Methods for calculating circular polarisation in magnetic white dwarfs

With regard to the problem of radiative transfer in the presence of a magnetic field, methods for solving the four interdependent differential equations for the four Stokes parameters I, Q, U and V (Hardorp et al., 1976) are presented. The accurate and easily programmed analytical method of Martin and Wickramasinghe (1979), based on a stepwise method in optical depth is compared with the approximate methods of Landstreet and Angel (1975) and of Brown et al. (1977), which give circular polarization results directly for flux rather than intensity; each method has been used in interpreting data from magnetic white dwarfs. It is concluded that the two approximate methods are not reliable for approximating the circular polarization in the continuum in the presence of absorption lines or absorption edges.