The Hanle Effect in 1D, 2D and 3D

TL;DR

This paper develops a comprehensive theoretical and numerical framework for modeling the Hanle effect in polarized line formation across 1D, 2D, and 3D media, incorporating advanced iterative methods for solving the coupled radiative transfer and atomic state equations.

Contribution

It extends existing polarization transfer methods to multi-dimensional media and demonstrates their effectiveness through model calculations including atmospheric inhomogeneities.

Findings

High convergence rate of the iterative methods.

Horizontal inhomogeneities significantly affect polarization signals.

Framework applicable to complex astrophysical media.

Abstract

This paper addresses the problem of scattering line polarization and the Hanle effect in one-dimensional (1D), two-dimensional (2D) and three-dimensional (3D) media for the case of a two-level model atom without lower-level polarization and assuming complete frequency redistribution. The theoretical framework chosen for its formulation is the QED theory of Landi Degl'Innocenti (1983), which specifies the excitation state of the atoms in terms of the irreducible tensor components of the atomic density matrix. The self-consistent values of these density-matrix elements is to be determined by solving jointly the kinetic and radiative transfer equations for the Stokes parameters. We show how to achieve this by generalizing to Non-LTE polarization transfer the Jacobi-based ALI method of Olson et al. (1986) and the iterative schemes based on Gauss-Seidel iteration of Trujillo Bueno and Fabiani Bendicho (1995). These methods essentially maintain the simplicity of the Lambda-iteration method, but their convergence rate is extremely high. Finally, some 1D and 2D model calculations are presented that illustrate the effect of horizontal atmospheric inhomogeneities on magnetic and non-magnetic resonance line polarization signals.