The Brightest Point X-Ray Sources in Elliptical Galaxies and the Mass Spectrum of Accreting Black Holes

We propose that the shape of the upper-end X-ray luminosity function observed in elliptical galaxies for point sources is a footprint of the black-hole (BH) mass spectrum among old X-ray transients formed in the galaxies. We show that this underlying BH mass spectrum is modified by a weighting factor that is related to the transient duty cycle and it generally depends on the BH mass and XRB donor type (main-sequence, red-giant, or white-dwarf donors). A duty cycle that depends on the binary mass-transfer rate relative to the critical rate for transient behavior is most probably favored. We also find that the derived BH mass spectrum slope depends on the strength of angular momentum loss due to magnetic braking for main-sequence donors. More specifically, we find that, for ``standard'' magnetic braking, BH XRBs with red-giant donors dominate the upper-end XLF; for weaker magnetic braking prescriptions main-sequence donors are found to be dominant. In both cases the BH mass spectrum has a differential slope of ~2.5 and an upper BH mass cut-off at ~20 Msun is needed to understand the very brightest of the BH XRBs in elliptical galaxies. We expect that our result will help to constrain binary population synthesis models and the adopted relations between black holes and the masses of their progenitors.