1. Stellar Magnetic Field_2
J. D. Landstreet 의 파일

2. Introduction
We now turn to three major questions connecting the atomic physics of magnetic fields with astronomy
Which of the various atomic effects of a magnetic field are actually observable in stars
How do we use these effects to obtain empirical information about stellar magnetic fields
To what extend do observations allow us to actually model the field structure of a star

3. Basic observation methods
To search for magnetic fields in stars, we could use either the splitting properties of Zeeman effect, or polarising properties
Direct line splitting can be detected in some stars, but only under somewhat exceptional circumstances: typical field (in kG) > v sin i (in km/s)
When we do detect splitting, measurement of (mean) displacement of sigma components from pi components gives direct measurement of average magnitude of field over visible hemisphere, often called “mean field modulus”, Bs or <B>

4. Mean field modulus
Segment of spectrum of magnetic Ap star HD (Mathys) shows visible Zeeman splitting in a field of about 6 kG
Laboratory and theoretical Zeeman patterns are shown beneath stellar spectrum

5. Field detection from spectropolarimetry
For most non-degenerate stars, field detection is achieved by spectropolarimetry, using polarisation properties of Zeeman effect
As we saw in first lecture, longitudinal field component produces first-order separation of line profiles in right and left circularly polarised light.
Measuring this separation yields an average of the line of sight component of the field over the visible stellar hemisphere (the linearly polarised transverse field component contributes the same profile to both right and left circularly analysed line profiles)
The quantity is usually called the “mean longitudinal field”, <Bz> or sometimes Be

6. Useful data analysis methods from equations of polarised transfer
If field is so weak that Zeeman splitting is small compared to natural width of local line profile, mean longitudinal field <Bz> may be found from
V(l) = gl2 (dI/dl) <Bz> (l in A)
(e.g. Landstreet 1982, ApJ 258, 639; Bagnulo et al 2002, A&A 389, 191)
If the lines are fairly weak (often used on strong lines too…)
where B is in G, l is in A, g is the mean Lande factor of the line, and I and V are functions of velocity shift v from line centre (e.g. Donati et al 1997, MN 291, 658). This result is widely used to interpret magnetic circular polarisation spectra, including LSD spectra (see below)

7. The oblique rotator model of magnetic A and B (Ap) stars
First non-zero (longitudinal) magnetic fields found in magnetic Ap stars (A and B stars of very peculiar atmospheric chemistry) by Babcock in 1947
When <Bz> is measured repeatedly for one Ap star, found to vary periodically with period that varies inversely with v sin i. Many such stars are also periodically variable in light and/or spectrum, with same period as field.
Clearly the period is the rotation period of the star, and the field varies because it is not axisymmetric. As the star rotates we see different field configurations on the visible hemisphere: the “oblique (dipole) rotator”
Because <Bz> usually varies almost sinusoidally, we deduce that the field is “simple”, roughly dipolar. Ratio of largest value of <Bz> to typical <B> is consistent with this idea

8. Example of observed Ap star variations
HD shows periodic variations in longitudinal field, He line strength, and photometric brightness and colour with a period of 9.53 d (Wade et al 1997, A&A 320, 172)

9. The oblique rotator
Sketch of the oblique rotator model of a star showing magnetic field lines (black vectors projecting from the surface) and the variation of abundance of a variable chemical element over the surface (colour coding)
As the star rotates about an axis other than the field axis, both field and spectrum vary.

10. Recent advances
Spectropolarimetry allows detection of remarkably small magnetic fields. Polarisation is measured differentially, so values as low as a few times 10-4 % of I can be measured reliably. This allows detection of magnetic fields as small as a few 10’s of G (in bright stars! e.g. Shorlin et al 2002, A&A 392, 637)
Linear polarisation, variable with the rotation period (hence intrinsic, not interstellar) has been detected in broad bands (Leroy 1995, A&AS 114, 79). This is apparently due to Zeeman linear polarisation in individual saturated spectral lines, and corresponds very well to line linear polarisation, now observed with Musicos and Espadons (Wade et al 2000, MN 313, 823)

11. Least squares deconvolution
Polarisation spectra of fainter stars often lack sufficient S/N to detect the very small signals due to the Zeeman effect. Donati has introduced and implemented a very valuable tool for co-addition of these small signals: LSD
This technique allows one to recover very small polarisation signals. In the case of V signals the individual polarisation profiles are sufficiently similar that the mean V signal may be treated as the signal of a single line; for Q and U (linear polarisation) signals, the dispersion of individual signals is much larger: it is not clear what the meaning of the mean signal is (except for providing detection and estimate of amplitude).

12. Detection of a weak field in e UMa using LSD (with TBL-Musicos)

13. Broad-band linear polarisation in 78 Vir
Upper panel: longitudinal magnetic field of Ap star 78 Vir
Lower panel: broad-band linear polarisation observed by Leroy (1995, AAS 114, 79) compared with value synthesized from LSD line profile linear polarisation in same bandpass (Wade et al 2000, MN 313, 851)

14. Moment techniques
The longitudinal field measurement can be viewed as the first order (wavelength or velocity) moment of the circular polarisation spectrum (and the equivalent width is the zero-order moment of the intensity spectrum): recall
Mathys (e.g. in Astrophysical Spectropolarimetry, eds Trujillo-Bueno et al, 2000, p 101) has shown that higher moments of the I and V spectra contain useful information about the configuration of the magnetic field under observation
Simplest modelling strategy: assume simple field structure, fit one or more field moments

15. Combined variations of several field moments
Typical variations of mean longitudinal field (upper left of each group) and mean field modulus (lower right) for two stars for which both fields are measured (models: Landstreet & Mathys 2000 A&A)
Also shown are two other field moments. Lower left panel shows “mean quadratic field” (similar to mean field modulus); upper right is “crossover field” which detects reversals of field polarity (cf Mathys 1995, A&A 293, 733 & 746)

16. Modelling with synthesis codes
Most physically correct method of deducing field structure from observed intensity and polarisation spectra is by computing spectra that match observations rather than fitting simple models to field moments.
Generally this requires model atmosphere and line synthesis programmes. Both may take magnetic effects into account at various levels:
Zeeman splitting of lines,
polarised radiative transfer,
magnetic field effects on hydrostatic equilibrium,
effects on convection and transport of chemical elements horizontally and vertically…

17. Physics and strategy of a simple code (Zeeman)
Zeeman (Landstreet 1988, ApJ 326, 967) is simple magnetic line synthesis programme
Reads in specifications of star, spectral window
Computes one or more (I, Q, U, V) spectra including magnetic line splitting and polarised radiative transfer, using line list and line parameters from VALD and precomputed Atlas atmosphere
Compares computed spectrum(a) with observed one(s), determines vrad, v sin i, and c2 of fit
If desired, iterates abundance of one element to fit one or many spectral lines chosen by programme
Contains simple parametrised models of magnetic field, abundance distribution over several co-axial rings. With several spectra, can optimise model

18. Fit to a spectrum of Sirius
Synthesis fits to non-magnetic stars can be very accurate
Example: Sirius

19. Simple parametrised model of 53 Cam
However, parametrised models which fit moment data usually do not describe more detailed polarisation spectra accurately (Bagnulo et al 2001, A&A 369, 889)

20. More powerful mapping methods do fit 53 Cam
Solution is to develop powerful mapping code which can fit field and abundance at many points on stellar surface by iterative adjustment (Kochukhov et al 2004, A&A 414, 613)

21. 53 Cam Fe abundance and field maps from 3 lines

22. Magnetic Field : 발표과제 A&A 392, 637 2002 : 임은경 A&A 341, 216 1999 : 최현정
IAUS, 243, “Measurements of magnetic fields on T Tauri stars” by C. M. Johns-Krull : 강원석
A&A 389, 191, 2002 : 신영우
MN 313, 823, 2000 : 권 륜영