On the maximum accretion luminosity of magnetized neutron stars: connecting X-ray pulsars and ultraluminous X-ray sources

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 1040 erg s−1 for the magnetar-like magnetic field (B ≳ 1014 G) and long spin periods (P ≳ 1.5 s). The relative narrowness of an area of feasible NS parameters which are able to provide higher luminosities leads to the conclusion that L ≃ 1040 erg s−1 is a good estimate for the limiting accretion luminosity of an 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 ultraluminous X-ray sources are accreting neutron stars in binary systems.