Polarized Line Formation in Multi-dimensional Media. V. Effects of Angle-Dependent Partial Frequency Redistribution

TL;DR

This paper investigates the combined influence of angle-dependent partial frequency redistribution and multi-dimensional transfer effects on polarized line formation in the solar spectrum, highlighting their significance for accurate polarization modeling.

Contribution

It introduces a Fourier decomposition-based numerical method for solving multi-D polarized radiative transfer with AD PRD effects, advancing the quantitative analysis of solar polarization.

Findings

AD PRD effects are significant and cannot be ignored.

Multi-D transfer amplifies the impact of AD PRD effects.

Magnetic fields modify the influence of PRD and multi-D effects.

Abstract

The solution of polarized radiative transfer equation with angle-dependent (AD) partial frequency redistribution (PRD) is a challenging problem. Modeling the observed, linearly polarized strong resonance lines in the solar spectrum often requires the solution of the AD line transfer problems in one-dimensional (1D) or multi-dimensional (multi-D) geometries. The purpose of this paper is to develop an understanding of the relative importance of the AD PRD effects and the multi-D transfer effects and particularly their combined influence on the line polarization. This would help in a quantitative analysis of the second solar spectrum (the linearly polarized spectrum of the Sun). We consider both non-magnetic and magnetic media. In this paper we reduce the Stokes vector transfer equation to a simpler form using a Fourier decomposition technique for multi-D media. A fast numerical method is also devised to solve the concerned multi-D transfer problem. The numerical results are presented for a two-dimensional medium with a moderate optical thickness (effectively thin), and are computed for a collisionless frequency redistribution. We show that the AD PRD effects are significant, and can not be ignored in a quantitative fine analysis of the line polarization. These effects are accentuated by the finite dimensionality of the medium (multi-D transfer). The presence of magnetic fields (Hanle effect) modifies the impact of these two effects to a considerable extent.