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 $10^{40}\,{\rm erg/s}$ for the
magnetar-like magnetic field ($B\gtrsim 10^{14}\,{\rm G}$) and long spin
periods ($P\gtrsim 1.5\,{\rm s}$). The relative narrowness of an area of
feasible NS parameters which are able to provide higher luminosities leads to
the conclusion that $L\simeq 10^{40}\,\,{\rm erg/s}$ 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.
