Continuum of an accretion column with a collisionless shock wave: analytical consideration

The problem of radiation scattering in a limited medium with a given Comptonization parameter has been studied for many years. It turns out that some well-known theoretical results can be applied in solving modern problems. Here, analytical solutions are considered for a continuum formed in a two-dimensional region under a collisionless shock in accretion columns. The Comptonization parameter is determined in an efficient way and takes into account reducing the average number of photon scatterings in the magnetic field. The behavior of the hardness ratio of the X-ray continuum is studied as a function of the usual parameters of the problem for the case of disk accretion. As an example, the known observations of Cep X-4 are considered.