Ultraluminous X-ray sources with He star companions

Ultraluminous X-ray sources (ULXs) are non-nuclear point-like objects observed with extremely high X-ray luminosity that exceeds the Eddington limit of a $10M_{\odot }$ black hole. A fraction of ULXs has been confirmed to contain neutron star (NS) accretors due to the discovery of their X-ray pulsations. The donors detected in NS ULXs are usually luminous massive stars because of the observational biases. Recently, the He donor star in NGC 247 ULX-1 has been identified, which is the first evidence of a He donor star in ULXs. In this paper, we employed the stellar evolution code MESA to investigate the formation of ULXs through the NS+He star channel, in which a He star transfers its He-rich material onto the surface of a NS via Roche-lobe overflow. We evolved a large number of NS+He star systems and provided the parameter space for the production of ULXs. We found that the initial NS+He star systems should have $\sim 0.7-2.6{\mathrm{M}}_{\odot }$ He star and $\sim 0.1-2500\mathrm{d}$ orbital period for producing ULXs, eventually evolving into intermediate-mass binary pulsars. According to binary population synthesis calculations, we estimated that the Galactic rate of NS ULXs with He donor stars is in the range of $\sim 1.6-4.0\times {10}^{-4}{\mathrm{y}\mathrm{r}}^{-1}$, and that there exist $\sim 7-20$ detectable NS ULXs with He donor stars in the Galaxy.