Theoretical black hole mass distributions

We derive the theoretical distribution function of black hole masses by stu dying 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 fun ction for the progenitors. Thus, we are able to derive the binary black hol e mass distribution. We examine how the calculated black hole mass distribu tions are modified by (1) strong-wind mass loss at different evolutionary s tages 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 wind s are even more important in close binaries. Wind mass loss leads to flatte r black hole mass distributions and limits the maximum possible black hole mass (less than or similar to 10-15 M-.). We also study the effects of the uncertainties in the explosion and unbinding energies for different progeni tors. The distributions are continuous and extend over a broad range. We fi nd no evidence for a gap at low values (3-5 M-.) or for a peak at higher va lues (similar to7 M-.) of black hole masses, but we argue that our black ho le 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 eff ect on binaries.