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It has been recently discovered that the transition of X-ray pulsars to thelow luminosity state ($L\lesssim10^{35}\,{\rm erg\,s^{-1}}$) is accompanied bya dramatic spectral change. Namely, the typical power-law-like spectrum withhigh energy cutoff transforms into a two-component structure with a possiblecyclotron absorption feature on top of it. It was proposed that these spectralcharacteristics can be explained qualitatively by the emission of cyclotronphotons in the atmosphere of the neutron star caused by collisional excitationof electrons to upper Landau levels and further comptonization of the photonsby electron gas. The latter is expected to be overheated in a thin top layer ofthe atmosphere. In this paper, we perform Monte Carlo simulations of theradiative transfer in the atmosphere of an accreting neutron star whileaccounting for a resonant scattering of polarized X-ray photons by thermallydistributed electrons. The spectral shape is shown to be stronglypolarization-dependent in soft X-rays ($\lesssim 10\,{\rm keV}$) and near thecyclotron scattering feature. The results of our numerical simulations aretested against the observational data of X-ray pulsar A 0535+262 in the lowluminosity state. We show that the spectral shape of the pulsar can bereproduced by the proposed theoretical model. The applications of the discoveryto the observational studies of accreting neutron stars are discussed.

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