Statistics of the frequency redistribution for gyroresonance radiation in the atmospheres of compact stars

We analyze in detail the statistics of the frequency redistribution of photons during the transfer of gyroresonance radiation under conditions typical of compact stars. The probabilities of photon escape from a scattering atmosphere of arbitrary optical thickness in a single scattering have been found. The effects of gyroresonance photon diffusion in space and in frequency have been simulated. We show that when photons escape from a semi-infinite atmosphere with weak absorption, the frequency redistribution effects lead to a considerable increase in the probability of photon escape from large optical depths and, consequently, modify significantly the dynamics of gyroresonance photon transfer for neutron stars and white dwarfs.