Polarized Line Formation in Multi-dimensional Media. IV. A Fourier Decomposition Technique to Formulate the Transfer Equation with Angle-dependent Partial Frequency Redistribution

Abstract

To explain the linear polarization observed in spatially resolved structures in the solar atmosphere, the solution of polarized radiative transfer (RT) equation in multi-dimensional (multi-D) geometries is essential. For strong resonance lines, partial frequency redistribution (PRD) effects also become important. In a series of papers, we have been investigating the nature of Stokes profiles formed in multi-D media including PRD in line scattering. For numerical simplicity, so far we have restricted our attention to the particular case of PRD functions which are averaged over all the incident and scattered directions. In this paper, we formulate the polarized RT equation in multi-D media that takes into account the Hanle effect with angle-dependent PRD functions. We generalize here to the multi-D case the method for Fourier series expansion of angle-dependent PRD functions originally developed for RT in one-dimensional geometry.