Download Magnetic fields and mass loss in massive stars

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 . . . . . . . . . . . . . . . . . . . . . . . .
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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 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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25
25
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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 . . . . . . . . . . . . . . . . . .
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36
40
40
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C ONTENTS
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41
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59
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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 . . . . . . . . . . . . .
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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 . . . . . . . . .
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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 . . . . . . . . . . . . . . . . . . . . . . . .
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Magnetic field measurements of O stars with VLT/FORS1
8.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . .
8.2 Observations & Method . . . . . . . . . . . . . . . . .
8.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . .
8.4 Conclusions . . . . . . . . . . . . . . . . . . . . . . . .
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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 . . . . . . . . . . . . . . . . . . . .
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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. Finally, in Chapter 9, we present the results of a search for radio synchrotron
emission in magnetic candidate O stars, and report the discovery of non-thermal
radio emission in ξ Per.
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15
C HAPTER 1
16
Het is heel eenvoudig. U moet in deze boom klimmen en de hoogste appel plukken! Dat is de appel
der zelfkennis. En die hangt nu eenmaal hoog.
Tuinman uit de Knollengaard
C HAPTER 2
ON
THE RELIABILITY OF STELLAR MAG -
NETIC FIELD MEASUREMENTS BASED ON
THE
LSD∗
METHOD
F. Leone, R. S. Schnerr, M. J. 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
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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,
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Preston, G. W. 1971, PASP, 83, 571
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Stift, M. J. 2000, A Peculiar Newsletter, 33, 27
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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. JDJ
acknowledges support from the Netherlands Foundation for Research in Astronomy (NFRA)
with financial aid from the Netherlands Organization for Scientific Research (NWO) under
53
C HAPTER 3
project 781-71-053. GAW acknowledges support from the Natural Sciences and Engineering
Council of Canada (NSERC) in the form of an NSERC postdoctoral fellowship held during the
course of this work.
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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
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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.
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in IAU Colloq. 139: New Perspectives on Stellar Pulsation and Pulsating Variable
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Henrichs, H. F., Neiner, C., & Geers, V. C. 2003, in ASP Conf. Ser., Vol. 305, “Magnetic
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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
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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.
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N UMERICAL SIMULATIONS OF UV WIND - LINE VARIABILITY: β C EPHEI
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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
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–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
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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
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←
–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).
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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.
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C HAPTER 5
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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
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φ
p
x
a
R
*
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by the star.
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N UMERICAL SIMULATIONS OF UV WIND - LINE VARIABILITY: β C EPHEI
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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
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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. This research has
been partly based on INES data from the IUE satellite and made use of the Simbad and ADS
databases maintained at CDS, Strasbourg, France.
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103
C HAPTER 6
104
C HAPTER 7
M AGNETIC FIELD MEASUREMENTS OF
OB- TYPE STARS
R. S. Schnerr, H. F. Henrichs, C. Neiner, E. Verdugo, J. de Jong, V. C. Geers,
K. Wiersema, B. van Dalen, A. Tijani, B. Plaggenborg, K. L. J. 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
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136
C HAPTER 8
M AGNETIC FIELD MEASUREMENTS OF O
STARS WITH VLT/FORS1 ∗
R. S. Schnerr, S. Hubrig & H. F. Henrichs
Astronomy and Astrophysics, (to be submitted)
Abstract
The presence of magnetic fields in O-type stars has been suspected for a long time.
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. This research has made use of VALD, ADS, SIMBAD. We would like to
thank R. Mokiem for help on theoretical spectra of O stars, and T. Szeifert for the use of data
reduction procedures.
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U kunt beter berusten’, zei de heer Dorknoper
goedig. ‘Op dit soort uitbarstingen van gedupeerden zijn wij, ambtenaren, voorbereid.
Ambtenaar Dorknoper
C HAPTER 9
R ADIO OBSERVATIONS OF CANDIDATE
MAGNETIC O STARS
R. S. Schnerr, K. L. J. Rygl, A. J. van der Horst, T. A. Oosterloo, J. C. A. Miller-Jones,
H. F. Henrichs, T. A. Th. Spoelstra & A. R. 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. The Westerbork Synthesis Radio Telescope is operated by ASTRON (the Netherlands
Foundation for Research in Astronomy) with support from the Netherlands Foundation for
Scientific Research NWO. The Very Large Array is part of the National Radio Astronomy Observatory, which is a facility of the National Science Foundation operated under cooperative
agreement by Associated Universities, Inc.
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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
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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.
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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.
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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.
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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
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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.
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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
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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
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