Populations of Ultraluminous X-ray Sources in Galaxies: Origin and Evolution

model of the population of ultraluminous X-ray sources (ULXs) in binary systems with black hole (BH) accretors is constructed by hybrid population synthesis and is compared with the model of the population of ULXs with magnetized neutron stars (NSs) that can be observed as pulsating ULXs (Kuranov et al. 2020). A model of the formation of BHs whereby their mass is determined by the mass of the CO core immediately before its collapse ( M_CO ) and ‘‘delayed’’ and ‘‘rapid’’ collapse models (Fryer et al. 2012) are considered. The possible transiency of ULXs due to accretion disk instability is taken into account. The parameters and evolution of ULXs in galaxies with a constant star formation rate (SFR) and in those with an old stellar population after an instantaneous star formation burst are computed. The maximum number of ULXs with BHs ( ∼10 ) is reached in galaxies with a stationary SFR=10M_⊙ yr ^-1 ∼1 Gyr after the beginning of star formation. ULXs observed after the end of star formation are close binary systems in which BHs and/or NSs formed before the end of star formation, while long-lived donors with a mass ∼M_⊙ continue to overflow their Roche lobes after its end or have filled their Roche lobes even later. Several Gyr after the end of star formation the number of ULXs in galaxies with a mass M_G=10^10M_⊙ is no more than 0.1, most of them are ULXs with NSs. Persistent sources with a Roche-lobe-overflowing optical star dominate in ULXs with NSs, irrespective of the adopted star formation model. The transient sources are an order of magnitude fewer. The ULXs accreting from the stellar wind of the optical component are an order of magnitude fewer than the sources with accretion via Roche lobe overflow.