001). The equivalent width (EW) of the C IV doublet at 1548.203/1550.777 Å and the magnetic field measurements folded with the rotation period of 12.00075 days are shown in Fig. 5.1. The magnetic extrema (minimum and maximum field strength) coincide with phases of minimum C IV EW and phases of zero field strength coincide with maximum C IV EW. This behaviour is indeed expected from a dipole magnetic field not strong enough to completely dominate the flow, but which does influence the wind up to a few stellar radii. As a result the stellar wind is guided towards the magnetic equator until it becomes to weak to further confine the wind. One would expect such a scenario to result in enhanced absorption in the magnetic equator and reduced absorption over the magnetic poles. From modelling of the rotational variability of the magnetic field strength the angle between the rotation axis and the magnetic axis (β) could be determined (Donati et al. 2001). Although both i and β are large, ∼90◦ , they are not very strongly constrained. The inequality of the two C IV EW minima, and the slight offset of the average magnetic field strength visible in Fig. 5.1 imply for a dipole field that the inclination cannot be exactly 90◦ . However, to keep the interpretation of the simulations as simple as possible, we have assumed both i and β to be 90 ◦ , which is an equator-on star with the magnetic axis in the rotational equator. In the spectra of this star regular Hα outbursts have been observed since 1933 (Karpov 1933, see Pan’ko & Tarasov 1997 for an overview of emission phases until 1995). However, the Hα emission showed no evidence of any rotational modulation, which is very difficult to understand in the presence of a dipole magnetic field with 69 C HAPTER 5 Blong(G) EW(C IV) [–700, 800]km/s its axis in (or close to) the rotational equator. If the emission would originate from a magnetically confined disk, comparable to what is seen in some strongly magnetic Ap/Bp stars (see Townsend et al. 2005) strong rotational modulation should definitely be observed. Motivated by these considerations, the system was closely examined by Schnerr et al. (2006) with spectroastrometric techniques, which has lead to the discovery that the emission originates not from the primary star but from the close companion which is in a ∼90 year orbit and which has been regularly observed by speckle interferometry. 5 P=12.00075(11) days Tmin=2449762.05(6) 4 3 2 1 0 –1 IUE 1978–1995, 81 spectra 150 100 50 0 –50 –100 –150 –200 TBL 1998–2001, 48 spectra –250 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 UV phase Figure 5.1: The EW of the C IV doublet of β Cep as a function of rotational phase for a rotation period of 12.00075 days (top) and the magnetic field measurement from 1998-2001 folded with the same period (bottom). Figure taken from Henrichs et al. (2005, see also Chapter 3). 5.3 Line profile calculations using SEI In radiation transfer of line driven winds, the Sobolev approximation is often used. The great advantage of this method is that it allows for an estimation of important parameters, such as optical depth, based on the local physical conditions only. For the calculation of the line profiles the Sobolev approximation is used in two different contexts. First to calculate the source function throughout the wind, and second to reduce the integrals along sight-lines required to solve the transfer equation for a given frequency, to a local problem in the resonance zone. It was pointed out by Hamann (1981) that most of the deviations in this approximation are due to solving the transfer equation and not to the calculation of the source function. 70 l2s4.lis @ plots4.i >> plots4.ps l2c4.lis @ plotc4g.i >> plotc4.ps l2n5.lis @ plotn5.i >> plotn5.ps N UMERICAL SIMULATIONS OF UV WIND - LINE VARIABILITY: β C EPHEI 0.6 0 –1000 0 1000 2000 Velocity (km s–1) (stellar rest frame) IUE Wavelength (Å) 32 spectra 1389 1392 1395 1398 1401 1404 1407 ← ← ← ← ← 0.6 ← ← ← ← ← ← ← ← ← ← ← ← ← 0.4 0.2 0.5 ← ← 1 ← IUE 1236 σobs/σexp 1.5 0.4 0 ← ← ← ← ← 0 –1000 –500 0 500 1000 1500 Velocity (km s–1) (stellar rest frame) Wavelength (Å) 32 spectra 1545 1548 1551 1554 1 ← ← 0.8 Quotient flux 1.5 0.65 @ plotc4g.i >> plot.ps ← ← ← ← ← 6 4 2 0 2 1 1 IUE 1 0 σobs/σexp 0.4 32 spectra 1245 1 ← ← ← ← 0.2 ← ← ← ← ← σobs/σexp σobs/σexp Quotient flux ← ← 1 ← –500 0 500 1000 1500 Velocity (km s–1) (stellar rest frame) Wavelength (Å) 33 spectra 1239 1242 1245 4 2 0 2 1.3 1 0.7 0 ← ← ← ← ← ← 0.8 ← ← ← ← 0.8 ← ← ← ← 0.6 ← ← ← ← ← ← ← ← ← ← ← ← ← 0.6 ← ← ← ← ← ← ← ← ← ← ← ← ← 0.6 ← ← ← ← ← ← ← ← ← ← ← ← ← 0.4 0.2 0 ← ← ← ← ← –1000 0 1000 2000 Velocity (km s–1) (stellar rest frame) 0.4 0.2 0 ← ← ← ← ← –1000 –500 0 500 1000 Velocity (km s–1) (stellar rest frame) 1500 Phase 0.8 Phase Phase 1 Phase 0.6 4 2 0 2 ← ← ← ← ← ← ← ← ← ob-list.lis ← ← ← ← ← Wavelength (Å) 1239 1242 3 2 1 0 0.5 0.7 ← ← ← ← ← ← ← ← ← ← ← ← ← ← ← 0 3.5 1 0.8 0.2 IUE 1236 2 ← ← ← ← 0.4 32 spectra 1554 3 0.8 ob-list.lis @ plotc4g.i >> plot.ps Wavelength (Å) 1548 1551 0 1 ← 1545 Phase 1 ← ← 8 6 4 2 0 4 Norm. Flux σobs/σexp 5 Quotient flux Phase 1 IUE Norm. Flux Norm. Flux σobs/σexp IUE Wavelength (Å) 32 spectra 1389 1392 1395 1398 1401 1404 1407 3 2 1 0 6 5 4 3 2 1 0 0.4 0.2 0 ← ← ← ← ← –500 0 500 1000 Velocity (km s–1) (stellar rest frame) 1500 Figure 5.2: UV wind line profiles of β Cep normalised by the average line profile, as observed with the IUE satellite of Si IV (left), C IV (middle) and N V (right). A clear modulation is visible with the rotation period of 12.0 days. Table 5.1: Stellar properties of β Cep, taken from Henrichs et al. (2000) and Donati et al. (2001), see also Chapter 3. M∗ 12 M R∗ 6.5 R log(L∗ /L ) 4.12 Prot 12.00 days Teff 26000 K Spectral type B1 IV Bpolar 360 G i 50–90◦ β ∼90◦ 71 C HAPTER 5 impact parameter p observer r z star Figure 5.3: The integrations for calculating the line profiles are performed along sight lines (z) with a fixed impact parameter p. This motivated Lamers et al. (1987) to develop a method that exploits the efficiency of the Sobolev approximation, but is more accurate. This method, Sobolev with Exact Integration (SEI), uses the Sobolev approximation to calculate the source function, but solves the transfer equation by direct integration. For all our line profile calculations we have used the SEI routine developed and described by Cranmer & Owocki (1996). This routine is designed to calculate line profiles for arbitrary geometries in 1, 2 and 3 dimensions. We have assumed atomic parameters for the 1548 Å C IV line and neglected interaction between the doublet members and limb-darkening. 5.3.1 Solving the transfer equation in the comoving frame Using the escape probability method introduced by Castor (1970), we calculate the source function Sν in the Sobolev approximation as (assuming that the ratio of collisional over radiative de-excitations = 0): Sν = I c βc , β (5.1) where Ic is the flux of the star, β = hPesc (µ, φ)i the angle-averaged escape probability and βc = hD(µ)Pesc (µ, φ)i is the core penetration probability, where D(µ) = 1 for rays intersecting the star and D(µ) = 0 otherwise. The variables µ (= cos θ) and φ denote a direction from a point in the wind, relative to the local radial di−τ rection. The photon escape probability is calculated as P esc (µ, φ) = 1−eτ , with τ = χvth /(d[~v · ~a]/d~a), where d[~v · ~a]/d~a is the derivative of the velocity component along the direction ~a, which is set by µ and φ. To calculate the integrals required to determine the angle averaged escape probability and all other integrals required for the line profile calculations, we have used Romberg’s method of numerical integration described in Press et al. (1992) with an 72 N UMERICAL SIMULATIONS OF UV WIND - LINE VARIABILITY: β C EPHEI estimated fractional accuracy of 0.2%. The line profiles are calculated by numerically integrating the formal solution to the transfer equation along sight-lines with a fixed impact parameter, as illustrated in Fig. 5.3, for many different sight-lines. The number of sightlines used is increased until the required precision of 0.2% of the flux is achieved. These integrals have to be performed for all relevant wavelengths or velocities; in our case 100 equidistant velocity points in the −1000 to +3000 km s −1 range. The local optical depth dτ = χdz is determined by χ(~r, ~v, ν) = πe2 1 ggf nCIV Φ(n~z · ~v, ν), me c ∆νD gl (5.2) 2 πe with m = 0.02654 cm2 s−1 , ∆νD = ν0 vth /c with ν0 the line frequency, vth the ion ec thermal speed, c the velocity of light, ggf = 0.38, gl = 2, nCIV the C IV number density, and n~z a unit vector along the sightline. The local line profile Φ(n~z · ~v, ν) is assumed to be given by a normalised Gaussian 2 e−(n~z ·~v/vth ) √ , Φ(n~z · ~v, ν) = π (5.3) where n~z · ~v/vth is the projected velocity offset relative to the centre of the line in units of the thermal velocity. 5.4 A phenomenological model From the observed variability in the UV line profiles shown in Figs. 5.1 and 5.2, it is clear that the absorption is reduced when we see the magnetic poles, and enhanced when we see the magnetic equator. The most straightforward way to explain this would be an enhanced density in the magnetic equator relative to the magnetic poles. Such an enhancement of the density in the equatorial regions could be expected due to the channelling of the wind by a dipole-like magnetic field which tends to guide the wind towards the magnetic equator. Before exploring more detailed models, it is useful to examine to what extent a very basic model with enhanced density in the equatorial regions would qualitatively reproduce the observed behaviour. For this purpose we have calculated line profiles for a model that has an artificially increased density near the magnetic equator. As we have not included rotation in our models, we have defined our polar coordinates relative to the magnetic axis for all models discussed in this paper. In this geometry θ is defined as the longitude relative to the magnetic axis, i.e. θ = 0 ◦ and θ = 180◦ define the magnetic poles, and θ = 90◦ denote the magnetic equator. Rotation is simulated by adjusting the viewing angle of the observer, where the phase is 0 for an observer at [θ = 0◦ , r → ∞]. 73 C HAPTER 5 Figure 5.4: Mass-loss rate as a function of azimuth angle (θ) for the phenomenological model where the mass loss scales with sin4 θ. For our model the mass loss rate of the star scales with the sin 4 θ, where θ is the azimuth angle relative to the magnetic axis. We have assumed a CAK wind (Castor et al. 1975), with a β-law velocity as a function of radial distance r: v(r) = v∞ (1 − R∗ /r)β , (5.4) with β = 0.8, v∞ = 1500 km s−1 and R∗ is the stellar radius. The density in the wind can then be written as Ṁ (θ) , (5.5) ρ(θ, r) = 4πr2 v(r) where we have parameterised the mass-loss rate as Ṁ (θ) = Ṁ0 sin4 θ, (5.6) with Ṁ0 = 2.7 · 10−8 M /yr. The dependence of the mass-loss rate on θ is shown in Fig. 5.4. At the effective temperatures of B stars of up to ∼30,000 K, all carbon is expected to be in the form of C II (Arnaud & Rothenflug 1985). The fact that C IV lines are observed is thought to be due to superionisation by X-rays. However, the precise fraction of C IV that is produced by X-rays is unknown, as is the exact origin of the X-rays. For this simple model we have assumed that the X-ray ionisation is constant throughout the wind, with a fixed ionisation fraction of C IV/C=0.01 and a solar carbon abundance of nC /n = 2.27 · 10−4 (Lodders 2003). The results of our line-profile calculations are shown in Fig. 5.5. One has to keep in mind that our calculations are for a singlet only. Although there are differences in the detailed line shapes, the main phase dependence of both the emission and absorption is reproduced. Maximum absorption is observed at the magnetic equator, and minimum absorption over the magnetic poles. As a result the whole profile appears to shift up and down, resembling the behaviour of the observations. 74 N UMERICAL SIMULATIONS OF UV WIND - LINE VARIABILITY: β C EPHEI Similar behaviour might be expected in the presence of a magnetic field, due to magnetic channelling of the wind. Therefore these results encouraged us to carry out full 2D-MHD simulations, from which we would expect qualitatively similar results. Wavelength (Å) 1545 1548 32 spectra 1551 Wavelength (Å) 32 spectra 1545 1548 1551 1.8 1 0.5 0.5 0.2 ← ← ← ← ← ← ← ← ← ← ← ← ← ← ← ← ← ← ← ← ← ← ← ← ← ← ← ← ← ← ← ← 0.8 0.6 0.4 0.2 0 1542 1.5 1 0 1 Phase 1.7 1539 15 10 5 0 2 Quotient flux σ /σ obs exp 1542 0 1 0.8 Phase Norm. flux σobs/σexp 1539 15 10 5 0 1.5 0.6 0.4 0.2 0 –1500 –1000 –500 0 500 1000 Velocity (km s–1) (stellar rest frame) ← 0.2 ← ← ← ← ← ← ← ← ← ← ← ← ← ← ← ← ← ← ← ← ← ← ← ← ← ← ← ← ← ← ← –1500 –1000 –500 0 500 1000 Velocity (km s–1) (stellar rest frame) Figure 5.5: Normalised line profiles (left) and line profiles divided by the average line profile (right) of the sin4 -model. Shown are a measure of the variability (top), the line profiles (middle) and a greyscale plot of the line profiles vs. rotational phase. The main phase dependence of both the emission and absorption observed in β Cep is reproduced. 5.5 2D-MHD simulations Our implementation of the generic ZEUS based code has been described in detail by ud-Doula & Owocki (2002, see also ud-Doula 2003), with modifications to include an energy balance with radiative cooling (ud-Doula 2003; Gagn é et al. 2005). Using this code we compute the relevant physical parameters in a non-equidistant mesh of 100 zones covering θ from 0 to 180◦ by 300 zones covering r from 1 to 10 R∗ . The total simulated time for a typical simulation is 5 · 105 seconds (∼6 days), and all relevant system parameters are saved every 104 seconds (∼2.8h), giving 50 snapshots per simulation. With the adopted stellar parameters from Table 5.1 the characteristic flow time of the system is of the order of Rmax /v∞ ∼ 10R∗ /1500 = 3 · 104 s. Since β Cep is a very slow rotator the dynamical effects of rotation could be neglected. The radius at which the co-rotation velocity equals the Kepler velocity is r ∼ 12R ∗ . 75 C HAPTER 5 Table 5.2: Summary of the basic parameters of the performed simulations. Shown are Q̄, the massloss rate of the non-magnetic models used to initialise the simulations, the terminal velocity of the non-magnetic models, and η∗ for a dipole magnetic field with a polar strength of 360 G. Ṁ1D v∞,1D 10−9 M /y km s−1 low-Ṁ 250 2.1 1277 intermediate-Ṁ 500 4.9 1313 high-Ṁ 1700 22.5 1324 model Q̄ η∗ 389 162 35 Instead, rotation of the system was accounted for by calculating line profiles for different viewing angles. The radiative driving is incorporated in the form of the Q̄-formalism as described by Gayley (1995). We have performed a series of simulations assuming a different efficiency of the radiative driving mechanism, determined by Q̄, and hence different mass-loss rates. The characteristic parameters of three representative models are shown in Table 5.2. The CAK parameters α and δ used for the radiative driving were set to 0.5 and 0.1, respectively. The MHD-simulations were initialised from the relaxed solution of a simulation with the same parameters, but without magnetic fields. These simulations were also run for 5 · 105 seconds, although a stable solution was always reached within several flow times. From the results of our simulations we calculate the line profiles using the SEI method. 5.5.1 Evolution of the simulations Snapshots of some typical models and geometries are presented in Figs. 5.6 and 5.7. The main characteristic of all runs is that they are highly variable. Quasi-stationary behaviour is observed once the influence of the initial conditions has disappeared, but no stable situation is reached. Guided by the magnetic field, material builds up in regions around the equator, and then either breaks out or falls back onto the star. A sketch of the important regions is shown in Fig. 5.8. The hot loop. A hot “loop” of low-density plasma is clearly visible in the temperature plots, but also in the density plots. The size of the loop depends strongly on the mass-loss rate. In the low-Ṁ model it extends to almost a stellar radius above the stellar surface. In the intermediate-Ṁ model the loop is only a fraction of a stellar radius in height and in the high-Ṁ model it has completely disappeared. This is most likely related to the higher density in the intermediate- and high- Ṁ models, which increases the efficiency of the radiative cooling. The collision region. Near and below the tops of the last closed field lines in the equator material is captured by the magnetic field lines and heated by shocks created by the inflowing wind. Density builds up here until it either falls back towards the star or breaks the magnetic field lines open and is blown away by the radiative driving. Some of the material that falls back towards the star is guided towards 76 N UMERICAL SIMULATIONS OF UV WIND - LINE VARIABILITY: β C EPHEI Log Density [g cm−3 ] Log Temperature [K] Figure 5.6: Snap-shots of the simulations. Shown are the evolution of the intermediate- Ṁ model of the density (log ρ [g cm−3 ], top) and temperature (log T [K], bottom) after (from left to right) 2, 3, 4, and 5·105 s. higher latitudes by magnetic field lines closer to the star and blown away at midlatitudes by the stellar radiation. The location and size of this region is most clearly seen in the density and temperature plots. The extent of the region is determined by the maximum radius at which the magnetic field is still able to determine the wind flow. As a result this region is smaller for the models with a higher mass-loss rate. The outflowing disk. Connected to the collision region is a hot, high density outflowing disk, which has a low outflow velocity due to the high densities. The material in this disk comes from material that breaks open the magnetic loops in the collision region and wind of higher latitudes that is still able to guide the material towards the equator although it is too weak to dominate the flow. The scale height of the disk is set by the ability of the shocked material in the disk to cool and contract. As the efficiency of the radiative cooling depends strongly on the density, the disks are thinner for a higher mass loss and more puffed-up when the mass loss is lower. Layers of the disk that are able to cool efficiently form thin, variable, outflowing “sheets”. The dynamics observed in these full 2D-MHD simulations is quite different from the simple enhancement of the density towards the magnetic equator as discussed in Sect. 5.4. Material from both hemispheres is guided towards the equator, but due to the shock-heating of the gas the temperatures are much too high to allow a 77 C HAPTER 5 Log Density [g cm−3 ] vr [km s−1 ] Log Temperature [K] vθ [km s−1 ] Figure 5.7: Snap-shots of the simulations. Shown are (from left to right) density (log ρ [g cm −3 ]), temperature (log T [K]), radial velocity (km s−1 ) and transverse velocity (km s−1 ) after 5·105 s for the low, intermediate, and high-Ṁ models (top to bottom). large fraction of C IV to be present in an extended region near the magnetic equator. Material that is cool enough to have a significant fraction of C IV in the equatorial region, is confined to thin sheets that at a given time only cover a small fraction of the stellar disk. Therefore it is not clear that the absorption along the equator is actually increased compared to that over the poles. 5.5.2 Calculating line profiles from 2D-MHD models The C IV observed in the stellar winds of B stars is thought to be related to superionisation by X-rays. As the origin of the X-rays is not completely understood, the precise fraction of C IV that is produced is unknown. To determine the C IV density as a function of temperature we have used a gaussian fit to the calculated C IV fractions by Arnaud & Rothenflug (1985, see Fig. 5.9). To mimic the production of C IV 78 N UMERICAL SIMULATIONS OF UV WIND - LINE VARIABILITY: β C EPHEI collision region outflowing disk star "hot loop" Figure 5.8: Sketch of the most notable regions observed in the simulations. by X-rays throughout the wind we have assumed a floor value of 3% at the low temperature end. We have adopted the solar abundance of carbon of n C /n = 2.27 · 10−4 from Lodders (2003). Figure 5.9: A gaussian fit to the calculated ionisation fractions of C IV by Arnaud & Rothenflug (1985), including a minimum ionisation fraction of 3% at the low temperature end to mimic the production of C IV by X-ray ionisation. To calculate line profiles from our simulation we have time-averaged the C IV density to remove all temporal variability and account for the fact that our simulations have no structure in the plane of stellar rotation. We have averaged the C IV density for each gridpoint for the last 30 snapshots, when all effects of the initialisation have faded and quasi-steady behaviour is observed. The radial and transverse components of the velocity at each gridpoint are determined by a weighted average of the velocity components with the C IV density. The highest C IV density near the 79 C HAPTER 5 1 0.5 1.5 Phase 0.8 0.6 0.4 0.2 0 10 5 0 1.5 1 1.4 1 0.5 1 Wavelength (Å) 32 spectra 1539 1542 1545 1548 1551 ← ← ← ← ← ← ← ← ← ← ← ← ← ← ← ← ← ← ← ← ← ← ← ← ← ← ← ← ← ← ← 1.4 –2000–1500–1000 –500 0–1 500 1000 Velocity (km s ) 0.5 1.5 1.4 1 0.5 1 0.6 ← ← ← ← ← ← ← ← ← ← ← ← ← ← ← ← ← ← ← ← ← ← ← ← ← ← ← ← ← ← ← ← 0.8 0.6 0.4 0.2 0 Wavelength (Å) 32 spectra 1539 1542 1545 1548 1551 1 0.5 1.5 1 0.6 ← Quotient flux Norm. flux σobs/σexp 10 5 0 1.5 –2000–1500–1000 –500 0–1 500 1000 Velocity (km s ) 0.5 1 0.8 Phase Wavelength (Å) 32 spectra 1539 1542 1545 1548 1551 Quotient flux Norm. flux σobs/σexp 10 5 0 1.5 Phase Quotient flux Norm. flux σobs/σexp magnetic equator is found in the cool, variable, outflowing disk, which only covers a fraction of the stellar disk. As a result of the time averaging, the relatively high density of C IV ions in this outflowing disk will be spread out over a larger area near the magnetic equator. This will tend to increase the total absorption over the equator, which, although perhaps not the most accurate approach, gives us the best chance of reproducing the observed behaviour. From these average parameters we have calculated line profiles using the SEI method. Examples of the line profiles of the low, intermediate and high- Ṁ model are shown in Fig. 5.10 Contrary to what we expected, the behaviour of the C IV is quite different from what is observed and what was reproduced with our simple phenomenological model. Instead of increased absorption, the absorption has actually decreased in the equatorial regions. This is due to the high temperatures in the equatorial regions, and the small height of the outflowing disk of material that has been able to cool. In the observations both the red and blue parts of the line show a higher (or lower) flux simultaneously. The line profiles of all the simulations show an anticorrelation between the emission and absorption part of the line profile: enhanced absorption in the blue wing of the line coincides with enhanced emission in the red wing and vice versa. When we compare the higher and lower flux phases of the red and the blue wings of the simulations with the observations, we see that the red part of the line shows similar variability with phase: higher flux near the magnetic poles and lower flux near the magnetic equator. The blue part of the line shows the opposite behaviour. 0.6 0.4 0.2 0 0.6 ← ← ← ← ← ← ← ← ← ← ← ← ← ← ← ← ← ← ← ← ← ← ← ← ← ← ← ← ← ← ← ← –2000–1500–1000 –500 0–1 500 1000 Velocity (km s ) Figure 5.10: Results of the line profile calculations of the low (left), intermediate (middle) and high- Ṁ (right) models. Line profile were calculated from the averaged C IV density of the last 30 snapshots, assuming a low temperature “floor” of 3% for the fraction C IV/C. 80 N UMERICAL SIMULATIONS OF UV WIND - LINE VARIABILITY: β C EPHEI 5.5.3 Understanding the line profiles Due to the magnetic field, mostly material from mid-latitudes is channelled towards the magnetic equator. As the magnetic field lines are almost radial over the poles, magnetic channelling is less effective in these regions. This effect is amplified by the radiative driving that is able to accelerate the less dense material at the mid-latitudes to higher velocities. As a result for a given radius the wind density first decreases with increasing θ when going from the magnetic pole towards the mid-latitudes, and then increases towards the magnetic equator. However, due to the high temperatures in the equatorial region, the C IV density can still be quite low. In the magnetic equator the density is higher and radiative driving is less efficient, resulting in lower radial velocities. In Fig. 5.7 we can see that the radial velocities in the outflowing disk are of the order of 300–700 km s−1 , where the low mass-loss models have lower speeds than the high mass-loss models due to the higher efficiency of magnetic channeling in the low mass-loss model. So although the C IV density may not be very high in the equatorial regions due to the temperatures, almost all of the material is absorbing photons at low velocities and no photons are absorbed at high velocities. This is reflected in the spectra as a function of phase. At the poles the wind is not much affected by the magnetic field. Going to the mid-latitudes densities decrease somewhat, as material has been guided towards the equator. As a result the velocities are higher and the absorption decreases compared to the poles. Closer to the equator the collision region and the region between the “hot loop” and the collision region begin to cover the star. As the radial velocities are very low there and some material is even falling back onto the star, photons are only absorbed at low velocities and not at higher velocities. This results in more absorption at low velocities and less absorption at higher velocities near the equator as compared to the poles. 5.6 An X-ray ring model The observations of β Cep show enhanced C IV absorption over the magnetic equator and reduced absorption over the magnetic poles. This behaviour is reproduced by our phenomenological model with enhanced density in the equatorial region, discussed in Section 5.4. We expected that magnetic channelling of the wind would naturally reproduce similar behaviour, but the 2D-MHD models described in Sect. 5.5 instead show reduced absorption near the equator relative to the poles. Since magnetic channelling does not seem to be able to explain the observed behaviour we have to consider alternative models. Up to now we have assumed a fixed ionisation fraction in the wind. Depending on the process producing the ionising X-rays, the ionisation fraction could vary significantly throughout the wind. One process that is likely to produce X-rays, is the stellar wind from one (magnetic) hemisphere that is channelled towards the magnetic equator by the magnetic field and collides with the wind of the other hemisphere. 81 C HAPTER 5 X−ray ring z y x b Figure 5.11: The geometry of our X-ray ring model. The radius of the ring is set by b. In the shock region that results from this collision, the wind can reach temperatures of up to 108 K. The strongest shock region will be at the largest radius where the magnetic field is still able to channel the stellar wind. At this radius the winds of the two hemispheres will collide with the highest velocity. This radius is typically the Alvén radius, which for β Cep (with η∗ ∼ 102 ) is of the order 2–4 R∗ . To simulate the line profiles that would be observed from a star where C IV is formed by ionisation by X-rays originating from a thin ring, we have used the toy model described in App. A. In this model the X-ray emission from the ring is assumed to be optically thin, and the ionisation fraction is assumed to be proportional to the X-ray intensity over the electron density. The spherically symmetric wind structure is defined by a β velocity law with β = 0.8 and v∞ = 1500 km s−1 and a mass-loss rate of 1.3 10−8 M year−1 . We have calculated line profiles from our X-ray ring model using our SEI code. Reasonable variability of the line profiles is only found for simulations where the radius of the ring is significantly smaller than the Alv én radius. Example line profiles of a simulation with b = 1.3 R∗ are shown in Fig. 5.12. This radius of the ring is similar to that of the ”hot loops”observed in the MHD simulations. Although this is a simplified model, the results are very encouraging. The line profiles have many similarities with the observed line profiles of β Cep in Fig. 5.2. The main phase dependence of both the absorption and the emission is reproduced, and the same double-peaked structure is visible in the amplitude of the variability shown in the top panel. A configuration as described here, where the X-rays originate from a non-rotationally symmetric geometry (as the axis of the magnetic field is in general different from that of the rotational axis) would result in rotationally modulated X-ray flux. The modulation expected for our X-ray ring model is calculated in App. B. Modulated X-ray flux, possibly with the rotation period, is indeed observed for the O7.5IIIe star ξ Per (Massa et al. 2005). 82 N UMERICAL SIMULATIONS OF UV WIND - LINE VARIABILITY: β C EPHEI 32 spectra 1551 1.3 1 0.5 0 1 Phase 0.8 0.6 0.4 0.2 0 1539 2 1 0 1.2 1.1 1 0.9 0.8 0.7 1 σobs/σexp Wavelength (Å) 1545 1548 0.6 ← ← ← ← ← ← ← ← ← ← ← ← ← ← ← ← ← ← ← ← ← ← ← ← ← ← ← ← ← ← ← ← Quotient flux 1542 0.8 Phase Normalized flux σobs/σexp 1539 2 1 0 1.5 0.6 0.4 0.2 0 –1500 –1000 –500 0 500 1000 Velocity (km s–1) (stellar rest frame) 1542 Wavelength (Å) 1545 1548 32 spectra 1551 1.2 0.8 ← ← ← ← ← ← ← ← ← ← ← ← ← ← ← ← ← ← ← ← ← ← ← ← ← ← ← ← ← ← ← ← –1500 –1000 –500 0 500 1000 Velocity (km s–1) (stellar rest frame) Figure 5.12: Line profiles for a wind where the number of absorbing ions is determined by the balance between the ionising flux from an X-ray ring and recombinations with free electrons. 5.7 Conclusions and discussion In an attempt to explain the line-profile variability that is observed in the UV wind lines of known magnetic massive stars, we have performed line profile calculations of toy-models and full 2D-MHD simulations of the stellar wind structure. The observations of the UV wind lines show enhanced absorption over the magnetic equator compared to the magnetic poles. A simple phenomenological model with enhanced density near the magnetic equator qualitatively reproduces this behaviour. Such an enhancement of density in the equatorial regions could result from the magnetic channelling of the wind by the magnetic field. However, when we try to reproduce this behaviour with full 2D-MHD simulations, these results are not confirmed. Due to shock heating of the gas, most material near the equator is too hot to contain much C IV. The material in the equatorial regions that is able to cool is confined to thin sheets, that cover only a fraction of the stellar disk. As a result, we find that in fact the absorption near the equator is reduced instead of increased, contrary to what is observed. It seems that a detailed treatment of the superionisation due to X-rays in the stellar wind is required to explain the observed behaviour. Our simple model of a thin Xray ring in the magnetic equator is already able to qualitatively reproduce the main characteristics of the observed variability. This could also explain why the terminal velocity observed in the wind lines of ∼700 km s−1 is lower than the theoretically 83 C HAPTER 5 predicted terminal speed. Perhaps the X-rays are produced relatively close to the star, and able to maintain a higher fraction of superionisation close to the star than further out in the wind. An alternative explanation could be that in B-type stars the outer parts of the wind remain invisible due to the lower mass loss rates (as compared to O stars). Appendix A: X-ray emission from a ring We estimate the ionisation fraction due to X-rays emitted from an optically thin, infinitely thin ring of radius |b| in an optically thin wind, as shown in Fig. 5.11. For this purpose, we calculate the mean intensity of X-rays at each point in the wind. In standard spherical coordinates a point in the xz-plane, as seen from a point on the ring are given by: ~r0 = ~r − ~b (5.7) where ~b = (b cos φ, bsinφ, 0) is a point on the ring, and ~r = (r sin θ, 0, r cos θ) is a point in the wind in the xz-plane The distance of this point in the wind to a point on the ring is given by: |r0 |2 = b2 + r2 − 2rb cos φ sin θ To calculate the mean intensity, we integrate the flux over the entire ring: Z dl F (~r, θ) = F0 0 2 |r | Z 2π dφ F0 b , = b2 + r2 0 1 − a cos φ (5.8) (5.9) with F0 the X-ray emissivity per unit length of the ring and a= 2rb sin θ . b2 + r 2 (5.10) As r > 0 and b > 0 this means that 0 < a ≤ 1. For this interval we can evaluate the integral as: F0 b 2π √ (5.11) F (~r, θ) = 2 b + r 2 1 − a2 For points on the ring a = 1 and we have a singularity, as we have assumed that the flux decreases as 1/r 02 and the ring is infinitely thin. As this concerns only a very 84 N UMERICAL SIMULATIONS OF UV WIND - LINE VARIABILITY: β C EPHEI small fraction of the points, we can solve this by setting a maximum value on a of 0.99. If we assume a simple two-level atom, the ionisation balance is determined by the ratio of X-ray ionisations to recombinations F (~r, θ) nupper ∝ , nlower ne (5.12) which gives the fraction of atoms in the upper level, as n upper + nlower = n for a two-level atom. Appendix B: X-ray variability due to star occultation In the model presented in Sect. 5.6 and Appendix A, where the X-rays originate from an infinitely thin ring, it is possible to calculate the expected X-ray lightcurve assuming that no X-rays are absorbed in the stellar wind. Occultation of a part of the X-ray ring by the star will result in variability. From the point of view of the observer, the star casts a shadow which has the shape of a cylinder with a radius of R∗ to the backside of the star (see Fig. 5.13a). The observer is assumed to be in the direction of x → −∞ and the star at the origin. The X-ray ring will disappear in the shadow behind the star, somewhere on the intersection of the surface of this ”shadow-cylinder”and a sphere with radius b, the radius of the ring. This intersection has the shape of a circle with a radius of R ∗ p around the x-axis at x = a = b2 − R∗2 (see Fig. 5.13b). For a given rotation phase of the star, the plane of the ring can be chosen to be parallel to the z-axis. The angle φ (see Fig. 5.13b) is then determined by the rotation axis and rotation phase of the star. Only if α < φ < π − α (φ ∈ [0, π]) part of the ring will be in the shadow of the star. From Fig. 5.13c we can see that p = a/ sin φ, which gives us the angle β = arccos p/b. The total fraction of the ring that is occulted is 2β/2π = arccos(p/b)/π. If the Xray ring is located in the magnetic equator, the angle φ can be calculated using ~ e~x · B/|B| = cos φ. Fig. 5.14 shows lightcurves for different b, with the rotation axis perpendicular to the line of sight, and a magnetic field axis which has an angle of 90 degrees with the rotation axis. Acknowledgements. RSS thanks A. de Koter for useful discussions and S. Cranmer for making his SEI code available. Bibliography Arnaud, M. & Rothenflug, R. 1985, A&AS, 60, 425 Berghöfer, T. W., Schmitt, J. H. M. M., & Cassinelli, J. P. 1996, A&AS, 118, 481 85 C HAPTER 5 xz−plane z z ring of radius b plane of the ring sphere of radius b star observer star b β p x xy−plane y plane of the ring star α b φ p x a R * Figure 5.13: Geometry of the X-ray ring and the occulted part of the ring by the star. Figure 5.14: Lightcurves for the X-ray flux coming from a ring with a radius of b · R ∗ , that is occulted by the star. 86 N UMERICAL SIMULATIONS OF UV WIND - LINE VARIABILITY: β C EPHEI Castor, J. I. 1970, MNRAS, 149, 111 Castor, J. I., Abbott, D. C., & Klein, R. I. 1975, ApJ, 195, 157 Cranmer, S. 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R., Howarth, I. D., Rauw, G., Lennon, D. J., Bond, H. E., Negueruela, I., Nazé, Y., Corcoran, M. F., Herrero, A., & Pellerin, A. 2004, ApJ, 617, L61 88 C HAPTER 6 ATTEMPTS TO MEASURE THE MAGNETIC FIELD OF THE PULSATING B STAR ν E RIDANI R. S. Schnerr, E. Verdugo, H. F. Henrichs & C. Neiner Astronomy and Astrophysics, 452, 969 (2006) Abstract We report on attempts to measure the magnetic field of the pulsating B star ν Eridani with the Musicos spectropolarimeter attached to the 2m telescope at the Pic du Midi, France. This object is one of the most extensively studied stars for pulsation modes, and the existence of a magnetic field was suggested from the inequality of the frequency separations of a triplet in the stars’ oscillation spectrum. We show that the inferred 5-10 kG field was not present during our observations, which cover about one year. We discuss the influence of the strong pulsations on the analysis of the magnetic field strength and set an upper limit to the effective longitudinal field strength and to the field strength for a dipolar configuration. We also find that the observed wind line variability is caused by the pulsations. 89 C HAPTER 6 6.1 Introduction The B2III star ν Eridani (HD 29248, V = 3.93) is known to show radial velocity variations for more than a century (Frost & Adams 1903). It was found to be a multimode non-radial pulsator belonging to the class of β Cephei variables with a main frequency of 5.76 c d−1 , identified as a ` = 0, p1 mode. Handler et al. (2004) and Jerzykiewicz et al. (2005) detected two independent low frequency, high-order g modes, demonstrating that the star also belongs to the class of Slowly Pulsating B (SPB) stars. The star has the richest known oscillation spectrum of all β Cephei stars. From a very extensive campaign (see Handler et al. 2004; Aerts et al. 2004; De Ridder et al. 2004; Jerzykiewicz et al. 2005, hereafter Paper I, II, III and IV), 34 photometric and 20 spectroscopic frequencies were detected, corresponding to 14 different pulsation frequencies. Among these 14, 12 are high-frequency modes, out of which 9 form three triplets, which are slightly asymmetric. The symmetric part is attributed to the effect of stellar rotation, whereas the asymmetric parts could be due to higher order rotational effects or due to a magnetic field. From line profile modeling Smith (1983) derived v sin i ≈ 12 km s−1 for the projected equatorial velocity. This value is consistent with a rotation period of 30 - 60 days as derived from the modeling of the splitting of the strongest triplet around 5.64 c d−1 , consisting of ` = 1 modes (Dziembowski & Jerzykiewicz 2003, hereafter DJ; Paper I; Paper II). DJ found that the asymmetry of this triplet, as measured from data of van Hoof (1961), could only partly be explained by the quadratic effects of rotation (see, e.g., Saio 1981) and suggested that a strong magnetic dipole field of the order of 5-10 kG could explain this discrepancy. In a more recent analysis (Paper I) the asymmetry was found to be a factor of 2 smaller than before, and Pamyatnykh et al. (2004) could entirely account for the asymmetry in terms of quadratic rotational effects. However, in Paper III and IV the asymmetry was again found to be larger, and a second and third triplet were detected around 6.24 c d−1 and 7.91 c d−1 . More advanced modeling of the different separations and asymmetries in all three triplets is still needed. It is clear that an observational limit for the magnetic field strength will constrain such models, but until now no magnetic measurements of this star are available. The specific prediction by DJ motivated us to observe this star with the Musicos spectropolarimeter at the Télescope Bernard Lyot (TBL, Pic du Midi, France) to search for the presence of a magnetic field, as the detection limit of this instrument is of the order of 100 G, which is far below the predicted value. An additional argument to search for a magnetic field was the observed stellar wind variability as recorded 25 years earlier by the International Ultraviolet Explorer (IUE) satellite. This paper describes our attempts to measure the magnetic field of ν Eri from spectropolarimetric observations. We show the UV line variability as observed by the IUE satellite (Sect. 6.2.1), describe how we interpret the signatures in our measurements as entirely due to the strong pulsations in this star rather than due to a magnetic field (Sect. 6.2.3) and set an upper limit to the field strength (Sect. 6.3). 90 ATTEMPTS TO MEASURE THE MAGNETIC FIELD OF THE PULSATING B STAR ν E RI Table 6.1: Epochs of the IUE observations with applied radial velocity corrections and continuum ratios used to normalise the spectra (see text). The calculation of the radial velocities is based on Paper III. Date SWP HJD Exp. vrad Normalisation 1979 (−2443900) s (km s−1 ) near C IV Feb. 23 4351 28.476 48.6 29.2 1.0337 Feb. 24 4352 28.500 54.8 8.8 1.0157 4353 28.528 54.8 −19.2 0.9977 4354 28.550 54.8 −25.5 0.9927 4355 28.572 54.8 −18.3 0.9850 4356 28.594 49.8 −2.3 0.9854 4357 28.618 49.8 17.6 0.9877 4358 28.642 49.8 26.8 0.9929 4359 28.663 49.8 21.5 0.9927 Mar. 29 4787 61.504 49.8 −5.7 1.0164 6.2 Observations and data analysis 6.2.1 IUE observations Specific behaviour of variable stellar wind lines belongs to the well-known indirect indicators of a magnetic field in early-type stars (see Henrichs et al. 2003, for a review). In Fig. 6.1 we show the UV line profile changes in ν Eri, as recorded with the IUE satellite in 1979. The epochs of the observations and the radial velocity variations due to pulsation, which have been used to correct the spectra, are given in Table 6.1. The temporal variance measures the ratio of the observed to the expected variability, and is very similar for the C IV wind profiles in all magnetic B stars. We calculated the expected variability as a function of wavelength with a noise model as described by Henrichs et al. (1994). The temporal variance spectrum of ν Eri (lower panel in Fig. 6.1) is very similar to that of a magnetic oblique rotator, such as ζ Cas (a B2IV star, see Neiner et al. 2003a). Although only 10 high-resolution IUE spectra of ν Eri exist, nine of which were taken within one day and the other one month later, the peaks around +100 km s−1 in both doublet members are significant at the 3 σ level. Although this variability is suggestive of the presence of a magnetic field in ν Eri, most of the variation is observed over one day. This period is consistent with known pulsation modes, which have periods between 0.126–2.312 days, rather than with the rotation period, expected to be of the order of months (see also Sect. 6.3.1). Before the temporal variance is constructed, the 10 spectra are normalised such that the equivalent widths summed over the wavelength bands [1465, 1510] Å and [1575, 1605] Å are equal to their average value. These regions were selected to be 91 C HAPTER 6 Normalized Flux IUE CIV 1544 1546 1 0 3 σobs/σexp ν Eri B2III Wavelength (Å) Feb–Mar 1979 1548 1550 1552 1554 1556 10 spectra 2 1 0 –1000 –500 0 500 1000 Velocity (km s–1) (stellar rest frame) 1500 Figure 6.1: Ultraviolet C IV line profile variability of ν Eri. The normalised flux in the upper panel is given in units of 10−9 erg cm−2 s−1 Å−1 . The lower panel display the ratio of the observed variance to the expected variance (σobs /σexp ). The significant variations at red shifted wavelengths (around ∼100 km s−1 ) are similar to those observed in other magnetic B stars, including the He strong and He weak stars. The spectra of ν Eri were corrected for the calculated radial velocity shift due to the pulsations. free from stellar wind affected lines. The normalisation is necessary because of the intensity variations due to the pulsations (see, e.g., Porri et al. 1994, Paper I). In Fig. 6.2 we show the inverse normalisation constants, which can be considered as a measure of the UV flux for the 9 spectra of Feb 23/24, 1979. The main timescale seen in the light curve is the same as found in several optical bands in Paper I, and corresponds to that of the strongest pulsation mode detected in this star. 6.2.2 Spectropolarimetry The magnetic field measurements were carried out with the Musicos spectropolarimeter attached to the 2m TBL at the Pic du Midi, France. We obtained 32 spectra of ν Eri between 8 Feb. 2003 and 14 Feb. 2004 (see Table 6.2) from which circularly polarised (Stokes V ) and unpolarised spectra (Stokes I) are calculated. The technique to carry out high-precision magnetic measurements with this instrument is extensively described by Donati et al. (1997) and Wade et al. (2000). Each set of four subexposures was taken in the usual λ/4-plate position sequence q1, q3, q3, q1, corresponding to ±45◦ angles. We used the dedicated ESpRIT data reduction package (Donati et al. 1997) for the optimal extraction of the échelle spectra and to obtain Stokes I and V spectra. We also calculate a Null polarisation, called Stokes N , which represent the pollution by non-magnetic effects and should be null for a perfect measurement. The package includes a Least-Squares Deconvolution (LSD) routine to calculate a normalised average Stokes I line profile and corresponding 92 ATTEMPTS TO MEASURE THE MAGNETIC FIELD OF THE PULSATING B STAR ν E RI u- band UV flux 1.02 1.01 1 0.99 0.98 0.97 0.4 0.45 0.5 0.55 0.6 HJD- 2443928 0.65 0.7 Figure 6.2: UV continuum flux near C IV measured with IUE (dots – typical errors are 0.002) and the normalised U-band flux (line) deduced from the photometric pulsation analysis in Paper I and III; the typical error range is indicated by the dashed lines. The timescales of the variability observed in the UV and in the U-band are very similar. Stokes V and N line profiles of all available spectral lines (we used 107-108 lines). If a magnetic field is present it will result in a typical Zeeman signature in the average Stokes V profile, from which the effective longitudinal component of the stellar magnetic field can be determined (see Sect. 6.3.2). 6.2.2.1 Polarisation signatures Stokes V and N spectra were calculated using the standard equations: V RV − 1 = ; I RV + 1 where RV4 = N RN − 1 = I RN + 1 I1⊥ · I3k I2k · I4⊥ I1⊥ · I3k I2⊥ · I4k 4 · and RN = · . I1k · I3⊥ I2⊥ · I4k I1k · I3⊥ I2k · I4⊥ (6.1) (6.2) The symbols Ik⊥ and Ikk represent the perpendicular and parallel beams emerging from the beam splitter of subexposure k, respectively. The λ/4-plate orientations during the two subexposure pairs {1, 4} and {2, 3} are perpendicular to each other. Although no significant magnetic fields are detected (see Table 6.3), in several cases the average Stokes V profiles (see Fig. 6.3 and 6.4) show a significant signature which could be interpreted as due to a magnetic field. However, significant signatures are also visible in the corresponding Stokes N profile, which makes a magnetic interpretation questionable, especially because of the large changes in the line profile due to pulsations during the 4 subexposures. We now consider the origin of the signatures. In an ideal instrumental setup, pulsations would not create signatures in Stokes V (or N ) since for each spectrum both 93 C HAPTER 6 Table 6.2: Journal of TBL observations, with epochs, exposure times and a comparison (O − C) between the measured radial velocities (vr,O ) and predicted radial velocities (vr,C ) based on the ephemeris and amplitudes of Paper III. Note that these values correspond reasonably well, provided that a constant difference of 14±1 km s−1 for the system velocity is taken into account. Nr. 1a 1b 1c 1d 2a 2b 2c 2d 3a 3b 3c 3d 4a 4b 4c 4d 5a 5b 5c 5d 6a 6b 6c 6d 7a 7b 7c 7d 8a 8b 8c 8d Date Mid HJD −2450000 2003 Feb. 8 2679.300 2679.308 2679.316 2679.323 2003 Oct. 25 2937.530 2937.548 2937.559 2937.570 2004 Feb. 4 3040.452 3040.461 3040.471 3040.480 2004 Feb. 6 3042.412 3042.421 3042.430 3042.439 2004 Feb. 8 3044.445 3044.454 3044.464 3044.473 2004 Feb. 10 3046.289 3046.298 3046.308 3046.317 2004 Feb. 12 3048.413 3048.422 3048.431 3048.441 2004 Feb. 14 3050.272 3050.282 3050.291 3050.300 Exp. vr,O vr,C O−C s km s−1 km s−1 km s−1 600 −9.7 −20.5 10.8 600 −0.9 −11.7 10.8 600 7.4 −2.3 9.7 600 16.7 6.1 10.6 900 22.4 8.2 14.2 900 31.2 16.6 14.6 900 36.6 23.1 13.5 900 43.4 31.5 11.9 750 19.5 1.6 17.9 750 14.3 −0.1 14.4 750 12.3 1.6 10.7 750 15.4 2.5 12.9 750 −3.3 −16.6 13.3 750 −6.6 −19.0 12.4 750 −7.6 −20.7 13.1 750 −6.8 −19.5 12.7 750 50.5 27.8 22.7 750 45.5 21.3 24.2 750 32.3 10.1 22.2 750 12.4 −3.5 15.9 750 0.7 −10.5 11.2 750 8.3 −1.4 9.7 750 15.9 8.0 7.9 750 23.4 14.5 8.9 750 27.6 14.2 13.4 750 29.5 14.4 15.1 750 30.9 14.9 16.0 750 33.5 18.2 15.3 750 9.8 −6.6 16.4 750 13.6 −1.9 15.5 750 18.3 3.6 14.7 750 23.2 8.8 14.4 94 ATTEMPTS TO MEASURE THE MAGNETIC FIELD OF THE PULSATING B STAR ν E RI Figure 6.3: LSD results for ν Eri on 8 Feb. 2003. The average intensity line profile (bottom), the Stokes V profile (middle) and the Stokes N profile (top) are shown. V and N are shifted up by 1.05 and 1.10 respectively for display purposes. Note the signature in V which is typical for a magnetic field, but the presence of a signature in N , generated by the pulsations, indicates that the Stokes V profile could be affected (see text). right-handed circular and left-handed circular polarisation spectra are recorded simultaneously, and different line shapes between the four subexposures of one magnetic field measurement should cancel exactly (see Eq. 6.2). The practical reason why they do not cancel is that the two spectra of one subexposure partially follow a different light path and are recorded on different pixels of the CCD. This is why usually at least 2 (and often 4) subexposures are used. As a consequence the two spectra may have a different intensity level and slight differences in wavelength calibration, on average typically several hundred m s−1 (Semel et al. 1993; Donati et al. 1997). Such inevitable inaccuracies cause the different line shapes between the different subexposures to appear in the resulting Stokes V spectrum. For stars that do not show strong changes in line shape this problem does not occur, because the differences between the two spectra of one subexposure are corrected by the next subexposure where the opposite circular polarization state is recorded through the same light path, on the same pixels and with the same wavelength calibration. In the following section we closely examine the effect of these differences. 6.2.3 Modeling the Stokes V and N profiles To investigate the effect of pulsations on the signatures in the Stokes V profile we developed a model that predicts Stokes V and N signatures from the Stokes I profiles of all four subexposures. For each subexposure we first fit the average line profile, 95 Norm. Flux C HAPTER 6 1 1 1 0.98 0.98 0.98 0.96 0.96 0.96 0.94 0.94 0.94 0.92 0.92 0.92 I 0.9 -100 0.75 0.5 1 -50 0 50 100 N 0 -50 -100 50 6 0.9 100 0.75 0.25 Flux (h) 2 0.9 -100 0.5 0.5 0.25 0.25 0 0 0 -0.25 -0.25 -0.5 -100 0.6 0.4 -50 0 50 V -50 0 50 100 0.6 0.2 -100 0.4 0.4 0.2 0.2 0 0 0 -0.2 -0.2 -0.4 -0.4 -0.4 -0.6 -0.6 -50 0 50 100 100 -50 0 50 100 0 50 100 0.6 -0.2 -100 50 -0.5 -100 100 0 0.75 -0.25 -0.5 -50 -0.6 -100 -50 0 50 100 -100 -50 Velocity (km/s) Figure 6.4: Stokes I, N and V profiles of observations 1 (left), 2 (middle) and 6 (right). These profiles were selected to illustrate the effect of the pulsation. In the Stokes I plots (top), the solid lines represent the model fits. The dashed lines are the four exposures that were used for one magnetic field measurement. In the plots of the Stokes N (middle) and V (bottom, in h), the dashed line represents the observations, the thin solid line the model, and the thick solid line the corrected observations after subtracting the model to correct for the effect of the pulsations. Note that the corrected Stokes N profiles are all consistent with zero, which indicates that the assumption of a constant velocity shift between the two beams is sufficient to explain the signatures in Stokes N for pulsation-affected profiles. The limits of [−0.04%,+0.04%] adopted in Sect. 6.3.3 as the maximum amplitude of any undetected, broad, magnetic polarisation signatures, are indicated by the dashed lines in the bottom left plot. resulting from the LSD method, with the following function: I(v, vrad , c1 , c2 , c3 , c4 ) = c1 exp[−f (v, vrad , c2 , c3 , c4 )], (6.3) in which " f (v, vrad , c2 , c3 , c4 ) = c2 exp − v − vrad [1 + c3 Sign(v − vrad )]c4 2 # . In this equation the only variable is the velocity parameter v, whereas the five constants are vrad the radial velocity of the line, c1 the continuum level, c2 the minimum intensity level relative to c1 , c3 the asymmetry parameter and c4 the full line width. These five constants are determined for each subexposure by a least-squares best fit procedure. 96 ATTEMPTS TO MEASURE THE MAGNETIC FIELD OF THE PULSATING B STAR ν E RI To model the error in the wavelength calibration between the two beams of one subexposure, we characterise the typical wavelength shift between the two beams with a velocity parameter vshift . From the resulting 8 line profiles (4 subexposures × 2 beams) we calculate Stokes V and N profiles, with a fixed value for v shift to be determined by the fit. It is important to note that such an offset in wavelength calibration has a different effect than the presence of a magnetic field. A magnetic field would cause the spectrum in one circular polarisation state to be shifted relative to the other due to the Zeeman splitting; this shift is of opposite sign in the q1 and q3 exposures due to the switching of the two polarisation states between the subsequent subexposures. In our case the shift is the same in both q1 and q3 subexposures because this parameter is related to the beams themselves. We determine the parameter vshift by a minimum χ2 fit of the calculated Stokes N profiles from our model to the measured Stokes N profiles. The results can be found in Table 6.3. To check whether these values are realistic, we have extracted several ThAr exposures in the same way as we do for our science exposures. Since ThAr exposures are used to wavelength calibrate the spectra, we would expect similar inaccuracies between the two beams in these exposures as for our science exposures. We indeed find shifts in velocity between spectral lines in the two beams, varying from ∼ −3 to +1 km s−1 , explaining the average shifts found. In Fig. 6.4 we show the Stokes I, N and V profiles of the three observations which were subjected to the strongest pulsations. It is clear that the features in the Stokes N profile can be fairly well reproduced with our simple model, which contains only one free parameter. The signatures in the Stokes V that are predicted by our model have a somewhat smaller amplitude and appear to be slightly broader than the observed profiles, but the overall shape is very similar. The broadness of the modeled profiles is probably due to the fact that we use only one parameter, vshift , to characterise the shift of the average line profile, while in reality there is a distribution for all the different lines. Furthermore, at some phases the line profiles show extended wings which are not represented in our model, and resulted in slightly broader model fits. With this modeled contribution to the Stokes V profile we can quantitatively determine the spurious effect on the magnetic field determination as will be done in Sect. 6.3.2. 6.3 Results and discussion 6.3.1 UV variability The variability observed in the wind-lines of ν Eri looks similar to that observed for the magnetic early B-type stars β Cep, ζ Cas, V2052 Oph and ω Ori (Henrichs et al. 2000; Neiner et al. 2003a,b,c). However, since the timescale of this variability is comparable to the timescale of the pulsations rather than the rotation period (1–2 months), one can conclude that it is the pulsations that are responsible for the observed variability. The observed range of wind variability estimated from the vari97 C HAPTER 6 ance is of order 50–100 km s−1 (Fig. 6.1), which is in the same range as the expected range from the pulsations in this star. This is similar to what is observed in the magnetic stars, implying that the same low-velocity part of the stellar wind is affected, even though different mechanisms are involved. This phenomenon, where the lowvelocity part of the stellar wind is influenced by strong pulsations has previously been observed in strong pulsators, such as BW Vul (Burger et al. 1982; Smith & Jeffery 2003). 6.3.2 Magnetic field measurements The longitudinal component of the magnetic field averaged over the stellar disc in Gauss, is, as usual, calculated as (in velocity space): R v V (v) dv R Beff = 2.14 × 1011 , (6.4) λ g c [1 − I(v)]dv where λ is the average wavelength of the used lines in nm, g is their averaged Land é factor, and c the speed of light in cm/s. To estimate the strength of the signal in N , we calculated Neff from the Stokes N profile analogous to Eq. 6.4. Table 6.3: Results of the TBL magnetic field measurements. The signal to noise ratio per pixel (S/N) was measured around 550 nm in the Stokes V spectrum (order 108). The HJD was calculated halfway the four subexposures used for each magnetic measurement. Measurements shown are the effective magnetic field as measured from the Stokes V profiles before and after correcting for the pulsations (Beff and Bcorr respectively) and similarly for the values for N . The last column gives the best-fit velocity shift between the two beams. nr. Date 1 2 3 4 5 6 7 8 2003 Feb. 8 2003 Oct. 25 2004 Feb. 4 2004 Feb. 6 2004 Feb. 8 2004 Feb. 10 2004 Feb. 12 2004 Feb. 14 HJD −2452000 679.3090 937.5507 1040.4632 1042.4229 1044.4563 1046.3001 1048.4243 1050.2834 S/N 560 430 120 590 430 560 510 670 Range Beff Bcorr σB Neff Ncorr σN Vel. shift (km s−1 ) (G) (G) (G) (G) (G) (G) (km s−1 ) [−63,68] −5 −7 42 20 25 41 −0.42±0.08 [−66,78] 5 2 61 63 61 62 −0.43±0.16 [−86,92] 437 419 314 57 78 316 −2.71±3.75 [−65,69] 59 59 39 26 26 36 0.15±0.36 [−137,105] 163 153 127 77 71 125 −0.43±0.36 [−59,65] 11 6 39 −75 −74 38 −0.71±0.08 [−65,71] 36 36 46 −2 −1 44 −0.43±0.36 [−61,65] −9 −11 31 −6 −6 29 −0.57±0.12 In Table 6.3 we show the effective magnetic field strength as measured from the observations both before and after subtracting the modeled signature of the pulsations. The integration ranges used are set at two times the width of the fitted line profile as determined from Eq. 6.3 (see also Table 6.3). In general, the lower and upper limits of the integration are different due to the varying shape of the line profile. 98 ATTEMPTS TO MEASURE THE MAGNETIC FIELD OF THE PULSATING B STAR ν E RI The difference in Beff and Neff with and without the correction for pulsations is quite small. This is because the signatures created by the pulsations are almost symmetric, and hence do not much influence the first moments that determine these quantities. No magnetic field has been detected. However, for some observations significant signatures in Stokes V are found. This could indicate that although the effective longitudinal magnetic field strength is zero, there is still evidence for the presence of a magnetic field. Using our simple model, we have shown that we are able to model the signatures found in Stokes N very well, and at the same time predict Stokes V profiles that are very similar in shape to the measured ones. From this we conclude that the profiles we detect in Stokes N and V are the result of the combined effects of the pulsations and inaccuracies in wavelength calibration that were not removed by our imperfect modeling of these effects. 6.3.3 Constraining the magnetic field Constraining the magnetic field of a star from Stokes V profiles is not straightforward. A Stokes V profile is only sensitive to the line-of-sight component of the field and a light-intensity weighted average over the visible stellar disc is involved, similar to the formation of a line profile. Since one also has to account for the rotational Doppler shifts of the lines, it will be clear that Stokes V profiles can be very different for stars with the same (polar) field strength Bp and v sin i, even for a simple dipolar configuration. To determine the constraints on the polar field strength from our spectropolarimetry we used a model that calculates Stokes V profiles from the Zeeman splitting of Pl an eo f th es Rotation axis → Ω ky Magnetic axis → B α i Line of sight Figure 6.5: For a given magnetic field strength, the amplitude of the Stokes V signature depends mainly on α, the angle between the rotation axis projected onto the plane of the sky and the magnetic axis. 99 C HAPTER 6 an absorption line. In this simple model a spectral line at rest wavelength λ 0 is split into two Zeeman components with wavelength λ0 −∆λH and λ0 +∆λH , where ∆λH is the typical wavelength shift corresponding to the local line-of-sight component of the magnetic field (Mathys 1989). To determine the final profile we integrate over the visible stellar disc, using a limb darkening constant = 0.3 (Gray 1992), v sin i = 40 km s−1 , and an intrinsic line width of 10 km s−1 . This high value for v sin i is required to reproduce the average line profile, which is broadened by pulsations and the averaging process. We checked this model by reproducing Stokes V profiles for β Cep which has a polar field strength of 360 G (Henrichs et al. 2000; Donati et al. 2001). From this model we find that for a given field strength and v sin i the amplitude of the Stokes V profile mainly depends on the angle between the rotation axis projected onto the plane of the sky and the magnetic axis (the angle α in Fig. 6.5). Although the shape of the profile and Beff depend on whether the magnetic axis is pointing towards or away from us (maximum and minimum Beff ) or lies in the plane of the sky (Beff = 0), the amplitude of the profile is rather independent of this. Example profiles and the dependence of the maximum amplitude on α are shown in Fig. 6.6. The maximum amplitude approximately scales with | sin α|. For our observations (except for nr. 3, which has a very low S/N), magnetic polarisation signatures in Stokes V with an amplitude larger than approximately 0.04% would have been detected (see Fig. 6.4). With our model it is possible to constrain the strength of a dipolar magnetic field for a given α. For a maximum amplitude of 0.04%, we find that the upper limit on the polar field strength is: B p . 300 [G]/ sin α Figure 6.6: Results of model calculations of Stokes V profiles for a star with a dipolar magnetic field with a polar strength of 300 G. The left plot shows profiles for an inclination of i=0 ◦ , an angle between the rotation and magnetic axis of β = 90◦ and for rotation angle φ = 0◦ (magnetic axis pointing towards observer, maximum Beff – solid line), φ = 30◦ (dashed line), φ = 60◦ (dashed-dotted line) and φ = 90◦ (zero Beff – dotted line). Although the shape of the signature and Beff vary, the maximum amplitude remains approximately constant. The middle plot shows the profiles for i=0 ◦ , φ = 90◦ and β = 0◦ (solid line), β = 30◦ (dashed line), β = 60◦ (dashed-dotted line) and β = 90◦ (dotted line). On the right we show the maximum amplitude of the Stokes V profile vs. α for φ = 90 ◦ (squares), φ = 45◦ (triangles) and φ = 0◦ (circles). The lines represent sin(α) normalised to α = 90◦ (with i=0◦ , β = α). The maximum amplitude roughly scales with sin(α) with a slight dependency on the orientation (as can also be seen in the left plot). 100 ATTEMPTS TO MEASURE THE MAGNETIC FIELD OF THE PULSATING B STAR ν E RI Figure 6.7: Upper limit to the magnetic field strength at the magnetic pole as a function of the angle α. (see Fig. 6.7). To hide the predicted field of Bp ≥ 5 kG, α would have to be smaller than about 3.5◦ . So the angle between the magnetic field axis and the projected rotation axis would have to be smaller than this 3.5◦ , for all observations. Generally (unless the rotation axis lies exactly in the plane of the sky) α depends on the rotational phase. Our observations of February 2004 cover a period of 10 days, which, with an estimated period of ν Eri of 1–2 months, corresponds to 1/3 to 1/6 of the full rotation period. Since there are two magnetic extrema every rotation period, the inclination of the rotation axis would have to be smaller than ∼10 ◦ to allow α to be ≤ 3.5◦ over this whole rotation phase, with both β (the angle between the rotation and the magnetic axis) and φ (the rotational phase) fine-tuned to minimise α. It seems very improbable to have all these parameters conspire to hide a magnetic signature. 6.4 Conclusions Although the presence of a magnetic field is a possible explanation for the asymmetry of the splitting of the triplet around 5.26 c d−1 , and the UV spectra show variability similar to what is observed in known magnetic stars, no magnetic field has been detected. ν Eri may still harbour a weak magnetic field, but it is highly unlikely that the observed pulsation mode splitting is the result of a 5–10 kG magnetic field. In the absence of a magnetic field, we can conclude that the observed UV variability is due to the strong pulsations in this star, which is supported by the short timescale of the variability. However, the asymmetry of the splitting of the pulsation triplet around 5.26 c d−1 remains unexplained. In view of the discovery of two more triplets with different splittings and asymmetries, more sophisticated modeling of this star and all three triplets is required before further conclusions can be drawn on the relation between the stellar rotation and the splitting, and asymmetry, of the triplets. 101 C HAPTER 6 Acknowledgements. EV and HFH would like to thank W. Dziembowski for inspiring discussions on ν Eri during the Mmabatho meeting on magnetic fields in South Africa, November 2002 when this project was initiated. Most of the TBL observations were taken in service mode. Without this efficient observing mode this project could not have been done. In particular we acknowledge M. Aurière and F. Paletou for observing. We are also indebted to the capable TBL staff for assisting with the observations, G. Handler for providing radial velocity information, and M. Smith, the referee, for his constructive comments. 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Rygl Astronomy and Astrophysics, (to be submitted) Abstract Recently, the first magnetic fields in O- and B-type stars not belonging to the Bp stars have been discovered. The unexplained cyclic UV wind-line variability observed in a significant fraction of the early-type stars is likely to be related to such fields. In an attempt to increase our understanding of magnetic fields in massive stars, we have obtained 136 magnetic field strength measurements of a sample of 25 selected OB-type stars. We present the UV wind-line variability of all selected targets and summarise the results of spectropolarimetric observations of these stars obtained with the MUSICOS spectropolarimeter at the TBL, Pic du Midi, between December 1998 and November 2004. From the average Stokes I and V line profiles obtained with the LSD method we have measured the magnetic field strengths, radial velocities, and first moment of the line profiles. No significant magnetic field was detected in any of our OB-type stars. Typical 1σ errors are between 15 and 200 G. A possible detection in the O9V star 10 Lac remains uncertain, as the magnetic field values critically depend on the applied correction for fringe effects in the Stokes V spectra. We have found excess emission in UV-wind lines centered around the rest wavelength to be a new indirect indicator for the presence of a magnetic field in early B-type stars. The most promising magnetic candidates for future observations are the B-type stars δ Cet and 6 Cep, and a number of O stars. Although some O and B stars have relatively strong dipolar fields causing periodic variability in the UV wind-lines, such strong fields are not widespread. If the variability observed in the UV wind-lines of OB stars is generally caused by surface magnetic fields, these fields are either relatively weak (. few hundred G) or local. 105 C HAPTER 7 7.1 Introduction Magnetic fields play an important role in many astrophysical contexts. They have been discovered in all stages of stellar evolution. Fields of the order of µG to mG have been measured in star-forming molecular clouds, which are dynamically important during the collapse of the cloud (e.g. Crutcher 1999). The young T Tauri stars have magnetic fields that guide the accreting matter in the inner part of disk (e.g. Valenti & Johns-Krull 2004), and recently the first detections have also been reported for the accreting Herbig Ae/Be stars (Hubrig et al. 2004; Wade et al. 2005; Hubrig et al. 2006b). On the main sequence, magnetic fields have been found in latetype stars, which are thought to have dynamo-generated fields, and early-type stars, such as the strongly magnetic Ap/Bp stars (see Mathys 2001, for an overview). Also the end products of stellar evolution, white dwarfs and neutron stars, have been found to have very strong (106 − 1015 G) magnetic fields (see Wickramasinghe & Ferrario 2000; Manchester 2004, for a review). It is not known whether all new-born neutron stars are strongly magnetic, but certainly a very significant fraction apparently is. The immediate (unsolved) question arises how these neutron stars obtained their magnetic field: did their progenitors (the O and B stars) have no significant field and is the field generated just after the collapse, or did they possess a field when they were born, which survived during their life including the supergiant stage, and which is then strongly amplified during the core collapse? In the massive OB stars (>9 M ) fields are not generated by contemporary dynamos like in main-sequence low-mass stars, and fossil fields (originating from the interstellar medium) could indeed survive in the radiative phase during contraction, because these stars do not become fully convective, as put forward by Ferrario & Wickramasinghe (2005). These authors also argue that conservation of a significant fraction of the magnetic flux of the massive stars during their lives is consistent with the strong fields observed in neutron stars, as a close analogy with the origin of magnetic fields in strongly magnetic white dwarfs. Constraints on magnetic fields in rotating massive stars with winds have been studied by Maheswaran & Cassinelli (1992), whereas mechanisms have been considered to generate a field during the main-sequence phase either in the convective core (Charbonneau & MacGregor 2001) or in shear-unstable radiative layers (MacDonald & Mullan 2004; Mullan & MacDonald 2005). Long-term effects of magnetic fields on the stellar interior have been studied by, e.g., Spruit (2002); Maeder & Meynet (2003, 2004). The work by Heger et al. (2005) demonstrated the dramatical influence of incorporating a magnetic field in the star’s evolution towards the collapse. Simple magnetic flux conservation arguments show that observed field strengths in neutron stars of 1012 G are easily reached from a progenitor with surface field of 100 G or even less. The main difficulty with this scenario, however, is that these fields have not been measured, the most likely reason being that the expected strength is below the current detection limits. Braithwaite & Spruit (2004) showed that the kG fields found in the Ap/Bp stars are likely to be fossil remnants of star formation. If this result can be extrapolated to 106 M AGNETIC FIELD MEASUREMENTS OF OB- TYPE STARS Table 7.1: Known magnetic OB stars and their properties Spec. v sin i Prot M i β Bpol Type (km/s) (d) (M ) (deg.) (deg.) (gauss) θ1 Ori C O4-6V 20 15.4 45 ∼45 42±6 1100±100 HD 191612 Of?p <77 538a ∼40 ∼45 ∼45 ∼1500 τ Sco B0.2V 5b 41 15 ∼70 ∼90 ∼500c ξ 1 CMa B0.5IV 20 <37 14 ∼500 β Cep B1IV 27 12.00 12 60±10 85±10 360±40 V2052 Oph B1V 63 3.64 10 71±10 35±17 250±190 ζ Cas B2IV 17 5.37 9 18±4 80±4 340±90 ω Ori B2IVe 172 1.29 8 42±7 50±25 530±200 a To be confirmed b Mokiem et al. (2005) c Field more complex than dipolar Name Reference Donati et al. (2002) Donati et al. (2006a) Donati et al. (2006b) Hubrig et al. (2006a) Henrichs et al. (2000) Neiner et al. (2003b) Neiner et al. (2003a) Neiner et al. (2003c) more massive B and O stars, which also have stable, radiative envelopes, one would expect to find more magnetic massive stars than the few examples discovered so far (see Table 7.1). Considering the wide-spread phenomena observed in massive stars that could very well be attributed to magnetic fields, such as UV wind-line variability, unusual X-ray spectra, Hα variability and non-thermal radio emission (as summarised by Henrichs et al. 2005), a comprehensive study to confirm this conjecture is warranted. To get more insight into the fraction of magnetic OB-type stars and the strengths of the magnetic fields, we selected a group of OB stars with indirect indications of a magnetic field. In Sect. 7.2 we discuss the indirect indicators in detail for all the program stars, in particular stellar wind variability and abundances. In Sect. 7.3 we describe how we obtained circular polarisation spectra which allow for the determination of the longitudinal component of the magnetic field integrated over the stellar disk, and discuss the observations and the data reduction procedure. In Sect. 7.4 and 7.5 we present the results and conclusions that can be drawn from this survey. 7.2 Indirect magnetic-field indicators and target selection Cassinelli (1985) presented the first comprehensive survey of the evidence of magnetic fields in atmospheres of massive stars as the most likely explanation for the observed non-radiative activity. Henrichs et al. (2005) discussed a number of unexplained observational phenomena in massive stars that can be considered as indirect indicators of the presence of a stellar magnetic field, and which we used as criteria to select our targets in this study. We have primarily included targets selected on their UV wind-line variability, abundance anomalies and X-ray emission, and some 107 C HAPTER 7 Table 7.2: Properties of program stars in this survey with the integration limits used to determine the magnetic field strength. Rotational velocities are taken from the Bright Star Catalogue (Hoffleit & Jaschek 1991, O stars), Abt et al. (2002, B stars) and Abt & Morrell (1995, A stars), unless indicated otherwise. Spectral types are from Walborn 1972, except α Cam which was taken from (Walborn 1973). Selection criteria are UV-line variability (UV), nitrogen abundance anomalies (N, Gies & Lambert 1992), available X-ray observations by Berghöfer et al. (1996, X), and known β Cep-type pulsator (var). Nr. v sin i vrad Int. limits Years Selection sets (km s−1 ) (km s−1 ) criteria B stars 886 γ Peg B2IV 2 0 4.1 [−37.4,+37.4] 2002 var 16582 δ Cet B2IV 1 5 13.0 [−47.4,+47.4] 2003 N,var 37042 θ 2 Ori Ba B0.5V 1 50b 28.5 [−77,+77] 2004 X 74280 η Hya B3V 3 95∗ 21 [−192,+196] 1998 var 87901 α Leo B7V 1 300∗ 5.9 [−452,+452] 1998 cal 89688 RS Sex B2.5IV 2 215 5 [−350,+350] 1998 var 116658 α Vir B1III-IV+B2V 1 130 1 [−368,+264] 2000 X,var 144206 υ Her B9III 3 20 2.7 [−21,+21] 2001 abun 147394 τ Her B5IV 35 30∗ −13.8 [−107,+105] 2001/2002/2003 abun 160762 ι Her B3IV 2 0 −20.0 [−18.4,+19.0] 2001 UV,var 182568 2 Cyg B3IV 1 100 −21 [−244,+203] 2003 abun 199140 BW Vul B2IIIe 5 45 −6.1 [−159,+83] 2002 UV,var 203467 6 Cep B3IVe 1 120 −18 [−222,+249] 2002 UV 207330 π 2 Cyg B3III 15 30 −12.3 [−96.6,+96.6] 2001/2002 N 217675 o And B6IIIpe+A2p 1 200 −14.0 [−430,+500] 2002 UV 218376 1 Cas B0.5IV 18 15 −8.5 [−94,+94] 2001/2002 UV,N B supergiants 34085 β Ori B8Ia: 4 40 20.7 [−87.8,+87.8] 2004 UV,X 91316 ρ Leo B1Iab 2 50 42.0 [−116,+116] 1998 UV 164353 67 Oph B5Ib 6 40 −4.7 [−75,+86] 2002 UV O stars 30614 α Cam O9.5Ia 4 95 6.1 [−203,+203] 1998 UV,X 34078 AE Aur O9.5V 1 5 59.1 [−70,+70] 1998 UV,X 36861 λ Ori A O8III((f)) 4 66 33.5 [−170,+170] 2004 UV 47839 15 Mon O7V((f)) 5 63 33.2 [−168,+168] 1998/2004 UV,X 149757 ζ Oph O9.5Vnnc 3 379 −15 [−664,+664] 2001/2002 UV,X 214680 10 Lac O9V 15 31 −9.7 [−83,+83] 1998/2003/2004 UV,X Magnetic calibration stars and other targets 65339 53 Cam A2pSrCrEu 1 15 −4.8 [−51,+60] 1998 112413 α2 CVn A0pSiEuHg 8 <10 −3.3 [−31,+44] 2000/2001/2003 182989 RR Lyrae F5 9 <10d −72.4 [−48,+33] 2003 ∗ Rotational standard of Slettebak et al. (1975) a Houk & Swift (1999) b Wolff et al. (2004) c Maı́z-Apellániz et al. (2004) d Peterson et al. (1996) HD Star Spectral Type 108 M AGNETIC FIELD MEASUREMENTS OF OB- TYPE STARS β Cephei pulsators, as indicated in the last column of Table 7.2. A further selection was made according to the location of the observatory, observing season, and a favourable position in the sky at the time when no other higher priority targets were observable. We discuss here the various backgrounds. 7.2.1 Indirect indicators 7.2.1.1 Stellar wind variability Specific wind variability has proven to be a particularly successful indirect indicator, as demonstrated by the discovery of the magnetic OB stars β Cep (Henrichs et al. 2000), ζ Cas (Neiner et al. 2003a), V2052 Oph (Neiner et al. 2003b), and θ 1 Ori C (Donati et al. 2002). These stars were selected because of the striking time behaviour of the UV stellar wind lines of C IV, Si IV and N V, which in the first three cases was characterised by a very regular modulation of the whole profile, centered around the rest wavelength of the transitions, and very similar to what is observed in the magnetic Bp stars. Time-resolved observations, primarily obtained with the IUE and FUSE satellites, showed that at least 60% of the O stars, 17% of the non-chemically peculiar B stars, and all of the Bp stars have variable wind-lines (Henrichs et al. 2005). For an excellent review on cyclical wind variability from O stars see Fullerton (2003) who summarised the properties of the about 25 O stars with sufficient timeseries available. Two different categories can be distinguished. Firstly, for the stars with large scale, dipole-like magnetic fields (the Bp stars and the stars in Table 7.1), this variability is likely due to material that is guided by the magnetic field which co-rotates with the star (Shore 1987; Schnerr et al. 2007). In these oblique rotators the timescale of the variability coincides with the rotation period. Secondly, cyclical variability with a timescale comparable to the estimated rotation period of the star is commonly observed (as summarised by Fullerton 2003), where the period does not keep phase over much longer periods. This is presumably the case for the majority of the earlytype stars. The variability is mostly in the form of the Discrete Absorption Components (DACs), which are distinct absorption features which repeatedly progress bluewards through the absorption part of the P-Cygni wind profiles in a few days, i.e. on the order of the rotation timescale of the star. For many stars only snapshots of UV-wind lines are available rather than timeseries, but from the characteristic shape of the DACs one may conclude that these stars likely behave similarly, even if the timescale is unknown. Cranmer & Owocki (1996) showed by hydrodynamical simulations that DACs can occur as a consequence of magnetic footpoints on the stellar surface, which is a strong motivation for the search presented in this paper, although also other azimuthal perturbations of the wind, such as non-radial pulsations, could cause similar effects. Non-radial pulsations of O stars, however, have timescales much shorter than the DAC recurrence timescales (de Jong et al. 1999; Henrichs 1999). Although they could possibly contribute, they are for this reason not likely to be the main cause. Kaper et al. (1997) presented observational argu109 C HAPTER 7 ments for a magnetic origin of DACs in OB stars by studying simultaneous wind and Hα variability. Hα emission, which is formed close to the stellar surface, often shows covariability with the DACs; see for example the well-documented case of the O stars ξ Per (de Jong et al. 2001) and ζ Pup (Reid & Howarth 1996). A systematic search for cyclical variability in Hα profiles of 22 OB supergiants was carried out by Morel et al. (2004). The general conclusion is that the DACs and Hα variability diagnose the same phenomenon. For the Be stars there is in addition to the magnetic and DAC type of UV resonance line variability as described above, a third intermediate type: in these cases the variable absorptions occur at a much lower velocity than where DACs are found, but these are unlike in the magnetic oblique rotators found at velocities significantly above zero. This was shown by Henrichs et al. (2005, see also ten Kulve 2004) who concluded from a exhaustive study of all spectra of 81 Be stars in the IUE archive that 57 stars exhibit no wind variability, 5 stars are of the magnetic type, 7 stars show DAC variability and 12 belong to the intermediate type. The working hypothesis is that all stars with these latter three types of variability have surface magnetic fields but differ in geometry and in the magnetic confinement parameter η, the ratio of the magnetic to the wind pressure, as defined by ud-Doula & Owocki (2002): η≡ 2 2 Beq R∗2 Beq /8π ≈ , 2 ρv 2 /2 Ṁ v∞ (7.1) in which Beq is the equatorial field strength at the surface of the star with radius R ∗ , mass-loss rate Ṁ and terminal wind velocity v∞ , with wind density ρ. If η > 1 the magnetic field will dominate the wind behaviour. This would be the case for typical wind parameters in early-type stars with field strengths of 50 – 100 G. In Figs. 7.2, 7.3, and 7.4 we show selected C IV and Si IV profiles with a measure of their variability, of all our targets for which high-resolution spectra in the short wavelength range are available in the IUE archive, also if they were not selected for this study for this particular reason. For some stars we show both spectral regions if they are of particular interest. Before calculating the variance we normalised the flux values to their average value at selected portions of the continuum which were not affected by stellar wind, and simply applied the resulting scaling factor for the whole spectrum. This was needed because the UV flux may vary (BW Vul being an extreme example), and also mixed absolute-flux calibrations of images taken through the large and small aperture over the more than 18 years of operations of the IUE satellite were sometimes left with some systematic error. Typical signal to noise ratios are around 20, which should be born in mind when no variability is reported. The temporal variance spectra in the bottom panels indicate the significance of the variability (Henrichs et al. 1994; Fullerton et al. 1996). For each set of observations a separate noise model was applied, adapted to the quality of the set (see Henrichs et al. 1994). In Fig. 7.1 we show the development of the Discrete Absorption Components in the O9V star 10 Lac, as an example of (presumably) cyclic variability, although the time span is not sufficient to see repeated recurrency. For producing 110 Flux (10–9 erg cm–2s–1Å–1) σobs/σexp M AGNETIC FIELD MEASUREMENTS OF OB- TYPE STARS 3 10 Lac O9V 11 – 31 August 1995 IUE NV Wavelength (Å) 52 spectra 1232 1234 1236 1238 1240 1242 1244 1246 2 1 0 4 2 0 1.2 1 0.8 0.6 0.4 0.2 0 60 Quotient Flux 1.2 0.7 ← ← ← ← ← ← ← ← ← ← ← ← ← ← ← ← ← ← ← ← ← ← ← ← ← ← ← ← ← Time (HJD – 2449900) 58 56 54 52 50 48 46 44 42 –1500 –1000 –500 0 500 1000 1500 2000 Velocity (km/s) (stellar rest frame) Figure 7.1: Timeseries of 20 days in August 1995 of the N V UV resonance lines of the slowly rotating O9V star 10 Lac, showing the appearance and development of the Discrete Absorption Components in both doublet members. The horizontal scale and the two panels at the top are the same as in Figs. 7.2 to 7.4. Third panel: Overplot of quotient spectra (see text); Bottom panel: Gray-scale representation of the quotient spectra. Arrows indicate the mid epochs of the observations. the grayscale image we constructed quotient spectra by using a template spectrum generated from the highest points of all spectra, taking the noise into account. This method was developed by Kaper et al. (1999). Similar DAC behaviour has been observed in the magnetic O star θ 1 Ori C, where the origin of the DACs could be traced back to the north magnetic pole (Henrichs et al. 2005), which gives strong support to our hypothesis that this type of wind variability has a magnetic origin. 111 C HAPTER 7 δ Cet B2IV 0 3 2 1 0 500 1000 –1000–500 0 500 1000 Velocity (km s–1) 4 2 3 3 spectra 2 1 RS Sex B2.5IV α Vir B1III + B2V 0 0 3 3 2 2 1 1 0 0 –1000–500 0 500 1000 –1000–500 0 500 1000 Velocity (km s–1) 13 spectra 2 1 55 spectra 1 BW Vul B2IIIe 0 3 2 1 0 500 1000 –1000–500 0 500 1000 Velocity (km s–1) 500 1000 1545 1548 1551 12 spectra 1 υ Her B9III τ Her B5IV 0 0 3 3 2 2 1 1 0 0 –1000–500 0 500 1000 –1000–500 0 500 1000 (stellar rest frame) σobs/σexp Flux (10–10 erg cm–2s–1Å–1) ι Her B3IV 0 3 2 1 0 –1000–500 0 σobs/σexp Flux (10–10 erg cm–2s–1Å–1) σobs/σexp Flux (10–09 erg cm–2s–1Å–1) 1 2 Wavelength (Å) 1545 1548 1551 1545 1548 1551 1545 1548 1551 2 11 spectra 4 η Hya B3V α Leo B7V 0 0 3 3 2 2 1 1 0 0 –1000–500 0 500 1000 –1000–500 0 (stellar rest frame) σobs/σexp Flux (10–09 erg cm–2s–1Å–1) 6 1 12 spectra Wavelength (Å) 1545 1548 1551 1545 1548 1551 1545 1548 1551 2 spectra 7 spectra σobs/σexp Flux (10–09 erg cm–2s–1Å–1) 1 σobs/σexp Flux (10–10 erg cm–2s–1Å–1) 8 12 spectra 1545 1548 1551 8 2 spectra 6 4 2 2 1545 1548 1551 σobs/σexp Flux (10–10 erg cm–2s–1Å–1) 2 γ Peg B2IV 0 3 2 1 0 –1000–500 0 σobs/σexp Flux (10–11 erg cm–2s–1Å–1) σobs/σexp Flux (10–09 erg cm–2s–1Å–1) 4 σobs/σexp Flux (10–11 erg cm–2s–1Å–1) σobs/σexp Flux (10–09 erg cm–2s–1Å–1) 25 spectra σobs/σexp Flux (10–09 erg cm–2s–1Å–1) Wavelength (Å) 1545 1548 1551 1545 1548 1551 1545 1548 1551 3 2 spectra 2 1 π Cyg B3III 1 Cas B0.5IV 0 0 3 3 2 2 1 1 0 0 –1000–500 0 500 1000 –1000–500 0 500 1000 (stellar rest frame) Figure 7.2: Top panels: UV spectra near the C IV resonance lines as observed with the IUE satellite of the first part of the B stars of our sample. Bottom panels: ratio of observed to the expected variance, which is a measure for the significance of the variability. The horizontal velocity scales are with respect of the rest wavelength of the principal member of the C IV doublet, corrected for the radial velocity of the star as listed in Table 7.2. Vertical dashed lines denote the positions of the rest wavelengths of the doublet members. 112 M AGNETIC FIELD MEASUREMENTS OF OB- TYPE STARS 0 9 6 3 β Ori B8Ia: CIV 1539 1542 σobs/σexp Flux (10–09 erg cm–2s–1Å–1) 0 1 3 9 35 spectra 6 3 β Ori B8Ia: Si IV 0 3 2 1 0 500 1000 –1000 0 Wavelength (Å) 1545 1548 28 spectra 1 ο And B6IIIpe CIV ο And B6IIIpe SiIV 0 0 3 3 2 2 1 1 0 0 1000 2000 3000 –1000–500 0 500 1000 –1000 0 1000 2000 3000 Velocity (km s–1) (stellar rest frame) Wavelength (Å) 1390 1395 1400 1405 1545 1548 1551 σobs/σexp Flux (10–09 erg cm–2s–1Å–1) σobs/σexp Flux (10–09 erg cm–2s–1Å–1) 35 spectra 6 σobs/σexp Flux (10–09 erg cm–2s–1Å–1) 0 4 2 0 500 1000 –1000 0 1545 1548 1551 0 3 2 1 0 –1000–500 6 Cep B3IVe SiIV 9 1390 1395 1400 1405 3 6 spectra 2 1 3 6 spectra 2 1 67 Oph B5Ib SiIV 0 0 4 4 3 3 2 2 1 1 0 0 1000 2000 3000 –1000–500 0 500 1000 –1000 0 1000 2000 3000 –1 Velocity (km s ) (stellar rest frame) 1551 1385 11 spectra ρ Leo B1Iab CIV 0 3 2 1 0 –2000 –1500 –1000 –500 0 500 Velocity (km s–1) (stellar rest frame) 67 Oph B5Ib CIV 1390 1395 1400 1405 σobs/σexp Flux (10–10 erg cm–2s–1Å–1) 0 6 4 2 0 –1000–500 1 σobs/σexp Flux (10–10 erg cm–2s–1Å–1) 6 Cep B3IVe CIV 2 σobs/σexp Flux (10–10 erg cm–2s–1Å–1) 1 Wavelength (Å) 1390 1395 1400 1405 1545 1548 1551 3 37 spectra 28 spectra σobs/σexp Flux (10–09 erg cm–2s–1Å–1) 37 spectra 2 σobs/σexp Flux (10–10 erg cm–2s–1Å–1) σobs/σexp Flux (10–10 erg cm–2s–1Å–1) 1545 1548 1551 1000 1390 Wavelength (Å) 1395 1400 1405 11 spectra 1 0 3 2 1 0 –2000 ρ Leo B1Iab SiIV –1000 0 1000 2000 Velocity (km s–1) (stellar rest frame) 3000 Figure 7.3: Same as Fig. 7.2, but for the second part of the B stars, for which the Si IV doublet is also shown. 113 C HAPTER 7 Wavelength (Å) 1385 1390 1395 1400 1405 6 σobs/σexp Flux (10 –2000 0 1540 2000 1550 4000 1540 2 1 0 2000 AE Aur O9.5V Si IV 0 3 2 1 0 –2000–1000 0 1000 2000 3000 Velocity (km s–1) (stellar rest frame) 1560 45 spectra 15 Mon O7V((f)) C IV 0 4 2 0 –4000 –2000 2 4000 4 2 Wavelength (Å) 1545 1550 1555 104 spectra 3 2 1 32 spectra 6 λ Ori A O8III((f)) Si IV 0 3 2 1 0 –3000 –1500 0 1500 3000 C IV ζ Oph O9.5Ve 1535 1540 1545 1550 1555 (10–09 erg cm–2s–1Å–1) 0 3 2 1 0 4 1380 1385 1390 1395 1400 1405 σobs/σexp Flux (10–09 erg cm–2s–1Å–1) 8 –11 1 10 5 spectra 0 3 2 1 0 –2000 –1000 0 1000 2000 Velocity (km s–1) (stellar rest frame) σobs/σexp 1410 erg cm–2s–1Å–1) 1400 38 spectra α Cam O9.5Ia Si IV 1530 σobs/σexp Flux (10–09 erg cm–2s–1Å–1) 1390 σobs/σexp Flux (10–09 erg cm–2s–1Å–1) σobs/σexp Flux (10–09 erg cm–2s–1Å–1) 1380 6 32 spectra λ Ori A O8III((f)) C IV 4 2 0 4 3 2 1 0 –3000 –1500 Figure 7.4: Same as Figs. 7.2 and 7.3, but for the O stars in our sample. 114 0 1500 M AGNETIC FIELD MEASUREMENTS OF OB- TYPE STARS We note here that no long UV wind-profile timeseries are available for the recently discovered magnetic B0.5IV star ξ 1 CMa (Hubrig et al. 2006a): apart from one isolated spectrum the 12 remaining spectra were taken within 7 hours, and no typical modulation is present, but the C IV profiles are strikingly similar to the profiles in β Cep during maximum emission phase. See Fig. 7.5 for a comparison. In this figure (lower part) we overplotted an averaged and scaled C IV profile of 1 Cas, a star with the same spectral type and with a comparable value for vsini, to bring out the contrast with an average B0.5IV star. Such unusual emission, centered around zero velocity and in this case extending about 500 km s−1 to either side, is only found among magnetic B stars, and is an additional indirect indicator in the absence of timeseries. σobs/σexpFlux (10–09 erg cm–2s–1Å–1) σobs/σexpFlux (10–09 erg cm–2s–1Å–1) IUE C IV 1542 HD 205021 β Cep B1 IV Wavelength (Å) 1545 1548 1551 81 spectra 1554 4 3 2 1 0 8 6 4 2 0 –1000 –500 0 500 1000 Velocity (km s–1) (stellar rest frame) HD 46328 ξ1 CMa B0.5IV IUE C IV Wavelength (Å) 1542 1545 1548 1551 2 1554 1500 13 spectra 1557 1 HD 218376 1 Cas B0.5IV 0 3 2 1 0 –1000 –500 0 500 1000 Velocity (km s–1) (stellar rest frame) 1500 Figure 7.5: Comparison between C IV profiles of the magnetic oblique rotators β Cep (top) and ξ 1 CMa (bottom). The panels are similar to Fig. 7.2. For β Cep sufficient data are available to cover several rotational periods, showing the gradual transition from an enhanced to a reduced contribution of emission centered near zero velocity, typical for magnetic B stars. For ξ 1 CMa the data span only several hours and no rotational modulation can be expected, but the unusual emission profiles are very similar to the most extreme emission profiles in β Cep. To appreciate the excess emission we overplotted the scaled profile of the B0.5IV star 1 Cas, which has a typical C IV profile for this spectral type. This excess emission, symmetric around zero velocity, is an additional indirect indicator for a magnetic early B-type star. 115 C HAPTER 7 7.2.1.2 Nitrogen enhancements Gies & Lambert (1992) determined CNO abundances for a number of O and B stars. When the magnetic field of β Cep was discovered, the star being selected because of its unusual wind modulation (Henrichs et al. 2000), we realised that this star belonged to the N-enhanced stars in the sample of Gies & Lambert (1992), and other stars of this subset were included in our observing program with the TBL at the Pic du Midi, which are ζ Cas, δ Cet, π 2 Cyg and 1 Cas. As an immediate result the star ζ Cas was discovered to be magnetic (Neiner et al. 2003a), which showed the same type of wind modulation as β Cep, and recently also ξ 1 CMa (which is not observable from the TBL) was found to be magnetic (Hubrig et al. 2006a). Recently Morel et al. (2006) determined abundances of several elements including nitrogen for a number of slowly rotating β Cephei stars, in particular γ Peg, ν Eri, δ Cet, ξ 1 CMa, V2052 Oph and β Cep, the latter four of which have N-enhanced abundances, and are also magnetic oblique rotators (except δ Cet, see below), which confirms this strong correlation. They also discuss possible theoretical explanations. We note that the B2 III star ν Eri was not found to be magnetic by Schnerr et al. (2006), in agreement with this correlation. 7.2.1.3 X-ray properties Strong X-ray emission from hot stars was discovered by the Einstein mission (Harnden et al. 1979; Seward et al. 1979). Some OB stars show variable hard X-ray emission that cannot be explained by instability-driven wind shocks and magnetospheres may play a key role in the X-ray emission process, as was shown for β Cep by Donati et al. (2001). Schulz et al. (2000) showed that the magnetic star θ 1 Ori C has broadened Xray line profiles, symmetric around their rest wavelengths, as opposed to other types of X-ray line profiles which are narrow or blue shifted (e.g. Cohen et al. 2003). For non-magnetic hot stars Oskinova et al. (2004) and Oskinova et al. (2006) successfully modelled these profiles by taking clumping effects into account. Our target selection was also based on the X-ray observations by the ROSAT All Sky Survey (Bergh öfer et al. 1996). 7.2.2 Target selection Specific remarks pertinent to most of our targets regarding the selection criteria are listed here, in the order they appear in Table 7.2. We have aimed to include the most recent references, most of which were not available at the time of our observations, but which often strengthen the argument to include the particular star in future searches. HD 886 (γ Peg) B2IV, a well-known β Cep variable. The UV spectra in Fig. 7.2 are not corrected for the radial velocity due to the pulsations, and no other significant variability has been observed. Peters (1976), Pintado & Adelman (1993), and Gies & Lambert (1992) find approximate solar abundances for CNO elements. 116 M AGNETIC FIELD MEASUREMENTS OF OB- TYPE STARS HD 16582 (δ Cet) B2IV. Gies & Lambert (1992) found a nitrogen excess in this multiperiod β Cephei star (Aerts et al. 2006), which was confirmed by Morel et al. (2006). This N enhancement is similar to the three other known magnetic β Cephei stars, which makes this star a very strong magnetic candidate, as was also noted by Hubrig et al. (2006a). The 12 C IV profiles do not show typical variability as observed in the other oblique rotators, but this is not surprising as these spectra were all taken within 6 hours (covering less than 2 pulsation cycles), much less then the estimated rotation period of 2 or 4 weeks of this pole-on viewed very slow rotator with v sin i '1 km s −1 (Aerts et al. 2006). HD 37042 (θ 2 Ori B) B0.5V. This target was brought to our attention by M. Gagné based on Chandra X-ray observations, which showed this target as a bright X-ray source. HD 74280 (η Hya) B3V. This β Cep variable has a slight underabundance of carbon (Kodaira & Scholz 1970), but no value for the N abundance was given. The 7 IUE spectra are snapshots sampled over 12 years, but no significant wind profile changes are apparent. HD 87901 (α Leo) B7V. The spectra of this star have been used for the correction of the fringes in the spectra. For completeness we show the wind profiles, which did not change over 16 years. HD 89688 (RS Sex) B2.5V. This is an unusually rapidly rotating β Cephei star. The two UV spectra were taken 4 years apart, but show no variation. HD 116658 (α Vir) B1III-IV+B2V. This X-ray emitter and β Cephei variable is in a 4-day binary orbit. The radial velocity shifts, rather than wind changes, cause the variability in the C IV line, which were sampled over 16 years, with a concentration of 12 spectra over one pulsation cycle. HD 144206 (υ Her) B9III is a slowly rotating HgMn star (Adelman 1992; Adelman et al. 2006), with no obvious UV profile variations over 12 years. HD 147394 (τ Her) B5IV. This is a slowly pulsating B star (Briquet et al. 2003) with varying reports on the metallicity (see Niemczura 2003; Rodrı́guez-Merino et al. 2005). The UV C IV profiles show no variability when the low quality of some of the earlier data are taken into account. HD 160762 (ι Her) B3IV. A β Cephei star for which Kodaira & Scholz (1970) reported a slight N enhancement, although Pintado & Adelman (1993) finds solar abundances and Grigsby et al. (1996) finds a significant underabundance in iron relative to the Sun. The small apparent UV profile changes in total flux are caused by calibration uncertainties of IUE observations taken with the small aperture. HD 182568 (2 Cyg) B3IV. A He-weak star (Lyubimkov et al. 2004) for which Bychkov et al. (2003) list a magnetic field measurement of 19 ± 298 G from Balmer line wing measurements. There is only one reliable high-resolution IUE spectrum (not included in the figures) which show normal wind profiles. HD 199140 (BW Vul) B2IIIe. This well-known β Cephei star has very large UV flux variations, and the normalised C IV profiles show only radial velocity shifts due to the pulsation. Stankov et al. (2003) report subsolar values for the abundance of He and some other elements, but normal values for N. 117 C HAPTER 7 HD 203467 (6 Cep) B3IVe. This is one of the few Be stars in our sample. The emission in Hα and in other lines of this star was recently investigated by Saad et al. (2006). The UV wind lines of C IV, Si IV (see Fig. 7.3) and also the Al III λ1855 doublet (not shown) exhibit very strong variability of the intermediate type as described in Section 7.2.1.1, which makes this target a strong candidate. HD 207330 (π 2 Cyg) B3III. Gies & Lambert (1992) report N enhancement for this star. The two IUE spectra were taken 4 hours apart, and are not significantly different. We note that the C IV profile shows only absorption without additional emission as in ξ 1 CMa (Fig. 7.5). HD 217675 (o And) B6IIIpe+A2p. This is a well known Be-shell star, and very recently reported to be part of a quadruple system (Olević & Cvetković 2006), with the closest ∼3 M companion in an moderately eccentric 33 day orbit. The companion in such a close orbit may effect the stellar wind. The displayed C IV and Si IV (and also the Al III λ1855 doublet not shown) line profile changes are similar to those in magnetic rotators. HD 218376 (1 Cas) B0.5IV. N enhancement was reported by Gies & Lambert (1992). The only two reliable IUE spectra were taken within 2 hours, and no variability is apparent. HD 34085 (β Ori) B8Ia:. DACs were reported by Halliwell et al. (1988) and Bates & Gilheany (1990), in particular in the UV Mg II λ2800 resonance doublet (not shown). The C IV profiles show similar behaviour. HD 91316 (ρ Leo) B1Iab. Morel et al. (2004) searched for rotationally modulated Hα profiles in this star but did not detect any periodicity between 4.9 and 21.3 days. The snapshot UV wind line profiles clearly show the presence of DACs, but no time series are available for this star. HD 164353 (67 Oph) B5Ib. Koen & Eyer (2002) reported a 2.3 d period in Hipparcos photometry. The 6 available UV wind spectra contain DACs in all resonance lines. HD 30614 (α Cam) O9.5Ia. The UV resonance lines are all saturated and show no variability (Kaper et al. 1996), but in contrast the simultaneously taken Hα spectra of this runaway star show rapid variability in the emission (Kaper et al. 1997). Kaper et al. (1997) found that Hα emission changes were accompanied by DAC variations for most of the ten O stars included in their study. Crowther et al. (2006) finds a systematic N enhancement (in particular N/C) for all studied OB supergiants, including α Cam. Markova (2002) report on rotationally-modulated wind perturbations, whereas Prinja et al. (2006) investigated wind and atmospheric covariability and found a possible 0.34d non-radial pulsation in the He λ5876 line. HD 34078 (AE Aur) O9.5V. This famous runaway star has likely had early dynamical interaction with the runaway O9.5V star µ Col and the O star binary ι Ori (Gualandris et al. 2004, and references therein), and therefore a different history as compared to other O stars. The CNO abundances were determined by Villamariz et al. (2002). No obvious UV variability can be concluded from the 5 spectra that were obtained. HD 36861 (λ Ori A) O8III((f)). The progression of DACs in the UV resonance lines were studied by Kaper et al. (1996) and Kaper et al. (1999), but simultaneously taken 118 M AGNETIC FIELD MEASUREMENTS OF OB- TYPE STARS Hα profiles did not vary. The C IV profiles almost reach saturation. HD 47839 (15 Mon) O7V((f)). Two sets of migrating DACs in the N V doublet were reported by Kaper et al. (1996) who measured their properties and could set a lower limit of 4.5 days to the recurrence timescale. Walborn (2006) noted that the UV spectra of this star have unexplained peculiarities, a property shared with the magnetic stars HD191612, τ Sco and ξ 1 CMa. HD 149757 (ζ Oph) O9.5Vnn. Villamariz & Herrero (2005) find N enrichment in this very rapidly rotating runaway star. The UV resonance lines show multiple DACs which were thoroughly investigated by Howarth et al. (1993), accompanied by optical spectroscopic pulsation studies by Reid et al. (1993). HD 214680 (10 Lac) O9V. Quantitative measurements of DACs in a timeseries in November 1992 are given by Kaper et al. (1996) and Kaper et al. (1999). The progression of the DACs in N V in August 1995 is illustrated in Fig. 7.1. A Fourier analysis of this dataset yielded a period of 6.8 ± 1.0 d. The CNO abundances were determined by Villamariz et al. (2002). HD 182989 (RR Lyrae) F5. This star was added to our targetlist because this wellknown pulsator has an unexplained modulation of the pulsation amplitude (the Blazhko effect, see Blažko 1907), which could be due to magnetic fields. 7.3 Observations & data reduction We have observed our targets and two magnetic calibrators (see Table 7.2) with the Musicos spectropolarimeter attached to the 2m Telescope Bernard Lyot (TBL) at the Pic du Midi, France. The technique to carry out high-precision magnetic field measurements with this instrument is extensively described by Donati et al. (1997) and Wade et al. (2000). A total of 460 spectra have been obtained between December 1998 and June 2003, with a spectral resolution of R '35000 within the range from 449 to 662 nm. For each measurement of the effective magnetic field strength, a set of four subsequent exposures is used. These are taken in the usual λ/4-plate position sequence q1, q3, q3, q1. We used the dedicated ESpRIT data reduction package (Donati et al. 1997) for the optimal extraction of échelle orders. The package includes a Least-Squares Deconvolution (LSD) routine to calculate a high S/N, average Stokes I line profile and corresponding Stokes V line profile of all available, magnetically sensitive, spectral lines. 7.3.1 Determining the spectral properties To properly combine all the available lines from a spectrum using the LSD method, accurate line depths are required. We have determined the depths of the lines by fitting the following function to the highest S/N spectrum of each star: 119 C HAPTER 7 F (d1..N , λ0,1..N , ∆, vrad ) = 1 − N X di exp(− (1 − i=1 λ λ0,i )c ∆ − vrad !2 ). (7.2) Here N is the number of lines in the spectrum, of which line number i has a restwavelength of λ0,i and a central line depth of di , ∆ is the velocity step in which the line depth has decreased by a factor of e, vrad the radial velocity of the star and c the speed of light. The fits were made using a Levenberg-Marquardt χ-squared minimalisation scheme. The hydrogen lines were excluded from this analysis, since they have a different shape (mostly due to Stark broadening) and can therefore not be used in the LSD method. For the stars that showed strongly asymmetric lines, we have used ∆ 0 instead of ∆, where ∆0 = ∆+a for λ > (1+vrad /c)λ0 and ∆0 = ∆−a for λ < (1+vrad /c)λ0 , and a is a new parameter giving the asymmetry of the lines. All spectra with a/∆ & 10% were considered to have strongly asymmetric lines. For the magnetic calibration stars 53 Cam and α2 CVn we have used theoretical line lists and line depths, as we have for the F5 star RR Lyrae. 7.3.2 Measuring the effective magnetic fields In combining the lines with the LSD method, we have given each line a weight of λi · di · geff,i ; the wavelength, depth and effective Landé factor of the line. From the average line profiles we calculated the effective longitudinal field strength B l , using Bl = 2.14 × 1011 R vV (v)dv R , λgav c [1 − I(v)]dv (7.3) (see Mathys 1989), where Bl is in gauss, v is the velocity relative to the line center, V (v) and I(v) are the average Stokes V and I profile, λ and gav are the average wavelength and Landé factor of all the lines used in the analysis, and c is the velocity of light in cm s−1 . The integration limits for the measurements of Bl are determined by the line width resulting from the fit to the spectral lines. For the stars with symmetric lines we used integration limits of [−2∆, +2∆] (with the minimum of the Stokes I profile shifted to zero velocity). For the stars with variable Stokes I profiles and asymmetric lines we have determined the limits by fitting the Stokes I profile resulting from the LSD. The range that we used is [−2∆0 , +2∆0 ], where ∆0 is defined similar as before and the limits are determined by the most extreme spectra. 120 M AGNETIC FIELD MEASUREMENTS OF OB- TYPE STARS 7.4 Results 7.4.1 The magnetic calibrators To test the instrument and to establish the orientation of the optics which determines the sign of the polarisation, we included observations of well-known magnetic stars. In Fig. 7.6 and 7.7 we show the longitudinal magnetic field strength of our magnetic calibrators α2 CVn and 53 Cam against magnetic (rotational) phase and compare them with earlier measurements by Wade et al. (2000). The ephemeris and period are from Farnsworth (1932, α2 CVn) and Hill et al. (1998, 53 Cam). Although the results mostly agree with the earlier measurements, which confirms the correct operation of the instrument, there are significant deviations. These can be due to real changes on the stellar surface, e.g. changing abundance patterns (as has been suggested by Wade et al. 2000), but are most likely related to small differences in the line lists used. Figure 7.6: Longitudinal magnetic field measurements as a function of phase for α 2 CVn (full circles) compared with measurements of Wade et al. (2000, open squares), one of our magnetic calibrator stars. The line is a second order Fourier fit to the points of Wade et al. (2000). Figure 7.7: Same as Fig. 7.6, but for 53 Cam. 121 C HAPTER 7 7.4.2 Magnetic field measurements The derived magnetic field strengths of the observed targets are listed in Table 7.3. The targets that have been observed most extensively or deserve further comments are discussed below in order they appear in the table. For the remaining targets no evidence for the presence of magnetic fields has been found. We also do not find any significant circular polarisation signatures in the Stokes V profiles in these targets, which would indicate a magnetic field. A useful quantity to determine the presence of a magnetic field is the weighted averaged field, hBav i, and its corresponding error hσav i for a set of measurements: Pn Bi /σi2 (7.4) hBav i ≡ Pi=1 n 2 i=1 1/σi and v u n uX 1/σ 2 hσav i ≡ t i (7.5) i=1 where Bi is the measured value with error σi of measurement i, and n is the total number of observations. If a series of measurements yields hB av i hσav i a field is likely present. The opposite is, of course, not true: if the average value equals zero, it does not imply the absence of a field, because the configuration can be symmetric. As an example, for our 6 values for α2 CVn we obtain hBav i =260 G and hσav i =18 G, which confirms that a field is indeed detected. 7.4.2.1 δ Cet As summarised in Sect. 7.2.2 this star belong to the strongest magnetic candidates in our sample of B stars. Only one reliable measurement could be obtained of 40 ± 28 G and no magnetic signature in Stokes V was found (see Fig. 7.8). Given the pole-on view of this very slow rotator (2 or 4 weeks period) this might be a difficult target to detect a field, especially if the angle between the rotation axis and the magnetic axis is near 90◦ , as is the case in a number of other magnetic B stars (see Table 7.1). In such a configuration no rotational modulation can be expected, and the intensityaveraged magnetic field over the visible hemisphere (the quantity we measure) tends to vanish. 7.4.2.2 η Hya The only B star for which we have a significant detection is η Hya. The three measurements that we have acquired over a period of three days give a weighted average of 374 ± 74 G (using Eqs. 7.4, 7.5). This is a 5σ result, but close inspection of the images shows that fringing on the CCD may have impacted this conclusion. In Fig. 7.9 we show the average Stokes V profile of these observations, and although a clear 122 V/IC M AGNETIC FIELD MEASUREMENTS OF OB- TYPE STARS 0.003 0.002 0.001 0 –0.001 –0.002 –0.003 1 TBL, 2004/10/24 I/IC 0.95 0.9 LSD profiles of δ Cet B = 40 ± 28 G S/N = 622 0.85 0.8 0.75 –200 –150 –100 –50 0 50 Velocity (km/s) 100 150 200 Figure 7.8: Results for δ Cet of 2003/10/24. Average intensity profile (bottom) and the Stokes V profile (middle) and N profile (top). No magnetic signature is present. signature can be seen at the position of the line, the continuum also appears to be affected by a typical modulation over 250 km s−1 intervals. To test whether fringing indeed affected our measurement, we have used observations of the non-magnetic star Vega from the same run to correct for the fringing of the spectra. The procedure we used to remove fringes is discussed in more detail by Verdugo et al. (2003). V/IC V/IC After the correction has been applied, no evidence for a magnetic signature in the Stokes V profile remains. From this we conclude that the Stokes V signature in this star, resembling a magnetic field signature, is a result of fringing. LSD profiles of η Hya TBL, 1998/12/17–20 0.001 B = 374 ± 74 G 0.0005 Uncorrected 0 –0.0005 –0.001 0.001 After fringe correction B = –108 ± 76 G 0.0005 0 –0.0005 –0.001 1 I/IC S/N = 1350 0.95 0.9 –500 –400 –300 –200 –100 0 100 200 300 400 500 Velocity (km/s) Figure 7.9: The weighted average of the three η Hya LSD profiles. Shown are the average intensity profile (bottom) and the Stokes V profile (top) before (dashed line) and after the fringe correction (full line). A marginal magnetic signature is present without correction for the fringes, which disappears, however, after the correction has been applied. 123 C HAPTER 7 7.4.2.3 τ Her We have two detections which are larger than 3σ: 506±161 G on 2002/06/12 and 390±124 G on 2003/06/16. These are, however, not confirmed by measurements from the same or adjacent nights. Applying Eqs. 7.4 and 7.5 for the whole dataset of 35 values, we find 23± 26 G, which is entirely consistent with a null result. 7.4.2.4 6 Cep This Be star is a strong magnetic candidate because of its wind behaviour (see Sect. 7.2.2), but only one measurement with a large error bar could be obtained: 1518 ± 766 G, due to the large value of v sin i which prohibits a more accurate measurement. 7.4.2.5 π 2 Cyg For the set of 15 measurements we obtain a weighted average of hB av i = −33 G and a corresponding error hσav i =30 G (Eqs. 7.4, 7.5), consistent with zero. None of the individual values are significant with typical errors of ∼ 120G, and hence no field has been detected. 7.4.2.6 o And Being a strong magnetic candidate because of its wind emission and modulation in spite of its late spectral type (B6), this star will likely remain a difficult target because of its high value of v sin i and possible contamination by its companion. 7.4.2.7 1 Cas A weighted average of hBav i = −1 G with a corresponding error hσav i =18 G (Eqs. 7.4, 7.5) is consistent with zero. Also for this star none of the individual values are significant, and hence no field has been detected among the 18 measurements. 7.4.2.8 15 Mon No significant detections have been found among the 5 measurements. This star remains a strong magnetic candidate in view of the similarities with other magnetic stars as discussed in Sect. 7.2.2. 7.4.2.9 10 Lac Although no clear Stokes V signature is found among the 15 individual magnetic field determinations of this O star, there is one possible significant detection at the 3.7σ level of 204 ± 55 G (see Fig. 7.10). In addition, we find hB av i = 44 ± 14 G. We have investigated the possible effects of fringes on the magnetic field measurements even though no clear modulation as seen in η Hya is apparent in the Stokes V spectra of 10 Lac. Assuming that the fringe patterns are the same as in η Hya, 124 M AGNETIC FIELD MEASUREMENTS OF OB- TYPE STARS and Vega and β Cep (see Henrichs et al. 2006) we find that after applying the fringe correction the magnetic field values have on average decreased by 59 G, resulting in hBav i = −18 ± 14 G. In Fig. 7.10 we show the Stokes V and I LSD profiles of measurement number 10 of Table 7.3 both before and after application of the fringe correction. The 3.7σ detection of 204 ± 55 G decreases to a value of 140 ± 55 G, or 2.5σ. Whether this result is more reliable is not clear as we cannot be certain that the fringe pattern in the spectra of 10 Lac is the same as in the fringe template used for the correction, in particular because the noise is relatively high. The cause of the fringes is not completely understood, so the fringes in 10 Lac could well be much weaker than in the much brighter targets where fringes are normaly seen. It is clear that the evidence for the presence of a magnetic field in 10 Lac depends strongly on our assumptions concerning the fringes and it is premature to claim a detection. Only a careful study of the instrumental effects responsible for the fringes, or new, higher signal to noise, observations with new instruments such as Narval at the TBL could provide more a definite answer. In view of the long recurrence timescale of the DACs (about 1 week or a multiple thereof) and the low value of v sin i of 31 km s−1 , the star is most likely a slow rotator which is viewed nearly equator on. LSD profiles of 10 Lac TBL10, 2004/11/05 V/IC 0.002 Uncorrected B = 204 ± 55 G 0 –0.002 V/IC 0.002 After fringe correction B = 140 ± 55 G 0 –0.002 1 0.95 I/IC 0.9 S/N = 234 0.85 0.8 0.75 0.7 –500 –400 –300 –200 –100 0 100 200 300 400 500 Velocity (km/s) Figure 7.10: Shown are the LSD intensity profile (bottom) and the Stokes V profile (top) of 10 Lac on 2004/11/05 (number 10 in Table 7.3). The integration limits were [-83, 83] km s −1 . 125 C HAPTER 7 7.4.2.10 RR Lyrae Our upper limits for the magnetic field strength of RR Lyrae confirm the results of Chadid et al. (2004). 7.4.3 Radial velocities and pulsations For all our observations we have measured the heliocentric radial velocity of the minimum in the Stokes I line profile, vmin , and the first moment of the Stokes I line profile vm1 , see Table 7.3. Of our targets, four are listed in the 9th Catalogue of spectroscopic binary orbits (Pourbaix et al. 2004). The single-lined binary ι Her indeed shows radial-velocity changes in our spectra. α Vir shows both a large radial velocity and an asymmetric line profile that are most likely due to its close double-lined binary nature. Not recognised as binaries from our observations are the single lined o And, for which we only have one spectrum, and π 2 Cyg, which has a rather small radial velocity amplitude of 7.8 km s−1 . RS Sex, BW Vul, τ Her and RR Lyrae show radial-velocity changes that are most likely due to pulsations. In 67 Oph and 1 Cas small changes in the radial velocity are observed, which could be an indication of binarity. 7.5 Conclusions In this survey of 25 OB type stars, we have not found conclusive evidence for magnetic fields in B type stars. A possible detection in the O9V star 10 Lac remains uncertain, as the magnetic field values critically depend on the applied correction for fringe effects in the Stokes V spectra. Only with detailed knowledge of the instrumental origin of the fringes improvement can be achieved. Although for some rapid rotators the error bars are too large to really constrain any realistic fields, for the majority of the targets, the error bars are of the order of 100 G or better. Similar results have been obtained in a large survey of B-type stars in open clusters and associations by Bagnulo et al. (2006). Although the effective field strength of course depends on the orientation of the rotation and magnetic axes, we can conclude from these results that strong (&500 G) fields are certainly not widespread among normal (non chemically peculiar) B-type stars. It is still possible that the UV wind-line variability, which is observed in a significant fraction of the OB stars (see Henrichs et al. 2005), is due to large scale magnetic fields. However, such fields will have to be of the order of fifty to a few hundred gauss to remain undetected in these surveys, but still have sufficient impact on the stellar winds. Another possibility is that the perturbation of the wind at the stellar surface (as modelled by Cranmer & Owocki 1996) is due to strongly magnetic spots. Since these spots cover only a small part of the stellar disk, the local magnetic fields can be quite strong, but still remain undetected. The finite lifetime of such spots would also explain why the UV line-variability has a timescale similar to the rota126 M AGNETIC FIELD MEASUREMENTS OF OB- TYPE STARS tion period, but is not strictly periodic over longer timescales. If the O star 10 Lac would be found to be magnetic, this would a be a strong argument in favour of one of these hypotheses. We have identified a number of stars suitable for follow-up studies: the B stars δ Cet and 6 Cep, and a number of O stars. In addition we have found excess emission in UV-wind lines centered around the rest wavelength to be a new indirect indicator for the presence of a magnetic field in early B-type stars. Acknowledgements. This research is partly based on INES data from the IUE satellite. We would like to thank the helpful staff of the Telescope Bernard Lyot (TBL). Based on data obtained with the TBL the Observatoire du Pic du Midi (France). This work has made use of the Simbad and ADS databases, operated at CDS, Strasbourg, France and the Vienna Atomic Line Database, operated at Institut für Astronomie, Vienna, Austria. 127 C HAPTER 7 Table 7.3: Summary of the results of the data analysis. The columns denote, respectively: sequence number of the observation, date of observation, Heliocentric Julian date, measured longitudinal component of magnetic field strength (integrated over the stellar disk) with 1σ errors, velocity of the minimum, and first moment of the Stokes I line profile both with 1σ errors, for all observed targets arranged in the same order as in Table 7.2. Beff gauss B stars γ Peg/HD 886 1446.656 3±20 1453.648 −1±17 δ Cet/HD 16582 1937.501 40±28 θ 2 Ori B/HD 37042 2315.694 143±99 η Hya/HD 74280 164.724 279±116 165.725 436±103 167.544 442±246 α Leo/HD 87901 161.766 −1303±848 RS Sex/HD 89688 164.760 584±1105 165.770 1071±1052 α Vir/HD 116658 731.353 −816±408 υ Her/HD 144206 1091.510 4±18 1091.531 35±23 1091.548 −27±25 τ Her/HD 147394 1075.399 −256±160 1087.371 −40±116 1087.394 −192±127 1438.364 80±167 1438.380 506±161 1440.385 −184±136 1440.402 115±142 1442.368 −128±131 1442.384 43±156 1444.380 −119±96 1446.443 363±430 1446.459 −5±157 1446.475 189±140 1447.363 −1±118 1447.379 97±116 Obs Date HJD nr year/m/d −2451000 1 2002/06/21 2 2002/06/28 1 2003/10/24 1 2004/11/06 1 1998/12/17 2 1998/12/18 3 1998/12/20 1 1998/12/14 1 1998/12/17 2 1998/12/18 1 2000/07/05 1 2001/07/01 2 2001/07/01 3 2001/07/01 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 2001/06/14 2001/06/26 2001/06/26 2002/06/12 2002/06/12 2002/06/14 2002/06/14 2002/06/16 2002/06/16 2002/06/18 2002/06/20 2002/06/20 2002/06/20 2002/06/21 2002/06/21 128 vmin km s−1 vm1 km s−1 −0.3±0.3 1.8±0.3 0.6±0.1 −0.5±0.1 9.9±0.2 −0.8±0.1 31±1 0.2±0.4 20±3 20±3 17±5 1±1 −1±1 3±2 21±35 17±16 9±12 13±14 −2±5 13±5 81±13 −46±4 4.0±0.2 4.0±0.3 4.1±0.2 −15±1 −14±1 −14±1 −18±2 −19±2 −16±1 −16±1 −16±3 −19±4 −15±2 −12±2 −13±2 −13±2 −13±3 −13±2 0.1±0.1 0.1±0.1 0.1±0.1 2.2±0.4 1.6±0.4 1.3±0.4 −3.2±0.5 −3.2±0.5 1.7±0.4 1.5±0.4 −1.9±0.6 −1.0±0.9 2.7±0.5 1.6±0.5 1.7±0.4 0.8±0.4 2.8±0.9 2.7±0.7 M AGNETIC FIELD MEASUREMENTS OF OB- TYPE STARS Table 7.3: continued. Obs nr 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 1 2 1 1 2 3 4 5 1 1 2 3 4 5 6 7 8 9 Date HJD Beff year/m/d −2451000 (gauss) 2002/06/23 1449.361 −160±138 2002/06/24 1450.365 101±108 2002/06/26 1452.372 −266±173 2002/06/26 1452.392 38±229 2003/06/07 1798.389 24±234 2003/06/07 1798.406 242±222 2003/06/08 1799.391 57±180 2003/06/08 1799.408 156±152 2003/06/10 1801.366 −141±348 2003/06/10 1801.383 −418±520 2003/06/10 1801.489 173±170 2003/06/11 1802.382 469±193 2003/06/11 1802.399 −52±155 2003/06/12 1803.454 −12±180 2003/06/16 1807.373 390±124 2003/06/17 1808.366 −179±209 2003/06/17 1808.384 −167±213 2003/06/18 1809.369 131±151 2003/06/19 1810.365 7±127 2003/06/22 1813.367 −68±179 ι Her/HD 160762 2001/06/18 1079.375 −19±15 2001/06/26 1087.423 8±14 2 Cyg/HD 182568 2003/06/09 1800.442 1192±2225 BW Vul/HD 199140 2002/06/22 1447.510 105±347 2002/06/22 1447.526 536±280 2002/06/22 1447.543 −402±260 2002/06/23 1448.525 92±168 2002/06/23 1448.541 −116±148 6 Cep/HD 203467 2002/06/19 1444.519 1518±766 π 2 Cyg/HD 207330 2001/06/22 1082.567 44±87 2001/06/25 1085.567 −64±106 2001/06/25 1085.584 −130±107 2001/06/27 1087.549 −42±139 2001/06/27 1087.588 202±156 2001/06/29 1089.575 −51±134 2001/06/29 1089.592 −112±135 2001/06/30 1090.576 −140±111 2001/06/30 1090.594 −74±126 129 vmin (km s−1 ) −16±3 −15±1 −13±2 −13±2 −18±6 −16±8 −22±2 −23±1 −12±2 −12±3 −15±1 −16±6 −17±6 −17±2 −14±1 −13±2 −13±2 −21±3 −18±1 −14±2 vm1 (km s−1 ) −4.7±0.5 −0.2±0.3 5.8±0.8 6.4±0.7 −1.6±1.4 −4.0±1.4 −7.1±0.4 −6.3±0.4 2.9±0.8 2.9±0.8 2.1±0.4 1.9±1.4 4.8±2.0 5.1±0.7 5.0±0.5 4.7±0.6 4.8±0.6 −5.7±0.7 −1.6±0.4 3.9±0.7 −30±0.3 −21±0.3 0.7±0.1 0.5±0.1 −25±20 4±10 17±1 42±1 70±1 26±8 51±25 −9±1 −13±1 −21±1 −18±3 −24±9 −10±21 −2±8 −8±4 −8±4 −8±4 −8±4 −8±4 −9±4 −9±4 −8±4 −8±4 −2±2 −1±2 −1±2 −1±2 −1±2 −1±2 −1±2 −1±2 −1±2 C HAPTER 7 Table 7.3: continued. Obs nr 10 11 12 13 14 15 1 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 1 2 3 4 1 2 1 2 3 4 5 6 Date HJD Beff vmin year/m/d −2451000 (gauss) (km s−1 ) 2002/06/13 1438.560 313±200 −9±5 2002/06/13 1438.576 −37±191 −9±5 2002/06/16 1441.550 −116±121 −9±4 2002/06/16 1441.567 −27±113 −9±4 2002/06/21 1446.501 51±123 −9±4 2002/06/25 1450.522 −36±69 −9±4 o And/HD 217675 2002/06/15 1440.561 331±988 −21±11 1 Cas/HD 218376 2001/06/24 1084.597 −111±74 −8±1 2001/06/24 1084.624 −72±60 −7±1 2001/06/24 1084.641 −65±60 −7±1 2001/07/02 1092.580 −105±85 −8±1 2001/07/02 1092.599 73±80 −8±1 2001/07/03 1093.583 23±60 −8±1 2001/07/03 1093.600 46±66 −9±1 2002/06/11 1436.541 33±71 −6±1 2002/06/11 1436.558 65±69 −6±1 2002/06/11 1436.574 −40±73 −6±1 2002/06/12 1437.544 −13±102 −6±1 2002/06/12 1437.560 24±92 −6±1 2002/06/12 1437.576 −165±84 −6±1 2002/06/14 1439.571 −83±80 −6±1 2002/06/14 1439.588 113±90 −6±1 2002/06/17 1442.528 154±85 −7±1 2002/06/17 1442.544 84±84 −7±1 2002/06/17 1442.564 87±73 −7±1 B supergiants β Ori/HD 34085 2004/11/07 2316.509 −42±50 3±1 2004/11/07 2316.515 −4±46 4±1 2004/11/07 2316.520 −7±41 4±1 2004/11/07 2316.531 1±27 3±1 ρ Leo/HD 91316 1998/12/15 162.752 30±45 41±1 1998/12/16 163.736 11±19 40±1 67 Oph/HD 164353 2002/06/15 1441.401 −33±50 −3±1 2002/06/17 1443.417 49±51 −1±1 2002/06/22 1448.411 −98±41 −1±1 2002/06/22 1448.427 0±40 −1±1 2002/06/26 1452.455 166±233 3±1 2002/06/26 1452.471 −248±85 3±1 130 vm1 (km s−1 ) −1±2 −1±2 −2±2 −2±2 −1±2 −1±2 19±6 −0.8±0.3 −0.6±0.2 −0.6±0.2 −0.9±0.3 −0.9±0.3 1.3±0.3 1.3±0.3 −0.4±0.3 −0.5±0.3 −0.4±0.2 −0.2±0.3 −0.1±0.3 −0.3±0.3 −0.4±0.3 −0.4±0.3 −0.4±0.3 −0.4±0.3 −0.2±0.3 0.9±0.2 −0.1±0.2 −0.1±0.2 0.9±0.2 1.1±0.3 0.4±0.3 2.3±0.4 2.6±0.4 1.9±0.6 1.8±0.6 2.7±0.5 2.6±0.4 M AGNETIC FIELD MEASUREMENTS OF OB- TYPE STARS Table 7.3: continued. Beff (gauss) O stars α Cam/HD 30614 161.698 208±177 162.672 37±186 164.680 3±84 165.683 206±78 AE Aur/HD 34078 163.680 54±46 λ Ori A/HD 36861 2315.487 −47±177 2315.543 45±137 2315.574 152±124 2315.619 56±69 15 Mon/HD 47839 161.658 204±215 2317.531 −44±165 2317.577 −92±151 2317.636 −27±137 2317.705 −114±180 ζ Oph/HD 149757 1081.388 −1189±721 1083.574 −1267±1692 1446.426 5678±3233 10 Lac/HD 214680 163.252 21±37 163.297 62±31 1799.607 −54±90 1802.588 39±69 1803.532 238±90 1807.556 66±62 1809.508 53±44 1811.622 7±50 2315.311 −45±52 2315.355 204±55 2315.400 52±57 2315.445 −17±65 2315.489 26±74 2317.396 49±60 2317.462 7±52 Obs Date HJD nr year/m/d −2451000 1 2 3 4 1998/12/14 1998/12/15 1998/12/17 1998/12/18 1 1998/12/16 1 2 3 4 2004/11/05 2004/11/06 2004/11/06 2004/11/06 1 2 3 4 5 1998/12/14 2004/11/08 2004/11/08 2004/11/08 2004/11/08 1 2001/06/20 2 2001/06/23 3 2002/06/20 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 1998/12/15 1998/12/15 2003/06/09 2003/06/12 2003/06/13 2003/06/17 2003/06/19 2003/06/21 2004/11/05 2004/11/05 2004/11/05 2004/11/05 2004/11/05 2004/11/07 2004/11/07 131 vmin (km s−1 ) vm1 (km s−1 ) 19±1 −1±1 16±1 8±1 −3.8±0.8 −3.7±0.9 −9.6±0.8 −3.1±0.7 54±1 0.5±0.3 25±1 35±1 35±1 35±1 1.7±1.0 1.3±0.4 1.6±0.5 0.9±0.4 36±1 35±1 35±1 35±1 34±1 −0.1±0.5 0.3±0.5 0.5±0.5 0.2±0.5 0.7±0.5 −43±4 −11±4 −7±4 −30.1±2.7 −18.0±3.3 1.6±3.7 −10±1 −10±1 −9±1 −9±1 −8±1 −9±1 −9±1 −9±1 −9±1 −9±1 −9±1 −9±1 −9±1 −9±1 −9±1 0.4±0.3 0.5±0.3 −0.4±0.3 −0.3±0.3 −0.3±0.3 −0.2±0.3 −0.3±0.3 −0.4±0.3 0.0±0.3 0.1±0.3 0.1±0.3 0.1±0.3 0.2±0.3 0.3±0.3 0.3±0.3 C HAPTER 7 Table 7.3: continued. Obs Date HJD Beff vmin nr year/m/d −2451000 (gauss) (km s−1 ) Magnetic calibrators and RR Lyrae 53 Cam/HD 65339 1 1998/12/14 161.741 −3607±95 −3±1 α2 CVn/HD 112413 1 2000/06/30 726.370 491±45 0±1 2 2001/06/19 1080.362 −101±37 2±1 3 2001/06/19 1080.443 −14±59 2±1 4 2001/06/20 1081.360 598±35 2±1 5 2001/07/02 1093.384 133±52 0±1 6 2003/06/06 1797.370 261±54 1±1 RR Lyrae/HD 182989 1 2003/06/06 1797.483 128±137 −54±1 2 2003/06/09 1799.529 184±97 −77±1 3 2003/06/10 1800.590 131±112 −88±1 4 2003/06/11 1801.545 151±178 −56±1 5 2003/06/13 1804.494 85±96 −96±1 6 2003/06/16 1807.462 −19±80 −80±1 7 2003/06/19 1810.455 6±68 −59±1 8 2003/06/22 1812.519 95±104 −88±1 9 2003/06/22 1813.456 −118±104 −47±1 vm1 (km s−1 ) 1.7±0.4 2.0±0.6 0.5±0.5 0.6±0.5 0.8±0.5 1.1±0.5 1.3±0.5 −0.7±0.3 −1.4±0.2 −1.9±0.2 −3.7±0.3 −0.9±0.3 −0.6±0.2 −0.2±0.2 −1.7±0.3 −2.0±0.3 Bibliography Abt, H. A., Levato, H., & Grosso, M. 2002, ApJ, 573, 359 Abt, H. A. & Morrell, N. I. 1995, ApJS, 99, 135 Adelman, S. 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The discovery of such fields would explain a wide range of well documented enigmatic phenomena in massive stars, in particular cyclical wind variability, Hα emission variations, chemical peculiarity, narrow X-ray emission lines and non-thermal radio emission. To investigate the incidence of magnetic fields in O stars, we have obtained high S/N spectropolarimetric observations at three different phases for a sample of 11 O stars, covering the ∼347-588 nm range with VLT/FORS1. From the circular polarisation spectra we have measured the effective magnetic field strength from the Zeeman splitting of the Balmer lines and lines of He I & II, C III, N III, O III and Fe III & IV. No evidence for the presence of magnetic fields was found, although errors as low as 32 G were achieved. We conclude that large scale magnetic fields of the order of several hundred gauss or more, are not present in the majority of O-type stars. If magnetic fields are to be responsible for the phenomena described above, they are likely of a more complex nature than simple dipole fields. ∗ Based on observations obtained at the European Southern Observatory, Paranal, Chile (ESO programme 075.D-0432(A) 137 C HAPTER 8 8.1 Introduction Stellar magnetic fields have been discovered across a large range of spectral types (see Charbonneau & MacGregor 2001). In late type stars, dynamos active in the convective layers are believed to be the origin of the observed magnetic fields. In earlier type stars, which have radiative envelopes, large scale magnetic fields of the order of a kilogauss have been discovered in the Ap/Bp stars, but the exact origin of these fields is not yet known (Charbonneau & MacGregor 2001; Braithwaite & Nordlund 2006). The lower temperature limit to the Ap/Bp star phenomenon is set by by the onset of strong convection in the outer layers. Towards hotter stars there is no such limit, and one would expect to find a continuation of the magnetic fields in the early B and O type stars (Mathys 1999). Indirect observational evidence for the presence of magnetic fields are the many unexplained phenomena observed in massive stars, that are thought to be related to magnetic fields. One of the main indications that massive stars have magnetic fields is the cyclic behaviour on a rotational timescale observed in the UV wind lines (e.g. Prinja 1988; Kaper et al. 1999; Henrichs et al. 2005). Other indications are variability (similar as in the UV) observed in the H and He lines (Moffat & Michaud 1981; Stahl et al. 1996; Rauw et al. 2001), narrow X-ray emission lines (Cohen et al. 2003; Gagné et al. 2005) and the presence of non-thermal radio emission (Bieging et al. 1989; Scuderi et al. 1998; Schnerr et al. 2006). Stars more massive than about 9 M end up as neutron stars or as black holes. A significant fraction of newborn neutron stars are strongly magnetised, with typical fields of ∼ 1012 G, and fields of up to ∼ 1015 G in the magnetars. Simple conservation of magnetic flux would imply field strengths of at least (5 R /10 km)−2 ∗ 1012 G ' 101 G as a minimum for their progenitors. This is similar to the minimum field strength required to explain the wind variability observed in the UV (several 10 1 G), as can be concluded from numerical simulations of wind behaviour in early type stars (ud-Doula & Owocki 2002). Direct measurements of the magnetic field strength in massive stars using spectropolarimetry to determine the Zeeman splitting of the spectral lines is difficult, as only very few spectral lines are available that are usually strongly broadened by their rapid rotation. So far a magnetic field has only been found in the two O stars θ 1 Ori C and HD 191612 (Donati et al. 2002, 2006a), and a handful of B stars (Henrichs et al. 2000; Neiner et al. 2003a,c,b; Hubrig et al. 2006; Donati et al. 2006b). To investigate the fraction of O stars with large scale magnetic fields, we have performed a survey of 11 O stars using FORS1 at the VLT, in search of magnetic fields. Our observations and the datareduction are described in Sect. 8.2, the results in Sect. 8.3 and the conclusions are presented in Sect. 8.4. 138 M AGNETIC FIELD MEASUREMENTS OF O STARS WITH VLT/FORS1 8.2 Observations & Method We have observed 11 O stars (see Table 8.1) with FORS1 at the VLT in spectropolarimetric mode. A log of our observations is shown in Table 8.2. All targets were observed at three different nights, to be able to see the rotational variation of the effective magnetic field. The spectra were obtained with a 0.4 00 slit and grism 600B, giving a spectral resolution of R≈2000 for the ∼347-588 nm range, covering all hydrogen Balmer lines from Hβ to the Balmer jump. Both right and left circular polarisation spectra were recorded every exposure, using the low gain readout mode to increase the S/N for our bright targets. Two types of settings were used (+45 and −45) between which the λ/4-plate was rotated by 90◦ , effectively switching the ordinary (O) and extraordinary (E) beams in the instrument. To eliminate systematic errors in measuring the circular polarisation (Stokes V ) due to time-variability of the spectrum, observations were performed in the sequence −45-+45-+45-−45. After the wavelength calibration and extraction of O- and E-spectra, they were normalised and projected on a new wavelength grid with a constant wavelength step of 0.1 Å. The average longitudinal magnetic field strength, hBl i, was determined from the polarisation signature of the Zeeman splitting in the Stokes V spectra using the relation: V = −geff ∆λz λ2 dI/dλhBl i + V0 , (8.1) where geff is the effective Landé factor, λ is the wavelength, dI/dλ is the slope in the unpolarised spectrum, V0 is the instrumental or continuum polarisation, and ∆λz = e , 4πme c2 (8.2) (Bagnulo et al. 2002; Mathys et al. 2000). For each sequence of observations, hBl i was determined by a linear regression of the spectral lines in the average spectrum, assuming g eff = 1. Magnetic fields were measured using only the hydrogen Balmer lines and using all available absorption lines of hydrogen and He I & II, C III, N III, O III and Fe III & IV. More details on the datareduction procedure can be found in Bagnulo et al. (2002) and Hubrig et al. (2003). 8.3 Results Example spectra of all our target stars and the identification of the main spectral lines are shown in Fig. 8.1. Compared to lower mass stars, less lines were available for measuring the magnetic field strength and the lines are not as deep. Even the strongest hydrogen lines have a maximum depth of about 40% below the continuum, as they are intrinsically weaker than in the B and A type stars and suffer from strong rotational broadening. As a result, magnetic signatures have a smaller amplitude than in stars of later spectral types. 139 C HAPTER 8 Table 8.1: Target stars discussed in this paper. Spectral types are from Maı́z-Apellániz et al. (2004), v sin i was taken from the Bright Star Catalogue (Hoffleit & Jaschek 1991). HD number 112244 135240 135591 151804 152408 155806 162978 164794 167263 167771 188001 Spectral v sin i type (km s−1 ) O8.5 Iab(f) 145 δ Cir O7.5 III((f)) 189 O7.5 III((f)) 121 O8 Iaf 124 O8: Iafpe 140 O7.5 V[n]e 162 O7.5 II((f)) 50 9 SGR O4 V((f)) 140 16 SGR O9.5 II-III((n)) 160 O7 III:(n)((f)) 90 9 SGE O7.5 Iaf 104 Other name P Cygni profiles and pure emission lines were found in several stars. All stars show evidence for emission in the C III line at 5695 Å. In HD 152408, Hβ to Hδ show emission and especially He II 4686 and N III 4634 & 4641 show strong emission. HD151804 also shows emission in Hβ, He II 4686 and N III 4634&4641, but not as strong as HD 152408. The lines that show evidence for emission were not used in the determination of the magnetic field strength, as these lines are (at least partly) formed in different regions and may have a different polarisation signature. It is possible that in some cases strong hydrogen absorption lines are partly filled in by emission, which would dillute the magnetic polarisation signature. However, as many lines are involved the effects are likely relatively small. The results of our magnetic field measurements are presented in Table 8.2. Both the results including all hydrogen lines in absorption as the results including all absorption lines are shown. Out of 11 stars observed at three (and one at four) different phases, no evidence for a magnetic field was found. This is the first time that magnetic field strengths were determined for such a large sample of stars, with an accuracy similar to the smallest errors obtained for O stars. For the magnetic O star HD 191612, Donati et al. (2006a) measured a magnetic field of hBl i = −220 ± 38 G, averaging a total of 52 exposures obtained over 4 different nights. This is similar to our typical errors of 32-70 G. 140 M AGNETIC FIELD MEASUREMENTS OF O STARS WITH VLT/FORS1 Figure 8.1: Normalised spectra of all the observed targets. Well known spectral lines have been indicated by the arrows, all Balmer lines from the Balmer jump to Hβ are visible. For clarity spectra are offset from 1 by n×0.5. Clear evidence of emission is seen in the stars HD 151804 and HD 152408. In all stars emission is seen in the C III line at 5695 Å 8.4 Conclusions Although there are many arguments to suspect the presence of magnetic fields in O stars, no evidence was found for magnetic fields in our sample of 11 O stars with typical upper limits for hBl i of the order of 95-140 G. As all stars were observed at 3 different phases, the main reason for this is not that the targets were observed at a phase where the effective field averaged over the stellar disk is zero. We conclude that large scale, dipole like, magnetic fields with polar field strengths of the order of several hundred gauss are not widespread among O type stars. It is however possible that more complex, smaller scale fields (possibly like solar flares), play a role. As the average field strength of a star with a more complex magnetic structure will be small, they are not easily detected by techniques that are sensitive to the average magnetic field strength over the stellar surface. Such complex configurations would be detectable if the circular polarisation signature of individual Zeeman splitted lines could be observed. For this purpose high resolution spectropolarimeters are required at large telescopes. 141 C HAPTER 8 Table 8.2: Measured magnetic field strengths of stars in our survey. Bhydro is the magnetic field as measured from the hydrogen lines only and Ball is the magnetic field as measured from all available absorption lines. The number of exposures denotes the total number of individual exposures used for the magnetic fields determination. Star HD 112244 112244 112244 135240 135240 135240 135591 135591 135591 151804 151804 151804 152408 152408 152408 155806 155806 155806 162978 162978 162978 164794 164794 164794 167263 167263 167263 167771 167771 167771 188001 188001 188001 188001 date y/m/d 2005/03/26 2005/04/15 2005/04/23 2005/04/15 2005/04/27 2005/07/02 2005/04/27 2005/07/02 2005/07/20 2005/04/16 2005/07/20 2005/08/14 2005/07/05 2005/07/20 2005/08/14 2005/04/16 2005/06/11 2005/07/05 2005/07/05 2005/08/13 2005/08/22 2005/05/30 2005/08/12 2005/08/13 2005/08/12 2005/08/12 2005/08/14 2005/05/30 2005/08/12 2005/08/13 2005/05/30 2005/08/12 2005/08/13 2005/08/15 Tstart h:m:s 03:53:27 03:56:23 02:16:05 05:38:02 06:08:49 02:18:11 05:29:34 01:45:10 01:32:21 08:39:21 00:25:15 01:17:17 04:55:26 02:18:19 01:46:09 09:17:49 07:05:01 05:26:41 06:00:17 02:36:27 03:15:02 08:22:27 02:39:53 02:06:35 03:14:00 23:46:51 02:17:45 08:52:04 03:44:12 01:09:19 10:13:36 04:16:31 03:07:43 03:23:40 142 nr exp 40 14 20 16 16 16 18 18 22 18 16 16 12 10 16 16 16 8 12 16 16 16 16 16 16 48 32 16 32 32 16 30 36 16 Bhydro Ball (gauss) (gauss) 45±49 −26±32 −123±66 13±45 154±78 −29±52 32±69 12±54 −9±63 32±53 45±65 −52±50 −136±55 −51±38 82±49 −20±35 −2±56 15±39 138±190 34±134 −11±91 −168±81 59±77 61±69 0±331 57±164 736±354 −249±224 −264±287 −206±206 −116±185 −72±113 −23±67 −51±39 −106±74 −96±45 −168±86 19±45 91±90 9±48 142±67 47±36 −57±57 −30±41 118±67 151±52 −26±64 −73±50 0±85 −20±64 −14±48 −6±36 −31±54 −51±38 15±68 −73±52 −8±56 53±40 −71±77 −29±61 129±64 91±41 22±61 5±40 −24±55 −23±36 −81±69 −80±45 M AGNETIC FIELD MEASUREMENTS OF O STARS WITH VLT/FORS1 Acknowledgements. 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Foley Astronomy and Astrophysics, 2006 (submitted) Abstract A number of O stars is suspected to have (weak) magnetic fields because of the observed cyclical variability in their UV wind-lines. However, direct detections of these magnetic fields using optical spectropolarimetry have proven to be very difficult. Non-thermal radio emission in these objects would most likely be due to synchrotron radiation. As a magnetic field is required for the production of synchrotron radiation, this would be strong evidence for the presence of a magnetic field. Such non-thermal emission has already been observed from the strongly magnetic Ap/Bp stars. We have performed 6 & 21 cm observations using the WSRT and use these, in combination with archival VLA data at 3.6 cm and results from the literature, to study the radio emission of 5 selected candidate magnetic O stars. Out of our five targets, we have detected three: ξ Per, which shows a non-thermal radio spectrum, and α Cam and λ Cep, which show no evidence of a non-thermal spectrum. In general we find that the observed free-free (thermal) flux of the stellar wind is lower than expected. This is in agreement with recent findings that the mass-loss rates from O stars as derived from the Hα line are overestimated because of clumping in the inner part of the stellar wind. 147 C HAPTER 9 9.1 Introduction All O-type stars have strong, line-driven winds. They usually have a thermal radio spectrum due to the free-free emission from the ionised stellar wind (Abbott et al. 1980; Bieging et al. 1989; Scuderi et al. 1998). This spectrum can be calculated using: Sν = !4/3 0.1 Te Ṁ 104 K 10−6 M yr−1 µ v −4/3 D −2 e ∞ mJy, 100 km s−1 kpc ν 0.6 7.26 10 GHz (9.1) (Wright & Barlow 1975; Panagia & Felli 1975; Scuderi et al. 1998), where D is the distance to the star, Ṁ is the mass-loss rate, Te the electron temperature, µe the mean atomic weight per electron, v∞ the terminal wind velocity and ν the observing frequency. However, about 30% of the O stars are found to show non-thermal radio emission (see, e.g., Bieging et al. 1989; Drake 1990; Scuderi et al. 1998; Benaglia et al. 2001). This is characterised by a flatter than thermal spectrum, i.e. defined as α < 0.6, with Sν ∝ ν α . White (1985) proposed that synchrotron radiation from the rapidly moving electrons of the wind in a stellar magnetic field could also contribute to the radio emission. This was confirmed by the discovery of non-thermal radio emission in the magnetic Ap/Bp stars (Drake et al. 1987, Cassinelli 1984 reports non-thermal emission found in σ Ori E by Churchwell). Among O stars only two magnetic stars are known: θ 1 Ori C (Donati et al. 2002) and HD 191612 (Donati et al. 2006). Nevertheless, strong indirect evidence exists that many O stars should have magnetic fields (e.g. Henrichs et al. 2005). One of the main arguments why many O stars are thought to have (weak) magnetic fields is that their winds show cyclic behaviour on a rotational timescale, which is typically a few days (see Fullerton 2003, for a review). The lack of magnetic field detections is most likely related to the fact that direct measurements of magnetic fields in O stars are extremely difficult, because of the very few available spectral lines in the optical region. The usual method to measure magnetic fields is to determine the magnetic Zeeman splitting of magnetically sensitive lines with optical spectropolarimetry. The sensitivity of this method decreases towards earlier spectral types, as these stars have fewer spectral lines in the optical region. The detection of non-thermal radio emission from O stars with such cyclic variability would be strong evidence that magnetic fields are indeed present in these stars. We have selected five candidate magnetic O stars that have been studied extensively in the ultraviolet (UV) in order to search for evidence of non-thermal radio emission. 148 R ADIO OBSERVATIONS OF CANDIDATE MAGNETIC O STARS Table 9.1: Stellar parameters of the selected O stars. Spectral types are from Walborn (1973, 1976). Hipparcos parallaxes were taken from Perryman et al. (1997). All other parameters were taken from the “preferred solution”of Markova et al. (2004), except for 10 Lac, for which we used Mokiem et al. (2005). We show both the distance from Hipparcos and the distance used for the spectral modeling. As this latter value is used to determine the mass-loss rates, this distance was also used for predicting the thermal radio flux. For the “preferred solutions”of Markova et al. (2004), we have scaled the distance from the original solution using the absolute magnitudes, as the reddening is assumed to be the same for both solutions. ξ Per α Cam 15 Mon λ Cep 10 Lac HD number 24912 30614 47839 210839 214680 Association/Runaway Runaway Runaway Mon OB1 Runaway Lac OB1 Spectral type O7.5III(n)((f))a O9.5 Ia O7 V ((f)) O6 I (n)fp O9 V Parallax (mas) 1.84±0.70 0.47±0.60 3.09±0.53 1.98±0.46 3.08±0.62 540+330 >440 323+67 510+150 320+90 Hip. distance (pc) −150 −47 −100 −50 765 710 1089 320 Spectral mod. dist. (pc) 895 Mass (M ) 52 22 25 58 27 Radius (R ) 25.2 19.6 9.9 23 8.3 Teff (103 K) 34.0 31.0 37.5 36.2 36.0 Luminosity (105 L ) 7.6 3.2 1.7 8.1 1.0 v∞ (km s−1 ) 2400 1550 2200 2200 1140 +8.8 Ṁ (10−6 M y−1 ) 4.0 ± 1.0 2.9 ± 0.9 1.2 ± 0.3 7.7 ± 2.3 6.1−5.5 × 10−2 a This is the spectral type given by Walborn (1973), however, a spectral type of O7.5I(n)((f)) was adopted by Markova et al. (2004). 9.2 Observations & data reduction For this study five targets have been selected from the 10 O stars listed by Kaper et al. (1996), which are the brightest and best studied O stars in the UV with the International Ultraviolet Explorer (IUE) satellite. All these targets show extensive stellar wind variability, some with well studied cyclic behaviour. The final selection was made on the criteria that the star should be observable with the Westerbork Synthesis Radio Telescope (WSRT) and that the star should have been previously detected in the radio region (α Cam, 15 Mon and λ Cep; for ξ Per archive observations from the Very Large Array –VLA– were available). We added 10 Lac because of its brightness and its rich UV history. The stellar parameters of these stars are listed in Table 9.1. The radio observations of our targets selected from the literature have been summarised in Table 9.2. The detection of a 42±5 mJy source near the optical position of ξ Per by Bohnenstengel & Wendker (1976) at 11 cm (2.7 GHz) is discussed in Sect. 9.3.1. To complement these measurements, and in order to determine the spectral slopes, we have used WSRT (6 and 21 cm) and VLA (3.6 cm) observations. We performed observations for all five selected O stars at 21 cm (1.4 GHz) with the WSRT during the period from September to November 2005. In addition, 10 Lac 149 C HAPTER 9 Table 9.2: Radio detections as a function of wavelength of our targets reported in the literature. When several measurements are available a weighted average is shown; upper limits are 3σ. Fluxes are from [1] Abbott et al. (1980), [2] Bieging et al. (1989), [3] Drake (1990), [4] Lamers & Leitherer (1993) and [5] Scuderi et al. (1998). Star Flux (mJy) 2 cm 3.6 cm 6 cm References α Cam 0.65 ± 0.13 0.44 ± 0.04 0.29 ± 0.04 2,5 15 Mon <0.4 0.40 ± 0.13 3 <0.33 & <0.18 2,3 λ Cep 0.38 ± 0.03 0.40 ± 0.25 1,4 was observed at 6 cm (4.9 GHz). All observations consisted of 12 h integrations in the Maxi-Short configuration, done in continuum mode with a bandwidth of 8×20 MHz. Gain and phase calibrations were done using the calibrator 3C286, except the observation of α Cam which was calibrated with 3C48. Earlier observations of ξ Per were performed in 1995 at 6 cm (6 observations in May and June, total of 26 h) , and 21 cm (5 observations in June, July and August, total of 39 hours). Due to the lower sensitivity of the WSRT at that time, the observations at each frequency were all combined. The 21 cm observations were calibrated using 3C48 and the 6 cm observations were calibrated using 3C48, 3C147 and 3C286. The reduction of the WSRT data was done using the MIRIAD software package. From the VLA archive we used an X-band (3.6 cm, 8.5 GHz) continuum observation taken on 11 Jan 1999 (program ID AS644-x) of ξ Per. This 0.68h observation was taken in C configuration with a bandwidth of 50 MHz. The data were reduced with AIPS , using 3C48 as a primary and B0411+341 as a secondary calibrator. 9.2.1 Distances and mass-loss rates As massive stars are relatively far away, the distances as determined by Hipparcos suffer from systematic errors (e.g. Schröder et al. 2004). When the spectral properties of stars are determined by modeling of the spectrum, the distance is often used to determine the absolute magnitude of the star which constrains the stellar radius. The distances in these studies have generally been derived from the relation between the spectral type and the luminosity of the star and possibly other stars from the same cluster. As the mass-loss rates found depend on the radius, we have adopted the distances used in the spectral modeling to calculate the predicted radio fluxes. 9.3 Results We detected three of our five selected targets (see Table 9.3). For ξ Per this was the first detection in the radio; all three stars have now been detected for the first time 150 R ADIO OBSERVATIONS OF CANDIDATE MAGNETIC O STARS at 21 cm. In general the flux was found to be lower than the predicted thermal flux using Eq. 9.1 and the stellar parameters from Table 9.1 (assuming typical values of µe = 1.3 and Te = 0.85 Teff ; Scuderi et al. 1998). Both the predicted thermal flux and a power law fit to the observations are shown in Fig. 9.1. We now present the results per source in order of RA: Table 9.3: Results of our new WSRT and archive VLA observations. The upper limits shown are 5σ upper limits. date freq. λ flux spectral array (d/m/y) (GHz) (cm) µJy index α May/Jun/95 4.9 6 ≤240 WSRT Jun/Aug/95 1.4 21 ≤190 WSRT 11/Jan/99 8.4 3.6 169±30 0.29±0.14 VLA 28/Nov/05 1.4 21 100±18 WSRT 30614 α Cam 09/Oct/05 1.4 21 156±12 0.57±0.06 WSRT 47839 15 Mon 13/Oct/05 1.4 21 ≤250 WSRT 210839 λ Cep 03/Oct/05 1.4 21 98±21 0.74±0.11 WSRT 214680 10 Lac 22/Sep/05 4.9 6 ≤95 WSRT 21/Sep/05 1.4 21 ≤95 WSRT HD star number name 24912 ξ Per 9.3.1 ξ Per In the 1995 WSRT observations, ξ Per was not detected at 6 and 21 cm. However, it was detected in the higher S/N 3.6 cm (VLA, Jan 1999) and 21 cm (WSRT, Nov 2005) observations. The flux was found to be lower than the predicted thermal flux by a factor of ∼2 (21 cm) to ∼3.5 (3.6 cm). The spectrum has a spectral index of α = 0.29 ± 0.14, which is lower than the thermal value of 0.6. This is evidence for the presence of a non-thermal contribution to the observed flux. Puls et al. (2006) found an upper limit for ξ Per of 120 µJy (3σ) from VLA observations on March 9, 2004. As this limit is not consistent with our detection at this wavelength, this might be an indication of variability. To check this, we retrieved the observations from the VLA archive. At the position of ξ Per, we measured a flux density of 154 ± 39 µJy, which, we agree, is not a reliable detection of the source (3.9σ). However, it is consistent with our detection of the source at 169 ± 30 µJy in 1999. Bohnenstengel & Wendker (1976) detected a source of 42 ± 5 mJy near the optical position of ξ Per. They concluded that this component is either due to an extended (∼2’) thermal source of about 10 mJy, or to blending of their components A and B, in which case they claim that component B has to have a very flat spectrum. As an interferometer such as the WSRT is not very sensitive to extended structures, we cannot exclude the presence of an extended source. We find that component B has a spectral index of α≈−1.1. It is detected at 5.8±0.2 mJy at 21 cm, its 6 cm flux is 151 C HAPTER 9 Figure 9.1: Radio spectra of the 5 selected targets. Shown are the new results, results taken from the literature, upper limits, the predicted thermal flux (Eq. 9.1, dashed line) and a fit to the observations (solid line). Distances used for estimating the thermal flux are the same as those used for the determination of the mass-loss rates using Hα. 1.5±0.1 mJy and at 3.6 cm it shows extended structure (1000 x200 ) but has very low flux density (peak of ∼0.2 mJy/beam). At 3.6 and 6 cm, component A can be resolved into two components with a separation of 12 ± 100 . The western component has a flux of 6.1 ± 1.1 (6 cm) and 2.6 ± 0.5 mJy (3.6 cm) and the eastern component 7.1 ± 0.9 (6 cm) and 3.0 ± 0.5 mJy (3.6 cm). In addition we found a third source at the position [α(2000)=03h 59m 03s, δ(2000)=+35◦ 49’18”], which is not detected at 6 cm (≤ 0.24 mJy) but is detected at 0.9±0.2 mJy at 21 cm. Given the low resolution of the Effelsberg telescope, we conclude that it is very likely that the source found by Bohnenstengel & Wendker (1976) is due to blending of all these components. 9.3.2 α Cam This star shows a thermal spectrum over the entire range from 2 to 21 cm. The flux is found to be lower than the predicted thermal flux by a factor of ∼2. 152 R ADIO OBSERVATIONS OF CANDIDATE MAGNETIC O STARS 9.3.3 15 Mon At 2 cm Drake (1990) found a 3σ upper limit of 400 µJy on 24 Jan 1987. At 6 cm Bieging et al. (1989) reported a 3σ upper limit of 330 µJy. Drake (1990) found an upper limit of 180 µJy on 22 Feb 1986, but one year later (24 Jan 1987) detected the source at the same wavelength at 400 ± 130 µJy. This marginal detection was not consistent with the upper limit of 180 µJy, which is an indication that the radio flux of 15 Mon is variable. Due to the unfavourable position, for an E-W array, of 15 Mon on the sky (close to the equator), our 5σ-upper limit of 250 µJy at 21 cm is relatively high compared to the expected thermal noise in a 12h run. 9.3.4 λ Cep Our detection of λ Cep at 21 cm allows for an accurate determination of the spectral index. We find that λ Cep has an approximately thermal spectrum, with a spectral index of α = 0.74±0.11. The flux is, however, a factor of ∼3–3.5 lower than predicted. 9.3.5 10 Lac We have not detected 10 Lac, with a 5σ upper limits of 95 µJy at both 21 and 6 cm. This is in agreement with the expected thermal flux based on the determination of −8 the mass-loss rate by Mokiem et al. (2005) of 6.1+8.8 M y−1 . Our 6 cm upper −5.5 × 10 −7 limit constrains the mass-loss rate to be lower than 1.3 × 10 M y−1 . 9.4 The effects of clumping in stellar winds As recently discussed by Fullerton et al. (2006) and Puls et al. (2006), it is generally found that mass-loss rates determined from Hα are higher by a factor of ∼3-8 than those derived from radio observations. This is thought to be due to enhanced clumping in the inner part of the wind where the Hα emission originates, compared to the outer part of the wind from which we receive the observed radio emission. As both the Hα and radio emission are proportional to the density squared, clumping in the wind results in an overestimate of the mass-loss rate. Since we use mass-loss rates derived from Hα to predict the thermal radio fluxes, the fact that the observed fluxes are lower than our predictions is consistent with stronger clumping in the inner part of the wind compared to the outer part. We have used the same distances as assumed in the Hα modelling. For the Hα modelling the distance (or absolute magnitude) is used to estimate the stellar radius, resulting in R ∝ D. In these models the mass-loss rate approximately scales with R as Ṁ ∝ R3/2 , which gives Ṁ ∝ D3/2 . Since the predicted radio flux scales as Sν ∝ Ṁ 4/3 D−2 (Eq. 9.1), one finds that the predicted radio flux is approximately independent of the distance. 153 C HAPTER 9 For α Cam and λ Cep, our results are in good agreement with the mass-loss rates determined by Puls et al. (2006), and for ξ Per, the flux observed at 3.6 cm is in agreement with the upper limits of both possible solutions quoted. 9.5 Conclusions We have detected three candidate magnetic O stars at radio wavelengths. Of these three ξ Per shows a non-thermal spectrum and α Cam and λ Cep show thermal spectra. As non-thermal radio emission is assumed to be due to synchrotron emission, the detection of a non-thermal radio spectrum in ξ Per strengthens the case that the observed UV line variability observed in this star is caused by a magnetic field. Recent numerical simulations (e.g. van Loo et al. 2005; van Loo 2005) suggest that both a magnetic field and a binary companion are required to explain non-thermal radio emission from massive stars. In these simulations, the synchrotron radiation from single massive stars with magnetic fields is produced relatively close to the star, where shocks occur that accelerate the electrons. This radiation is absorbed in the stellar wind due to the large free-free opacity. When a star has a massive binary companion, the electrons are accelerated in the wind-wind collision region, where the radio emission can escape owing to the lower opacity (τ radio . 1). However, as ξ Per is a single runaway star (Gies & Bolton 1986), it seems that at least for some single stars it is possible to have a (mildly) non-thermal radio spectrum. The detection of variability in the radio flux of close binary stars suggest that stellar winds are not as optically thick as generally assumed (Blomme 2005). Due to porosity effects, clumping and asphericity of the mass loss due to magnetic fields, it might be possible to observe radio emission from much closer to the central star. For producing synchrotron emission, a magnetic field is necessary but not sufficient, as relativistic electrons are also required. In the case of ξ Per, and other possibly single massive stars with non-thermal radio spectra, the precise origin of the relativistic electrons needs further investigation. In principle, variability of the radio flux of ξ Per could change the spectral index since the data at different wavelengths are taken at different epochs. However, observed radio variability of massive stars is usually related to the orbit of a massive companion. Such variability is not expected for ξ Per, but as the mechanism responsible for the relativistic electrons is not completely understood we plan future observations to confirm the non-thermal character of the radio spectrum, and check if variability is present. The runaway stars λ Cep and α Cam, which are presumably single (Gies & Bolton 1986), have a thermal radio spectrum, but it can not be excluded that they have a magnetic field. λ Cep has a much denser stellar wind, and the non-thermal emission might all be absorbed. In the case of α Cam, the magnetic field might be too weak to produce observable non-thermal emission, but the lack of non-thermal emission could also be due to the location (closer to the star) or strength of the shocks required to produce the relativistic electrons. 154 R ADIO OBSERVATIONS OF CANDIDATE MAGNETIC O STARS Finally, we confirm recent results by Fullerton et al. (2006) and Puls et al. (2006) that the mass-loss rates as derived from free-free radio emission are significantly lower than those derived from Hα modelling, which is a signature of enhanced clumping in the inner part of stellar wind. Acknowledgements. We are grateful to J. Puls and M.R. Mokiem for useful discussions on Hα modelling, and to C. Stanghellini for discussions on the radio observations of ξ Per from 2004. This work has made use of the Simbad and ADS databases, operated at CDS, Strasbourg, France. 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L. 1985, ApJ, 289, 698 Wright, A. E. & Barlow, M. J. 1975, MNRAS, 170, 41 156 This writing business. Pencils and what-not. Over-rated, if you ask me. Silly stuff. Nothing in it. Eeyore N EDERLANDSE S AMENVATTING Overal in het heelal zijn magneetvelden gevonden: in planeten, het interplanetaire medium, de zon, sterren, stervormende moleculaire wolken, het interstellaire medium, in sterrenstelsels en zelfs tussen de sterrenstelsels. De sterkte van deze magneetvelden varieert van enkele picogauss (10−12 G) in het intergalactische medium tot enkele megagauss (106 G) en petagauss (1015 G) in witte dwergen en neutronensterren, de laatste overblijfselen van ontplofte sterren. Het onderzoek beschreven in dit proefschrift is gericht op magneetvelden in sterren, en wel zware sterren. Dit zijn sterren zwaarder dan ongeveer 9 zonsmassa’s, die uiteindelijk zullen eindigen als een neutronenster of een zwart gat. Hoewel we deze sterren in ons eigen sterrenstelsel, de Melkweg, relatief makkelijk kunnen bestuderen, zijn er nog steeds talloze aspecten van hun evolutie en gedrag die nog niet goed begrepen zijn. Een van deze aspecten is de rol van magneetvelden. Modelberekeingen hebben aangetoond dat de aanwezigheid van magneetvelden grote invloed kan hebben tijdens de vorming, de verdere evolutie, en het gedrag van een ster. Met name de oorsprong van de velden in neutronensterren en magnetars (neutronensterren met zeer sterke magneetvelden) is niet duidelijk. Het is mogelijk dat gedurende de vorming van een neutronenster tijdens de collaps van een zware ster, die gepaard gaat met een supernova exlosie, een dergelijk sterk veld opgewekt wordt. Hierbij wordt verondersteld dat ervoorafgaand geen veld van betekenis aanwezig is. Er zijn echter steeds meer aanwijzingen dat zware sterren gedurende hun leven wel degelijk magneetvelden van betekenis hebben, en dat die versterkt kunnen worden tijdens het ineenstortingsproces. Dat er zeer jonge magnetische zware sterren gevonden zijn wijst op een fossiele oorsprong, waarbij het veld al bij de geboorte uit het interstellaire medium is meegekregen. Dit in tegestelling tot de zon en andere lichte sterren waarin het magneetveld intern wordt opgewekt door een dynamoproces. Op dit moment is er maar een handvol magnetische zware sterren bekend, waarschijnlijk omdat het meten van magneetvelden in zware sterren veel moeilijker is dan in lichtere sterren. De reden hiervoor is dat zware sterren veel minder spectraallijnen hebben in het optisch golflengtegebied (zichtbaar licht) die gebruikt kunnen worden voor het meten van het Zeeman effect waaruit het magneetveld wordt afgeleid (zoals beschreven in hoofdstuk 1 en 2). Waarschijnlijk is het aantal magnetische zware sterren dat tot nog toe is gevonden slechts het topje van de ijsberg. De leidraad in dit proefschift is het zoeken naar magneetvelden in zware sterren, 159 N EDERLANDSE S AMENVATTING en het onderzoeken welke invloed deze velden hebben op de uitstromende sterrenwind. Hiervoor zijn zowel waarnemingen als theoretische berekeningen gedaan. De theoretische en observationele motivatie voor dit onderzoek wordt hieronder samengevat. Theoretische motivatie In tegenstelling tot de zon hebben zware sterren geen convectieve buitenlaag waarin magneetvelden kunnen worden opgewekt door dynamowerking. Bij deze sterren is alleen de kern is convectief, en in de buitenlagen wordt de energie door middel van straling naar buiten getransporteerd. Daarom is hier een ander mechanisme nodig om een magneetveld op te wekken, of in iedere geval niet af te breken indien de ster bij de geboorte reeds een magneetveld heeft. Grote vooruitgang is geboekt bij de iets lichtere A en B sterren (tussen de 4 en 9 zonsmassa’s). Van deze sterren is hoogstwaarschijnlijk zo’n 10% magnetisch (die met spectraaltype Ap/Bp). Deze sterren worden gekarakteriseerd door hun afwijkende chemische samenstelling in de atmosfeer, en zullen door hun iets lagere massa niet eindigen als neutronenster maar als witte dwerg. De verhouding tussen het aantal magnetische en niet-magnetische A en B sterren komt overeen met de verhouding tussen het aantal magnetische en niet-magnetische witte dwergen. Dit is een sterke aanwijzing dat de magneetvelden in de witte dwergen de gecomprimeerde velden van de Ap/Bp sterren zijn. Sinds recentelijk een theoretisch stabiele magnetische configuratie gevonden is voor de velden in de Ap/Bp sterren, is het aannemelijk geworden dat deze magneetvelden van fossiele oorsprong zijn. Doordat moleculaire wolken sterk samentrekken tijdens de stervorming, worden de relatief zwakke velden in deze wolken versterkt. Het zo gevormde veld van de nieuwe ster vervalt vervolgens, tot een stabiele magnetische configuratie bereikt wordt. De interne structuur van deze sterren is vergelijkbaar met die van zwaardere sterren, en het is dus goed mogelijk dat stabiele magneetvelden van fossiele oorsprong ook in zware sterren aanwezig zijn en blijven tot de collaps tot neutronenster of zwart gat. Observationele motivatie In zware sterren zijn veel nog onbegrepen verschijnselen te zien die moeilijk te verklaren zijn zonder de aanwezigheid van magneetvelden. Het beste voorbeeld daarvan is de goed gedocumenteerde variabiliteit van sterrenwinden, die te zien is in spectraallijnen in het ultraviolet (UV). De tijdschaal van de variabiliteit heeft een duidelijk verband met de rotatieperiode van de ster, al is de variabiliteit vaak niet strikt periodiek. Dit is vergelijkbaar met het zogeheten cyclische gedrag van zonnevlekken, die een magnetische oorsprong hebben. Deze vlekken draaien mee met het zonsoppervlak, maar resulteren niet in strikt periodiek gedrag, omdat ze slechts 160 N EDERLANDSE S AMENVATTING tijdelijk leven en er nieuwe ontstaan op andere plaatsen. Ook in lijnen in het zichtbare deel van het spectrum van zware sterren, zoals Hα, wordt een vergelijkbare cyclische variabiliteit waargenomen. Andere belangrijke indirecte aanwijzingen voor de aanwezigheid van magneetvelden zijn niet-thermische radiostraling, relatief hoog energetische r öntgenstraling, smalle röntgenemissielijnen en afwijkende abundanties van bepaalde atomen in de atmosfeer. Dit laatste is het geval in de meeste bekende magnetische sterren, en het waarnemen van sterren met afwijkende abundanties heeft inderdaad geleid tot het vinden van een aantal nieuwe magnetische B sterren. Bij de zwaardere O sterren heeft een afwijkende abundantie echter een andere oorsprong, en is de cyclische variabiliteit van de sterrenwind de voornaamste indirecte aanwijzing dat magneetvelden een rol spelen. Een klein aantal OB sterren vertoont wel een strikt periodieke windvariabiliteit, zoals bijvoorbeeld de vroege B ster β Cephei. Dit wordt veroorzaakt door een permanent dipoolveld dat scheef staat ten opzichte van de rotatieas. Bij de meeste zware sterren wijst het cyclische gedrag echter op een veld dat niet permament aanwezig is, zoals bij de zon. De grootste uitdaging is het detecteren van dit type magneetvelden. Dit proefschrift Het eerste hoofstuk geeft een inleiding over het belang van magneetvelden in sterren, en hoe gepolariseerd licht gebruikt kan worden om kwantitatieve metingen te doen. De meest effectieve methode waarmee de aanwezigheid van (zwakke) magneetvelden in sterren kunnen worden aangetoond is de analyse van spectraallijnen met behulp van circulair gepolariseerd licht. In hoofdstuk 2 wordt onderzocht of met Least-Squares Deconvolution methode ook kwantitatief de juiste waarde van het magneetveld wordt gevonden. De conclusie is dat deze methode zeer effectief is voor het detecteren van nieuwe magneetvelden, maar dat de bepaalde veldsterktes niet in alle gevallen even nauwkeurig zijn. Veel aandacht in dit proefschrift gaat uit naar de B ster β Cephei. In hoofdstuk 3 wordt de ontdekking van het magneetveld in deze ster beschreven. De periode van 12.00075 dagen, die zichtbaar is in de variabele sterrenwind, is ook de periode waarmee de waargenomen sterkte van het magneetveld varieert, en is de rotatieperiode. Ook wordt in dit hoofdstuk een verbeterde baanbepaling gegeven van het dubbelstersysteem waarvan β Cephei deel uit maakt. De begeleider is tot nu toe alleen met speckle interferometrie waargenomen. De juiste interpretatie van de onbegrijpelijke Hα emissie in in deze ster heeft lang op zich laten wachten. Dit soort emissie doet sterk denken aan hetgeen waargenomen wordt in de snel roterende B emissie sterren, maar β Cephei is met een periode van 12 dagen een langzaam draaiende ster. Bovendien is in deze spectraallijn de rotatieperiode van de ster niet terug te vinden, hetgeen wel het geval is in alle andere lijnen die gevormd worden in de sterrenwind. In hoofdstuk 4 is beschreven hoe door middel van spectro-astrometrische waarnemingen eenduidig is aangetoond dat de 161 N EDERLANDSE S AMENVATTING Hα emissie niet van β Cephei zelf afkomstig is, maar van zijn begeleider, die waarschijnlijk een normale B emissie ster is. Hoe de interactie van het magneetveld en de sterrenwind aanleiding geeft tot variabiliteit wordt kwantitatief onderzocht met numerieke simulaties in hoofdstuk 5. Het blijkt dat röntgenemissie waarschijnlijk een belangrijke rol speelt bij het veroorzaken van deze variabiliteit. In hoofdstuk 6 laten we zien dat de B ster ν Eridani geen sterk magneetveld kan hebben, hetgeen wel was voorspeld uit de waargenomen pulsatiefequenties in deze ster. Onze bovenlimieten leggen daarom sterke randvoorwaarden op aan modellen voor de inwendige structuur van deze ster. Nieuwe magneetveldmetingen met de Musicos spectropolarimeter van de Telescope Bernard Lyot op de Pic du Midi in Frankrijk en met FOcal Reducer and low dispersion Spectrograph (FORS) van de Very Large Telescope in Chili, beschreven in hoofdstuk 7 en 8, tonen aan dat magneetvelden met een dipoolcomponent van enkele honderden Gauss niet vaak voorkomen in O en B-type sterren. Tenslotte beschrijven we in hoofdstuk 9 de ontdekking van niet-thermische radio emissie in de O ster ξ Persei, hetgeen naast de cyclische variabiliteit in de sterrenwind een onafhankelijke indirecte bevestiging is van de aanwezigheid van een magneetveld in deze ster. Een directe meting van het magneetveld is nog steeds niet gelukt ondanks zeer intensieve pogingen. Dit geeft sterke randvoorwaarden aan de sterkte en vorm van het magneetveld. Conclusie en toekomstig werk Het aantonen van de blijkbaar zwakke (honderd gauss of minder) of kleinschalige magneetvelden blijft experimenteel zeer moeilijk in zware sterren. Dit komt doordat er relatief weinig spectraallijnen beschikbaar zijn voor het meten van het Zeeman effect. We hebben met verschillende instrumenten aan diverse grote telescopen gezocht: de 8 m Very Large Telescope (VLT) in Chili, de 3.6 m Telescopio Nazionale Galileo (TNG) op La Palma, en de 2 m Telescope Bernard Lyot in Frankrijk. Ondanks dat we een redelijk aantal sterren onderzocht hebben, zijn er geen magnetische sterren gevonden met de beschikbare instrumentatie. Zeer recentelijk is echter een nieuwe generatie spectropolarimeters gebouwd die een 20 maal hogere gevoeligheid hebben en ook met een veel groter spectraal bereik. Hiermee zijn al nieuwe detecties zijn gedaan voor een O en een B ster. Dit bevestigt ons vermoeden dat het kleine aantal magnetische zware sterren slechts het topje van de ijsberg is. Deze nieuwe instrumenten (Espadons in Hawaii en Narval, op de Pic du Midi, Frankrijk, in gebruik vanaf december 2006), kunnen tot de limiet waarnemen waarbij grootschalige magneetvelden te zwak zijn om de sterrenwind te verstoren. Van deze nieuwe instrumenten wordt in de nabije toekomst erg veel verwacht. Belangrijke aandachtsgebieden zijn verder de magneetvelden in zeer jonge sterren, en de interactie hiervan met de omringende schijf. Ook de rol van differenti ële rotatie in het opwekken van magneetvelden in zware sterren is nog niet begrepen. 162 N EDERLANDSE S AMENVATTING Een beschrijving van hoe magneetvelden in zware sterren zich gedragen tijdens de evolutie, en of/hoe deze tijdens de collaps versterkt kunnen worden tot de extreme sterkte zoals in de neutronensterren en magnetars, is een uitdaging voor de theorie. Het geringe aantal beschikbare waarnemingen blijft echter een begrenzende factor. 163 N EDERLANDSE S AMENVATTING 164 E NGLISH S UMMARY Throughout the Universe magnetic fields have been found: in planets, the interplanetary medium, the Sun, stars, star forming molecular clouds, the interstellar medium, in galaxies and even between galaxies. The magnetic field strengths range from a few picogauss (10−12 G) in the intergalactic medium to several megagauss (106 G) and petagauss (1015 G) in white dwarfs and neutron stars, the remains of exploded stars. The research described in this thesis is aimed at magnetic fields in stars; in particular massive stars. These stars are more massive that about 9 solar masses, and will end their lives as neutron stars or black holes. Although we can quite easily study such stars in our own Galaxy, the Milky Way, many aspects of their evolution and behaviour are still not very well understood. One of these aspects is the role of magnetic fields. Simulations show that the presence of magnetic fields can have an enormous impact during the formation of the star, its evolution and its behaviour. Especially the origin of the fields in neutron stars and magnetars (strongly magnetized neutron stars) is unknown. A possibility is that these magnetic fields are generated during the collapse of a massive star in a supernova explosion. This scenario assumes that no relevant magnetic fields are present before the collapse. However, there is increasing evidence that massive stars do have magnetic fields, and these fields could be amplified during the collapse. The discovery of magnetic fields in very young massive stars suggests a fossil origin, where the magnetic field originates from the star’s parental molecular cloud. Contrary to stars like the Sun where magnetic fields are generated by a dynamo process. Currently only a handful magnetic massive stars are known, probably because the detection of magnetic fields in massive stars is much more challenging than in low-mass stars. This is due to the much smaller number of spectral lines in the optical region that are available for measuring the Zeeman effect, which is used to determine the magnetic field strength (see Chapter 1), in massive stars compared to stars of lower masses. The magnetic massive stars that have been found up to now are likely only the tip of the iceberg. The main subject of this thesis is the search for magnetic fields in massive stars, and determining the impact of such fields on the stellar wind. To this end both observations and simulations have been done. Below we summarise the theoretical and observational motivation for this research. 165 E NGLISH S UMMARY Theoretical motivation Contrary to the Sun massive stars do not have convective outer layers, where dynamo processes can generate magnetic fields. Massive stars only have a convective core, and in the outer layers energy is transported towards the surface by radiation. Therefore they need a different mechanism to generate a magnetic field, or maintain it if it is already present at birth. Major progress has been achieved for the somewhat lower mass A- and B-type stars. Approximately 10% of these stars (the Ap/Bp stars) are almost certainly magnetic. These stars are characterized by their peculiar chemical abundances, and will end their lives as white dwarfs due to their lower masses. The ratio of magnetic and non-magnetic A and B stars is similar to the ratio of magnetic and non-magnetic white dwarfs. This strongly suggests that the magnetic fields in white dwarfs are the compressed fields of the Ap/Bp stars. Now that recently a theoretically stable magnetic configuration has been found for the magnetic fields in Ap/Bp stars, it is likely that these fields are of a fossil origin. The relatively weak magnetic fields that are present in molecular clouds are amplified during the contraction required for star formation. This field of the newly formed star then decays until it reaches a stable configuration. The internal structure of Ap/Bp stars is similar to that of more massive stars, so it is certainly possible that stable magnetic fields of a fossil origin are also present in massive stars, and survive until the collapse towards a neutron star or black hole. Observational motivation Many unexplained phenomena are observed in massive stars that are hard to understand without the presence of magnetic fields. The main example is the well documented variability of stellar winds, visible in spectral lines in the ultraviolet (UV). The timescale of the variability shows a clear relation with the stellar rotation period, although it is often not strictly periodic. This is similar to the cyclic behaviour of sunspots, which have a magnetic origin. These spots corotate with the surface of the Sun, but do not result in strictly periodic behaviour because they have a finite lifetime, and new spots appear at different locations. Also in lines in the optical region, such as Hα, similar cyclic variability is observed. Other important indirect indicators for the presence of magnetic fields are nonthermal radio emission, hard X-ray emission, narrow X-ray emission lines, and peculiar abundances. Peculiar abundances have been found in most known magnetic stars, and has been used to identify new B stars that were indeed found to be magnetic. In the more massive O stars peculiar abundances have a different origin, and the cyclic wind variability is the most important indication that magnetic fields play a role. A small number of OB stars, as e.g. the early B star β Cephei, do show strictly periodic wind variability. This is caused by a stable dipolar field of which the axis 166 E NGLISH S UMMARY makes an angle with the rotation axis. However, in most of the massive stars the cyclic behaviour suggest more variable fields, as in the Sun. The main challenge is detecting this type of magnetic fields. This thesis The first chapter is an introduction to the importance of stellar magnetic fields and to the use of the polarisation of light to determine magnetic field strengths. The most effective method to determine the presence of (weak) magnetic fields in stars, is the analysis of the circular polarisation of light near spectral lines. In Chapter 2 we investigate whether the Least-Squares Deconvolution method also yields correct quantitative field strengths. We conclude that this method is very effective for detecting new magnetic fields, but that quantitative field measurements can show significant deviations. A large part of this thesis concerns the B star β Cephei. In Chapter 3 we report the discovery of the magnetic field in this star. The period of 12.00075 days, visible in the variable stellar wind, is also the period of the modulation of the magnetic field, and is the rotation period of the star. In this chapter we also give an improved determination of the orbital parameters of the binary orbit of β. Until now, the companion has only been resolved with speckle interferometry. The origin of the Hα emission from this star has long been a complete mystery. The emission is very similar to that observed in the rapidly rotating B emission stars, but β Cephei, with a period of 12 days, is a slow rotator. In addition, the emission shows no variability with the rotation period, although this period is visible in all other wind lines. In Chapter 4 we describe how we have used spectro-astrometry to conclusively show that the Hα emission does not originate in β Cephei itself, but stems from its close companion, which is likely a classical B emission star. How the interaction between the magnetic field and the stellar wind results in variability is quantitatively modeled using numerical simulations in Chapter 5. It is found that X-ray emission likely plays an important role in causing the variability. In Chapter 6 we show that the strong magnetic field that was predicted to be present in the B star ν Eridani based on the observed pulsation frequencies in this star is not present. Our limits on the magnetic field strongly constrain models of the internal structure of this star. New magnetic field measurements with the Musicos spectropolarimeter at the Télescope Bernard Lyot at the Pic du Midi in France and with the FOcal Reducer and low dispersion Spectrograph (FORS) at the Very Large Telescope in Chile presented in Chapters 7 and 8 show that large scale (dipole like) magnetic fields of a few hundred gauss or more are not common among O and B stars. Finally, in Chapter 9, we describe the discovery of non-thermal radio emission in the O star ξ Persei. Besides the cyclical variability of the stellar wind, this is additional evidence of the presence of a magnetic field. In spite of many attempts, we 167 have no direct detection of the magnetic field in this star. This strongly constrains the strength and geometry of the magnetic field. Conclusions and future work Detecting the apparently weak (less than a few hundred gauss) or local magnetic fields in massive stars remains a serious observational challenge. The reason for this is the small number of spectral lines available for measuring the Zeeman effect. We have used different instruments at various large observatories: the 8 m Very Large Telescope (VLT) in Chile, the 3.6 m Telescopio Nazionale Galileo (TNG) on La Palma, and the 2 m Télescope Bernard Lyot in France. Although we have observed a reasonable number of stars, no new magnetic stars have been discovered with the available instruments. However, recently a new generation of spectropolarimeters has become available with 20 times higher efficiency and a much larger spectral range. With these instruments, a new magnetic O and B star have already been discovered. This confirms our suspicion that the small number of known magnetic massive stars is just the tip of the iceberg. These new instruments, Espadons in Hawaii and Narval at the Pic du Midi in France, are able to detect large scale fields down to the limit where the fields are too weak to have a significant impact on the stellar wind. Significant progress is expected from these instruments in the near future. Other important areas where progress can be made are the magnetic fields of very young stars, and the impact of these fields on their accretion disks. Also the role of differential rotation in generating magnetic fields in massive stars is still unexplored. Understanding the changes of magnetic fields during the evolution of massive stars, and their relation to the enormous fields found after the collapse in neutron stars and magnetars, remains a major theoretical challenge. However, the limited constraints currently set by observations are an important barrier. D ANKWOORD Ik hou niet zo van cliche’s, maar toch wil ik graag wat mensen bedanken voor hun hulp, ondersteuning of bijdrage. Zeker als het onderzoek wat minder voortvarend ging heb heb ik daar veel aan gehad. Ten eerste Huib, omdat je ondanks dat je het niet altijd even makkelijk had altijd je uiterste best voor mij hebt gedaan. Verder natuurlijk Mirte die hoe ik ook in de put zit, altijd het beste in mij naar boven weet te halen. Jouw directheid en discipline is precies wat ik nodig heb. Bovendien is het met jou altijd lachen, en hou ik natuurlijk heel veel van je. Ook heb ik veel gehad aan mijn ouders Margu érite en Maarten en mijn broertje Maikel, omdat ze mij zonder enige objectiviteit in alle omstandigheden steunen. Ik kon altijd terecht bij Neeltje, Thomas en andere goede vrienden, of ik nu over serieuze wetenschap wilde praten of alleen mijn frustraties wilde uiten. I would also like to thank some of the many people that have been of great help to my research, and from whom I have learned a lot: Stan, Asif and Rich, Eva, Coralie, Franco, Rene Oudmaijer, John Telting, Martin Stift, Swetlana Hubrig, Tom Oosterlo, Alexander, James and Klaas. Een apart woord van dank voor Kazi, omdat we ondanks het beroerde weer een ontzettende leuke waarneemrun hebben gehad op de Pic, en daarna natuurlijk ook nog veel andere avonturen (o.a. met visibilities) hebben beleefd. Tot slot nog dank aan Joop voor het nalezen van mijn verhaal over polarisatie, en Alex en Lex voor advies. 169 L IST OF PUBLICATIONS Refereed publications F F F F F F F F On the Hα emission from the β Cephei system, R.S. Schnerr, H.F. Henrichs, R.D. Oudmaijer and J.H. Telting 2006, A&A Letters, 459L, 21 A study of the magnetic field in the photospheric and circumstellar components in Herbig Ae stars, S. Hubrig, M.A. Pogodin, R.V. Yudin, M. Schöller and R.S. Schnerr, A&A (accepted, astro-ph/0610439) Radio observations of candidate magnetic O stars, R.S. Schnerr, K.L.J. Rygl, A. van der Horst and H.F. Henrichs, A&A (submitted) On the reliability of stellar magnetic field measurements based on the Least-Squares Deconvolution method, F. Leone, R.S. Schnerr, M. Stift and H.F. Henrichs, A&A (submitted) Linear and circular polarisation of diffuse interstellar bands, N.L.J. Cox, N. Boudin, B.F. Foing, R.S. Schnerr, C. Neiner, J.-F. Donati and P. Ehrenfreund, A&A (submitted) Attempts to measure the magnetic field of the pulsating B star ν Eridani, R.S. Schnerr, E. Verdugo, H.F. Henrichs and C. Neiner 2006, A&A, 452, 969 Detailed study of the persistently bright atoll LMXBs GX 9+9, GX 9+1 and GX 3+1, T.J. Reerink, R.S. Schnerr, M. van der Klis and S. van Straaten, A&A, (submitted) Peculiar spectral and power spectral behaviour of the LMXB GX 13+1, R.S. Schnerr, T.J. Reerink, M. van der Klis, J. Homan, M. Méndez, R.P. Fender and E. Kuulkers 2003, A&A, 406, 221. Non-refereed publications F F Radio observations of candidate magnetic O stars, R.S. Schnerr, K.L.J. Rygl, A. van der Horst and H.F. Henrichs 2006, in ASP Conf. Ser.: Mass loss from stars and the evolution of stellar clusters, ed. A. de Koter, L.J. Smith & L.B.F.M. Waters, (submitted, astro-ph/0609387) Measurements of stellar magnetic fields with FORS1 in spectropolarimetric mode, S. Hubrig, T. Szeifert, M. Schöller and R.S. Schnerr 2006, in Proc. of the SPIE, Vol. 6269: Ground-based and Airborne Instrumentation for Astronomy, ed. I.S. McLean and M. Iye, p. 626929 171 L IST OF PUBLICATIONS F F F Magnetic field and UV-line variability in β Cephei, R.S. Schnerr, H.F. Henrichs, S.P. Owocki, A. ud-Doula and R.H.D. Townsend 2006, in ASP Conf. Ser.: Active OBStars: Laboratories for Stellar & Circumstellar Physics, ed. S. Stefl, S.P. Owocki and A. Okazaki (in press, astro-ph/0603418) Observed magnetism in massive stars, H.F. Henrichs, R.S. Schnerr and E. ten Kulve 2005, in ASP Conf. Ser. 337: The Nature and Evolution of Disks Around Hot Stars, ed. R. Ignace & K. Galey, p. 114 Do A-type supergiants have magnetic fields?, E. Verdugo, H.F. Henrichs, A. Talavera, A.I. Gomez de Castro, R.S. Schnerr and V.C. Geers 2005, in ASP Conf. Ser. 337: The Nature and Evolution of Disks Around Hot Stars, ed. R. Ignace & K. Galey, p. 324 172