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One of the models explaining the high luminosity of pulsing ultra-luminousX-ray sources (pULXs) was suggested by Mushtukov et al. (2015). They showedthat the accretion columns on the surfaces of highly magnetized neutron starscan be very luminous due to opacity reduction in the high magnetic field.However, a strong magnetic field leads also to amplification of theelectron-positron pairs creation. Therefore, increasing of the electron andpositron number densities compensates the cross-section reduction, and theelectron scattering opacity does not decrease with the magnetic fieldmagnification. As a result, the maximum possible luminosity of the accretioncolumn does not increase with the magnetic field. It ranges between 10$^{40} -10^{41}$ erg s$^{-1}$ depending only slightly on the magnetic field strength.

Importance of electron-positron pairs on the maximum possible luminosity of the accretion columns in ULXs