We derive the theoretical distribution function of black hole masses by studying the formation processes of black holes. We use the results of recent two-dimensional simulations of stellar core collapse to obtain the relation between remnant and progenitor masses and fold it with an initial mass function for the progenitors. Thus, we are able to derive the binary black hole mass distribution. We examine how the calculated black hole mass distributions are modified by (1) strong-wind mass loss at different evolutionary stages of the progenitors and (2) the presence of close binary companions to the black hole progenitors. The compact-remnant distribution is dominated by neutron stars in the mass range 1.2-1.6 M☉ and falls off exponentially at higher remnant masses. Our results are most sensitive to mass loss from stellar winds (particularly from Wolf-Rayet stars), and the effects of winds are even more important in close binaries. Wind mass loss leads to flatter black hole mass distributions and limits the maximum possible black hole mass (≲10-15 M☉). 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 (3-5 M☉) or for a peak at higher values (∼7 M☉) 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.
Stars: Binaries: General - Black Hole Physics - Stars: Evolution - Stars: Mass Loss - Stars: Neutron - Stars: Supernovae: General