Spectral line polarization with angle-dependent partial frequency redistribution

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 T K Q (i, Ω )( 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 I K (K = Q = 0, K = 2, Q = 0, 1, 2). The components with Q = 1, 2a re 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 I K is a solution to a standard radiative transfer equation. The source term S K 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.