POLARIZED LINE FORMATION IN MULTI-DIMENSIONAL MEDIA. II. A FAST METHOD TO SOLVE PROBLEMS WITH PARTIAL FREQUENCY REDISTRIBUTION

Abstract

In the previous paper of this series (Anusha & Nagendra 2010), we presented a formulation of the polarized radiative transfer equation for resonance scattering with partial frequency redistribution (PRD) in multi-dimensional media for a two-level atom model with unpolarized ground level, using the irreducible spherical tensors T K Q (i,) for polarimetry. We also presented a polarized approximate lambda iteration (PALI) method to solve this equation using the Jacobi iteration scheme. The formal solution used was based on a simple finite volume technique. In this paper, we develop a faster and more efficient method which uses the projection t echniques applied to the radiative transfer equation (the Stabilized Preconditioned Bi-Conjugate Gradient method). We now use a more accurate formal solver, namely the well known 2D (two dimensional) short characteristics method. Using the numerical method developed in Anusha & Nagendra (2010), we can consider only simpler cases of finite 2D slabs due to computational limitations. Using the method developed in this paper we could compute PRD solutions in 2D media, in the more difficult context of semi-infinite 2D slabs as well. We present several solutions which may serve as benchmarks in future studies in this area. Subject headings: line: formation – radiative transfer – polarization – scattering– Sun: atmosphere