Spectral line polarization with angle-dependent partial frequency redistribution IV. Scattering expansion method for the Hanle effect

Abstract

Context. The partial frequency redistribution (PRD) effects in line scattering are necessary ingredients for interpreting the linear polarization observed in strong resonance lines. It is a common practice to use angle-averaged PRD functions for simplicity (obtained by averaging over all scattering angles). It has been established that the use of angle-dependent PRD functions instead of angle-averaged functions is essential for weak fields.

Aims. Here we present an efficient iterative method to solve the polarized line radiative transfer equation in weak magnetic fields using angle-dependent PRD functions.

Methods. Based on the theory of Stokes vector decomposition for the Hanle effect combined with the Fourier azimuthal expansion of the angle-dependent PRD function, we try to formulate an efficient numerical method of solving the concerned transfer problem in one-dimensional media. This iterative method (referred to as the scattering expansion method, SEM) is based on a series expansion of the polarized source vector in mean number of scatterings (Neumann series expansion). We apply the SEM approach to handle both the exact and various approximate forms of the Hanle scattering redistribution matrix.

Results. The SEM is shown to be an efficient method to solve angle-dependent PRD problems involving the Hanle effect. We show that compared to the earlier methods such as the perturbation methods, the SEM is stable and faster. We find that angle-dependent PRD significantly affects the Stokes U parameter.