Spectral line polarization with angle-dependent partial frequency redistribution. II. Accelerated lambda iteration and scattering expansion methods for the Rayleigh scattering

Abstract

Context. The linear polarization of strong resonance lines observed in the solar spectrum is created by the scattering of the photospheric radiation field. This polarization is sensitive to the form of the partial frequency redistribution (PRD) function used in the line radiative transfer equation. Observations have been analyzed until now with angle-averaged PRD functions. With an increase in the polarimetric sensitivity and resolving power of the present-day telescopes, it will become possible to detect finer effects caused by the angle dependence of the PRD functions.

Aims. We devise new efficient numerical methods to solve the polarized line transfer equation with angle-dependent PRD, in plane-parallel cylindrically symmetrical media. We try to bring out the essential differences between the polarized spectra formed under angle-averaged and the more realistic case of angle-dependent PRD functions.

Methods. We use a recently developed Stokes vector decomposition technique to formulate three different iterative methods tailored for angle-dependent PRD functions. Two of them are of the accelerated lambda iteration type, one is based on the core-wing approach, and the other one on the frequency by frequency approach suitably generalized to handle angle-dependent PRD. The third one is based on a series expansion in the mean number of scattering events (Neumann series expansion).

Results. We show that all these methods work well on this difficult problem of polarized line formation with angle-dependent PRD. We present several benchmark solutions with isothermal atmospheres to show the performance of the three numerical methods and to analyze the role of the angle-dependent PRD effects. For weak lines, we find no significant effects when the angle-dependence of the PRD functions is taken into account. For strong lines, we find a significant decrease in the polarization, the largest effect occurring in the near wing maxima.