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

¹ Instituto de Astrofísica de Canarias, C. Vía Láctea s/n, 38205 La Laguna Tenerife, Spain
e-mail: belluzzi@iac.es
² Departamento de Astrofísica, Facultad de Física, Universidad de La Laguna, 38206, La Laguna Tenerife, Spain
³ Dipartimento di Fisica e Astronomia, Università di Firenze, Largo E. Fermi 2, 50125 Firenze, Italy
⁴ Consejo Superior de Investigaciones Científicas, Spain

Received: 18 October 2012
Accepted: 25 January 2013

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 when 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.