Theoretical Black Hole Mass Distributions

We derive the theoretical distribution function of black hole masses by studying the formation processes of black holes. We use the results of recent 2D simulations of core-collapse to obtain the relation between remnant and progenitor masses and fold it with an initial mass function for the progenitors. We examine how the calculated black-hole mass distributions are modified by (i) strong wind mass loss at different evolutionary stages of the progenitors, and (ii) the presence of close binary companions to the black-hole progenitors. Thus, we are able to derive the binary black hole mass distribution. The compact remnant distribution is dominated by neutron stars in the mass range 1.2-1.6Msun and falls off exponentially at higher remnant masses. Our results are most sensitive to mass loss from winds which is even more important in close binaries. Wind mass-loss causes the black hole distribution to become flatter and limits the maximum possible black-hole mass (<10-15Msun). We also study the effects of the uncertainties in the explosion and unbinding energies for different progenitors. The distributions are continuous and extend over a broad range. We find no evidence for a gap at low values (3-5Msun) or for a peak at higher values (~7Msun) of black hole masses, but we argue that our black hole mass distribution for binaries is consistent with the current sample of measured black-hole masses in X-ray transients. We discuss possible biases against the detection or formation of X-ray transients with low-mass black holes. We also comment on the possibility of black-hole kicks and their effect on binaries.