Polarized Redistribution Matrix for Hanle Effect

Abstract

A redistribution matrix describes the correlations in frequency, direction of propagation and polarization between the absorbed and the re-emitted photons in the process of atomic scattering. Recently, Bommier (1997a, b) has derived new expressions for this matrix, for lines formed in the presence of magnetic fields. Her derivation is based on the solution of the master equation for the atomic density matrix; it is valid in an arbitrary magnetic field. In the general case, redistribution in frequency and in polarization are coupled. However, for weak fields, cut-off appproximations may be proposed. The frequency space is divided in several domains where the redistribution matrix is a linear combination of elementary redistribution matrices. In each domain, frequency and polarization redistribution are decoupled.

We have implemented this cut-off approximation in polarized radiative transfer calculations with angle averaged frequency redistribution functions and compared the results with those obtained using previous expressions of the redistribution matrix. We find that there are small differences on the emergent polarization in the frequency range between the core and the wing only.