Modelling Magnetic Fields in Stars: The Input

The Zeeman Effect both splits (or effectively, broadens) and polarises a spectral line under the influence of a magnetic field. Observing stellar spectra in both circularly and linearly polarised light allows for a measure of the line-of-sight and the transverse field. Observing a star throughout a rotation cycle should allow for a reconstruction of stellar magnetic field geometry and topology. High signal to noise ratio data is necessary, however.

Donati et al. (1987) developed a technique known as Least-Squares Deconvolution (LSD) which uses many lines to get an "average" line in a spectrum. For a given spectral type, LSD uses an atlas of lines characterized by wavelength, depth and magnetic splitting strength, g. Using the three parameters as scaling factors, a mean "polarisation signature" is found to match the observed spectrum. The hope is that mean signatures will reflect global parameters.

The problem with using LSD is determining how much of what you see is real. LSD's main approximation is that the Zeeman Effect affects all lines in some scalable way. Lines are actually split and polarised in different ways depending on the values of the quantum numbers, J and the splitting stengths, g of the upper and lower atomic levels for each line, thereby creating different Zeeman patterns (Figure 1, Mathys 1989) The saturation of lines is also a concern. The issue is further complicated by the fact that one is integrating over the stellar disk of a rotating star, with the resultant spectral line made up of components which are affected by the whole field geometry.

To investigate the limitations of LSD, spectra were synthesized using the ZEEMAN code developed by Landstreet, with work by Wade. ZEEMAN is an LTE radiative transfer code which treats the effect of a stellar magnetic field. Our synthesis used a strong magnetic field at an angle to the line-of-sight. A linelist from VALD was adopted for a star with log g = 4.0, T=10000K. The same linelist was used as the atlas for LSD, thereby eliminating any errors of incorrect line depths or splitting strengths. The atlas was subdivided into subatlases based on splitting pattern and line strength (two of the factors in the LSD scaling relations). LSD was run on the synthesized spectrum, using each subatlas, and the polarisation profiles compared.

See page of figures

Conclusions

It may be seen that the Zeeman pattern does influence the resultant LSD profiles, although it had less of an effect when the test star had a rotational velocity of 10 km/s than 20 km/s. Also, the profiles of weak lines may not be simply scaled into those of strong lines. Future work will strive to find a subset of lines, by depth and Zeeman pattern, which will give us high S/N profiles but will also be physically modellable. This work is in an effort to eventually model stellar magnetic fields with the excellent spectropolarimetric data we have obtained (Wade et al. 1999).

References

Donati J.-F., Semel M., Carter B.D., Rees D.E., Cameron A.C., 1997, MNRAS 291, 658
Mathys G., 1989, Fund. Cosmic Phys. 13, 143
Wade G.A., Donati J.-F., Landstreet J.D., Shorlin, S.L.S., 1999, MNRAS, submitted

---

Stephen L. S. Shorlin      Stephen originally comes from Jeffrey's, Nfld. He completed a B. Sc. in physics at Memorial University of Newfoundland, and he went on to an M. Sc. in astronomy at Saint Mary's University. He is currently a Ph. D. candidate at The University of Western Ontario where he studies magnetic fields in mid-to-upper main sequence stars. Steve is an observer and in his short career has been clouded, rained, snowed and/or "humiditied" out on three continents, plus Hawaii. He's also an excited expectant father.

---