Spectral line polarization with angle-dependent partial frequency redistribution

I. A Stokes parameters decomposition for Rayleigh scattering

UNS, CNRS, OCA, Laboratoire Cassiopée, BP 4229, 06304 Nice Cedex 4, France
e-mail: frisch@oca.eu

Received: 7 June 2010
Accepted: 30 July 2010

Abstract

Context. The linear polarization of a strong resonance lines observed near the solar limb is created by a multiple-scattering process. Partial frequency redistribution (PRD) effects must be accounted for to explain the polarization profiles. The redistribution matrix describing the scattering process is a sum of terms, each containing a PRD function multiplied by a Rayleigh type phase matrix. A standard approximation made in calculating the polarization is to average the PRD functions over all the scattering angles, because the numerical work needed to take the angle-dependence of the PRD functions into account is large and not always needed for reasonable evaluations of the polarization.

Aims. This paper describes a Stokes parameters decomposition method, that is applicable in plane-parallel cylindrically symmetrical media, which aims at simplifying the numerical work needed to overcome the angle-average approximation.

Methods. The decomposition method relies on an azimuthal Fourier expansion of the PRD functions associated to a decomposition of the phase matrices in terms of the Landi Degl’Innocenti irreducible spherical tensors for polarimetry (i Stokes parameter index, Ω ray direction). The terms that depend on the azimuth of the scattering angle are retained in the phase matrices.

Results. It is shown that the Stokes parameters I and Q, which have the same cylindrical symmetry as the medium, can be expressed in terms of four cylindrically symmetrical components (K = Q = 0, K = 2, Q = 0,1,2). The components with Q = 1,2 are created by the angular dependence of the PRD functions. They go to zero at disk center, ensuring that Stokes Q also goes to zero. Each component is a solution to a standard radiative transfer equation. The source term are significantly simpler than the source terms corresponding to I and Q. They satisfy a set of integral equations that can be solved by an accelerated lambda iteration (ALI) method.