2020ApJ...902..125A

Recent observational and theoretical results have suggested that some of ultraluminous X-ray (ULX) sources may contain neutron star (NS) accretors. However, the formation channel and properties of donor stars of NS ULXs remain uncertain. By adopting the nonconservative and rotation-dependent mass transfer model in the primordial binary evolution, we investigate the way to form pulsar ULXs like observed pulsar ULXs in a systematic way. Our simulation results indicate that pulsar ULXs with Be stars and intermediate or/and high-mass donors match observed apparent luminosities, orbital periods, and observationally indicated donor masses of known pulsar ULXs. ULXs with Be and intermediate donors are main contributors. The route of accretion-induced collapse of WDs has a 4.5% contribution to the NS ULXs, 4.0% of NSs in ULXs are formed through electron-capture supernovae (SNe), and 91.5% of NSs in ULXs are born with core-collapse SNe. We also studied the evolution of pulsar ULXs to double compact star systems. We do not find NS-black hole systems (merging in a Hubble time) that evolved from pulsar ULXs. Pulsar-white dwarf (WD) cases that evolve through pulsar ULXs have significant contributions to the whole NS-WD gravitational wave sources. Contributions of pulsar-WD and pulsar-NS cases that experienced pulsar ULXs are ∼40% and 11% among all LISA NS-WD and NS-NS sources, respectively. Monte Carlo simulation noise with different models give a nonnegligible uncertainty.