The Mass Distribution of Stellar-Mass Black Holes
  We perform a Bayesian analysis of the mass distribution of stellar-mass black
holes using the observed masses of 15 low-mass X-ray binary systems undergoing
Roche lobe overflow and five high-mass, wind-fed X-ray binary systems. Using
Markov Chain Monte Carlo calculations, we model the mass distribution both
parametrically---as a power law, exponential, gaussian, combination of two
gaussians, or log-normal distribution---and non-parametrically---as histograms
with varying numbers of bins. We provide confidence bounds on the shape of the
mass distribution in the context of each model and compare the models with each
other by calculating their relative Bayesian evidence as supported by the
measurements, taking into account the number of degrees of freedom of each
model. The mass distribution of the low-mass systems is best fit by a
power-law, while the distribution of the combined sample is best fit by the
exponential model. We examine the existence of a "gap" between the most massive
neutron stars and the least massive black holes by considering the value, M_1%,
of the 1% quantile from each black hole mass distribution as the lower bound of
black hole masses. The best model (the power law) fitted to the low-mass
systems has a distribution of lower-bounds with M_1% > 4.3 Msun with 90%
confidence, while the best model (the exponential) fitted to all 20 systems has
M_1% > 4.5 Msun with 90% confidence. We conclude that our sample of black hole
masses provides strong evidence of a gap between the maximum neutron star mass
and the lower bound on black hole masses. Our results on the low-mass sample
are in qualitative agreement with those of Ozel, et al (2010).
