Radiative transfer and Faraday effect in turbulent atmospheres

We investigated the system of transfer equations for the Stokes parameters I, Q and U in turbulent atmospheres. The extinction coefficients alpha = alpha(0) + alpha', the number density of free electrons n = n(0) + n' and magnetic field B = B-0 + B' are considered as stochastic values. The dependence of the averaged Stokes parameters I-0, Q(0) and U-0 on fluctuating parts of these coefficients is investigated. It is found that the extinction coefficient for the averaged Stokes parameters is smaller than the average value alpha(0). The existence of magnetic and number density fluctuations gives rise to an additional decrease of the magnitude of linear polarization. These fluctuations also decrease the positional angle of polarization compared with its mean value. We have found that it is possible to write the radiative transfer equations for I-0, Q(0) and U-0 with the renormalized coefficients (effective extinction coefficient, Faraday rotation parameter and additional extinction coefficient for polarized radiation components). The only condition for doing this is that the characteristic correlation length R-1 of turbulence should be small compared to the photon free path. The conservative Milne problem is solved analytically for the case of large Faraday rotation (mean or fluctuating) along the photon free path. The magnetic field fluctuations change drastically the spectrum of linear polarization for large wavelengths. The spectrum acquires the form. proportional to 1/lambda(4) whereas the atmospheres without magnetic fluctuations give 1/lambda(2)-dependence. The lambda-dependence of the positional angle. also changes considerably.