Fast Iterative Techniques for Polarized Radiative Transfer in Spherically Symmetric Moving Media

Abstract

For a more precise modeling of polarized spectral lines formed in extended and expanding stellar atmospheres, the solution of the radiative transfer equation for the Stokes vectors must be obtained in a spherical geometry rather than in a planar geometry. In this paper, we present the modern iterative techniques based on operator perturbation to solve the spherically symmetric polarized radiative transfer equation with velocity fields. We consider scattering on a two-level atom and account for partial frequency redistribution. An accurate numerical solution to such problems requires the use of spatial grids with higher resolution. Consequently, Jacobi-based methods lead to slower convergence rate. The convergence rate can be improved by a factor of 2 or more when fast iterative schemes based on Gauss–Seidel (GS) and successive overrelaxation (SOR) methods are used over the Jacobi-based method. Here we present the Jacobi, GS, and SOR iterative techniques for solving the abovementioned problem, and discuss their convergence behavior.