Spectrum formation in X-ray pulsars at very low mass accretion rate: Monte Carlo approach

Recently, it has been discovered that the transition of X-ray pulsars to the low luminosity state ( $L\lesssim 10^{35}\, {\rm erg\ \rm s^{-1}}$ ) is accompanied by a dramatic spectral change. That is, the typical power-law-like spectrum with high-energy cut-off transforms into a two-component structure with a possible cyclotron absorption feature on top of it. It was proposed that these spectral characteristics can be explained qualitatively by the emission of cyclotron photons in the atmosphere of the neutron star caused by collisional excitation of electrons to upper Landau levels and further Comptonization of the photons by electron gas. The electron gas are expected to be overheated in a thin top layer of the atmosphere. In this paper, we perform Monte Carlo simulations of the radiative transfer in the atmosphere of an accreting neutron star while accounting for a resonant scattering of polarized X-ray photons by thermally distributed electrons. The spectral shape is shown to be strongly polarization-dependent in soft X-rays ( $\lesssim 10\, {\rm keV}$ ) and near the cyclotron scattering feature. The results of our numerical simulations are tested against the observational data of the X-ray pulsar A 0535+262 in the low-luminosity state. We show that the spectral shape of the pulsar can be reproduced by the proposed theoretical model. We discuss applications of the discovery to the observational studies of accreting neutron stars.