Radiative transfer in atmospheres with a large chaotic magnetic field

Abstract

ABSTRACT We derive the radiative transfer equations for all Stokes parameters of continuum radiation in atmospheres with any value of homogeneous magnetic field $\boldsymbol{B}$. The explicit formulas for cross-sections and the phase shifts are given with allowance for absorption effects. We consider the scattering of non-polarized radiation in an optically thin envelope with a dipole magnetic field. The presented theory is valid for magnetic fields B ≤ 1010G. In general, a magnetic field consists of the mean value $\boldsymbol{B_0}$ and the chaotic part $\boldsymbol{ B^{\prime }}$. The latter is assumed to have an isotropic distribution over directions and a Gaussian-type distribution over the value B′. It is shown that for B0(G)λ(μm) ≪ 108, the fluctuations play a dominating role. This case is considered in detail. First of all, we derive the system of transfer equations for observed averaged Stokes parameters. The averaging procedure consists of two stages: the averaging of fluctuations $\boldsymbol{B }^{\prime }$ over values and the averaging of these over all directions. The averaging over Gaussian fluctuations B′ is carried out using the exponential Fourier transform of polarizability tensor components and the known formula for the averaged exponential. This technique is available for arbitrary values of a magnetic field, both large and small. The system of transfer equations for four averaged Stokes parameters, I, Q, U and V, splits up into two independent systems – for I, Q and V, U parameters. The form of equations for the case of large magnetic fluctuations differs strongly from the Thomson scattering. These equations describe the large decrease of linear and circular polarization of observed radiation.