SIMBAD references

We propose that the shape of the upper-end X-ray luminosity function (XLF) observed in elliptical galaxies for point sources carries valuable information about the black hole (BH) mass spectrum among old X-ray transients formed in the galaxies. Here we present the line of arguments and analysis that support this connection and the methodology for deriving the BH mass spectrum slope from the observed XLF slope. 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 host galaxy age, the BH mass, and the X-ray binary (XRB) donor type (main-sequence, red giant, or white dwarf donors). We find that the observed XLF is dominated by transient BH systems in outburst (a prediction possibly testable by future observations) but that the assumption of a constant duty cycle for all systems leads to results inconsistent with current observations. We also find that the derived BH mass slope depends on the strength of the 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 but that for weaker magnetic braking prescriptions, main-sequence donors are found to be dominant. The methodology presented here can be used in the future as our understanding of the transient duty and its dependence on binary and mass transfer properties improves. Under certain assumptions for this dependence, we derive a differential BH mass spectrum slope of ≃2.5; an upper BH mass cutoff at ≃20 M_☉is needed to understand the very brightest of the BH XRBs in elliptical galaxies. We also show that our quantitative results are robust against expected variations by factors of a few of the outburst peak X-ray luminosities. We expect that our analysis will eventually help to constrain binary population synthesis models and the adopted relations between black holes and the masses of their progenitors.