Polarized scattering with Paschen-Back effect, hyperfine structure, and partial frequency redistribution in magnetized stellar atmospheres

TL;DR

This paper develops a comprehensive theoretical framework for polarized scattering in magnetized stellar atmospheres, incorporating hyperfine structure, Paschen-Back effect, and partial frequency redistribution, with applications to solar magnetic field diagnostics.

Contribution

It introduces a new PRD matrix including hyperfine interference effects under arbitrary magnetic fields, advancing the modeling of polarized line formation in stellar atmospheres.

Findings

The PRD matrix captures hyperfine and magnetic field effects on polarization.

Magnetic field influences in the Paschen-Back regime are characterized.

The model aids in diagnosing solar magnetic fields through polarization signatures.

Abstract

$F$-state interference significantly modifies the polarization produced by scattering processes in the solar atmosphere. Its signature in the emergent Stokes spectrum in the absence of magnetic fields is depolarization in the line core. In the present paper, we derive the partial frequency redistribution (PRD) matrix that includes interference between the upper hyperfine structure states of a two-level atom in the presence of magnetic fields of arbitrary strengths. The theory is applied to the Na I D$_2$ line that is produced by the transition between the lower $J=1/2$ and upper $J=3/2$ states which split into $F$ states because of the coupling with the nuclear spin $I_s=3/2$. The properties of the PRD matrix for the single-scattering case is explored, in particular, the effects of the magnetic field in the Paschen--Back regime and their usefulness as a tool for the diagnostics of solar magnetic fields.