Hanle effect with angle-dependent partial redistribution

Abstract

The polarized line transfer equation for the Hanle effect is solved in the framework of an exact partial frequency redistribution (PRD) theory developed by Bommier (1997a,b). In that theory the effect of collisions on the Hanle effect is considered self-consistently. We follow that approach in the line transfer computations presented here. The theory formulated by Bommier clearly recognizes two levels of approximations for exact PRD, in order to facilitate the solution of the line transfer equation. The second level employs angle-dependent redistribution functions, and numerically represents a more difficult problem compared to the third level, which involves only the use of angle-averaged frequency redistribution functions. We present a method which can solve the problem in both the levels of approximation. The method is based on a perturbative approach to line polarization. Although computationally expensive, it offers the only practical means of solving the angle-dependent Hanle PRD problem. We discuss the numerical aspects of assembling the so called “frequency domain dependent redistribution matrices”, and also an efficient way of computing the scattering integral. Some examples are presented to illustrate the interesting aspects of the Hanle-PRD problem with angle-dependent frequency redistribution. A comparison of the emergent profiles computed under angle-averaged and angle-dependent redistribution is carried out, and the effect of collisions is investigated. We show that it is necessary to incorporate an angle-dependent redistribution mechanism especially in the computation of the Stokes U parameter. We demonstrate that the use of simple frequency domains is good enough in practical applications of the Hanle PRD theory.