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 10(40) erg s(-1) for the magnetar-like magnetic field (B greater than or similar to 10(14) G) and long spin periods (P greater than or similar to 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 similar or equal to 10(40) 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.