The Milne problem with chaotic magnetic field

Abstract

ABSTRACT We consider the semi-infinite plane-parallel electron atmosphere with chaotic magnetic field B′ ≤ 1010 G, when the parameter $x^{\prime 2}=(\omega _{B^{\prime }}/\omega)^2 \simeq 0.87 \times 10^{-16}\lambda ^2(\mu \mathrm{ m}) B^{\prime 2}(G)$ can be both ≪1 and ≫1. Regular magnetic field $\boldsymbol{B}_0$ is absent. All magnetic fluctuations are assumed as Gaussian type and isotropic. The isotropic magnetic fluctuations $\boldsymbol{B}^{\prime }$ give rise to the same extinction for all Stokes parameters and the additional extinction factor h for parameters Q and U, which arises due to chaotic Faraday rotations. We consider the Milne problem, which is described by the system of transfer equations for intensity I and parameter Q. It is shown that the phase matrix depends on parameter G(B′), which is equal to 3 for x′2 ≪ 1 and to 27 for x′2 ≫ 1. The calculations demonstrate that the polarization of outgoing radiation strongly depends on parameter h and degree of absorption ε.