  It has been recently discovered that the transition of X-ray pulsars to the
low luminosity state ($L\lesssim10^{35}\,{\rm erg\,s^{-1}}$) is accompanied by
a dramatic spectral change. Namely, the typical power-law-like spectrum with
high energy cutoff 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 latter is 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 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. The applications of the discovery
to the observational studies of accreting neutron stars are discussed.
