We study properties of luminous X-ray pulsars using a simplified model of the accretion column. The maximal possible luminosity is calculated as a function of the neutron star (NS) magnetic field and spin period. It is shown that the luminosity can reach values of the order of $10^{40},{rm erg/s}$ for the magnetar-like magnetic field ($Bgtrsim 10^{14},{rm G}$) and long spin periods ($Pgtrsim 1.5,{rm s}$). The relative narrowness of an area of feasible NS parameters which are able to provide higher luminosities leads to the conclusion that $Lsimeq 10^{40},,{rm erg/s}$ is a good estimate for the limiting accretion luminosity of a NS. Because this luminosity coincides with the cut-off observed in the high mass X-ray binaries luminosity function which otherwise does not show any features at lower luminosities, we can conclude that a substantial part of ultra-luminous X-ray sources are accreting neutron stars in binary systems.
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