The transfer of polarized radiation in resonance lines with partial frequency redistribution, J-state interference, and arbitrary magnetic fields

A radiative transfer code and useful approximations

¹ IRSOL Istituto Ricerche Solari “Aldo e Cele Daccò”, Università della Svizzera italiana (USI), 6605 Locarno-Monti, Switzerland
e-mail: ernest.alsina@iac.es
² Instituto de Astrofísica de Canarias (IAC), 38205 La Laguna, Tenerife, Spain
³ Departamento de Astrofísica, Universidad de La Laguna (ULL), 38206 La Laguna, Tenerife, Spain
⁴ Leibniz-Institut für Sonnenphysik (KIS), 79104 Freiburg, Germany
⁵ Euler Institute, Università della Svizzera italiana (USI), 6900 Lugano, Switzerland
⁶ Consejo Superior de Investigaciones Científicas (CSIC), Spain

Received: 16 December 2021
Accepted: 25 April 2022

Abstract

Aims. We present the theoretical framework and numerical methods we have implemented to solve the problem of the generation and transfer of polarized radiation in spectral lines without assuming local thermodynamical equilibrium, while accounting for scattering polarization, partial frequency redistribution (due to both the Doppler effect and elastic collisions), J-state interference, and hyperfine structure. The resulting radiative transfer code allows one to model the impact of magnetic fields of an arbitrary strength and orientation through the Hanle, incomplete Paschen-Back, and magneto-optical effects. We also evaluate the suitability of a series of approximations for modeling the scattering polarization in the wings of strong resonance lines at a much lower computational cost, which is particularly valuable for the numerically intensive case of three-dimensional radiative transfer.

Methods. We examine the suitability of the considered approximations by using our radiative transfer code to model the Stokes profiles of the Mg  II h & k lines and of the H I Lyman-α line in magnetized one-dimensional models of the solar atmosphere.

Results. Neglecting Doppler redistribution in the scattering processes that are unperturbed by elastic collisions (i.e., treating them as coherent in the observer’s frame) produces a negligible error in the scattering polarization wings of the Mg II resonance lines and a minor one in the Lyman-α wings, although it is unsuitable to model the cores of these lines. For both lines, the scattering processes that are perturbed by elastic collisions only give a significant contribution to the intensity component of the emissivity. Neglecting collisional as well as Doppler redistribution (so that all scattering processes are coherent) represents a rough but suitable approximation for the wings of the Mg II resonance lines, but a very poor one for the Lyman-α wings. The magnetic sensitivity in the scattering polarization wings of the considered lines can be modeled by accounting for the magnetic field in only the η_I and ρ_V coefficients of the Stokes-vector transfer equation (i.e., using the zero-field expression for the emissivity).