Theoretical formulation of Doppler redistribution in scattering polarization within the framework of the velocity-space density matrix formalism

TL;DR

This paper develops a comprehensive theoretical framework for modeling Doppler redistribution effects in scattering polarization, incorporating velocity-space density matrix correlations within the polarized radiative transfer equations.

Contribution

It introduces a novel formalism that explicitly accounts for velocity-space density matrix correlations in polarized radiative transfer, extending the traditional complete redistribution approximation.

Findings

Derived coupled equations for velocity-dependent source functions.

Established the equivalence between the density matrix and redistribution matrix formalisms.

Provided a detailed description of pure Doppler redistribution physics.

Abstract

Within the framework of the density matrix theory for the generation and transfer of polarized radiation, velocity density matrix correlations represent an important physical aspect that, however, is often neglected in practical applications by adopting the simplifying approximation of complete redistribution on velocity. In this paper, we present an application of the Non-LTE problem for polarized radiation taking such correlations into account through the velocity-space density matrix formalism. We consider a two-level atom with infinitely sharp upper and lower levels, and we derive the corresponding statistical equilibrium equations neglecting the contribution of velocity-changing collisions. Coupling such equations with the radiative transfer equations for polarized radiation, we derive a set of coupled equations for the velocity-dependent source function. This set of equations is then particularized to the case of a plane-parallel atmosphere. The equations presented in this paper provide a complete and solid description of the physics of pure Doppler redistribution, a phenomenon generally described within the framework of the redistribution matrix formalism. The redistribution matrix corresponding to this problem (generally referred to as R_I) is derived starting from the statistical equilibrium equations for the velocity-space density matrix and from the radiative transfer equations for polarized radiation, thus showing the equivalence of the two approaches.