Fast Numerical Methods for Polarized Line Radiative Transfer in the Presence of Hanle Effect

Abstract

The Hanle effect provides a diagnostic tool for weak magnetic fields which do not give rise to a measurable Zeeman effect, such as turbulent fields or magnetic canopies. The lines which are sensitive to the Hanle effect are formed under non-LTE conditions, by scattering of photons. Inversion methods for such diagnostics require to solve the non-LTE polarized transfer equation for a large number of magnetic configurations. Fast numerical methods are thus highly required. We present an Approximate Lambda Iteration method to treat the Hanle effect for lines formed with complete frequency redistribution. Referred to as PALI-H, this method is an extension of ALI methods first developed for non polarized line transfer. The starting point is to recast the polarized transfer equation into a vectorial integral equation for a 6-component source function. We show that the convergence of the method is independent of the strength and direction of the magnetic field. The method is very fast and allows to handle any type of depth-dependent magnetic field