Comptonization in Ultra-Strong Magnetic Field: A Numerical Solution of the Radiative Transfer Problem

Abstract

We consider the radiative transfer problem in a plane‐parallel slab of thermal electrons in presence of an ultra‐strong magnetic field (B≳4.4×1013 G). Under such conditions, the magnetic field behaves as a birefringent medium for the propagating photons, and the electromagnetic radiation is splitted into two polarization modes, ordinary and extraordinary, having different cross‐sections. When the optical depth of the slab is large, the ordinary‐mode photons are significantly more Comptonized and the photon field is dominated by the isotropic component. For sub‐relativistic electron temperatures, it is possible to treat the full kinetic Boltzmann equation for such photons using the Fokker‐Planck approximation. The full solution is then obtained by the method of variable separation. We report the numerical solution obtained for eigenvalues and eigenfunctions of the space operator, and consider the emerging Comptonization spectrum of the ordinary‐mode photons for energies significantly less than the cyclotron energy, which is of the order of MeV for the intensity of the magnetic field here considered.