Abstract
X-ray binaries with black hole (BH) accretors and massive star donors at short orbital periods of a few days can evolve into close binary BH systems (BBH) that merge within the Hubble time through stable mass transfer evolution. From observational point of view, upon the Roche-lobe overflow, such systems will most likely appear as ultra-luminous X-ray sources (ULXs). To study this connection, we compute the mass transfer phase in systems with BH accretors and massive star donors () at various orbital separations and metallicities using the MESA stellar evolution code. In the case of core-hydrogen and core-helium burning donors (cases A and C of mass transfer) we find the typical duration of super-Eddington mass transfer of up to and , with rates of and , respectively. Given that roughly ULXs are found per unit of star formation rate (), and assuming that of all the observed ULXs form merging BBH, we estimate the rate of BBH mergers from stable mass transfer evolution to be at most .
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