Observing and Modelling Stellar Magnetic Fields

Abstract

In this chapter, we examine the question of how spectropo- larimetric observations of magnetic stars may be modelled, and how modelling techniques may be used to extract much detailed informa- tion about the stellar magnetic field and other characteristics of the magnetized stellar atmosphere. In the preceding chapter, we discussed how the energy levels of atoms are split by a magnetic field, and how this leads in turn to splitting of spectral lines in to multiple components, an effect called the Zeeman or Paschen-Back effect depending on the field strength. We saw that the polarisation characteristics of these components provide valuable tools for detection and measurement of stellar magnetic fields, and that polarisation measurements allow one to obtain, in a straight-forward way, an estimate of the mean line-of-sight field component averaged over the visible hemisphere (the mean longitudinal field h Bzi ). We also saw that, if the field is large enough and ve sin i small enough, observation of splitting of spectral lines into discrete components makes it possible to estimate the mean field modulus h Bi , again averaged over the visible hemisphere. Finally, we looked at some simple multipole models of stellar field structure that can reproduce simple data-sets such as observed values of h Bzi , or of h Bzi and h Bi , over a stellar rotation, and how these models lead to the fundamental conceptual model known as the oblique rotator. Determination of mean field values directly from the spectra (in the same way as radial velocities and projected rotation velocities are derived), and the modelling of such integral or moment data with simple geometric field structures, provide a useful and valuable source of information about global characteristics of the stellar field. However, such models are based on data-sets that are often