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 -2overflow 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. This difference indicates that the low-mass subsample is not consistent with being drawn from the distribution of the combined population. 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. Our analysis generates posterior distributions for M 1% ; the best model (the power law) fitted to the low-mass systems has a distribution of lower-bounds with M 1% > 4.3 M with 90% confidence, while the best model (the exponential) fitted to all 20 systems has M 1% > 4.5 M 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), although our broad model-selection analysis more reliably reveals the best-fit quantitative description of the underlying mass distribution. The results on the combined sample of low-and high-mass systems are in qualitative agreement with Fryer & Kalogera (2001) although the presence of a mass gap remains theoretically unexplained.

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We report photometric and spectroscopic observations of the black hole binary GRO J1655[40 in complete quiescence. In contrast to the 1995 photometry, the light curves from 1996 are almost completely dominated by ellipsoidal modulations from the secondary star. Model Ðts to the light curves, which take into account the temperature proÐle of the accretion disk and eclipse e †ects, yield an inclination of and a mass ratio of The precision of our determii \ 69¡ .50^0¡ .08Q \ M 1 /M 2 \ 2.99^0.08. nations of i and Q allow us to determine the black hole mass to an accuracy of B4% (M 1 \ 7.02^0.22The secondary starÏs mass is The position of the secondary on the M _ ).M 2 \ 2.34^0.12 M _ . Hertzsprung-Russell diagram is consistent with that of a B2.3 star that has evolved o † the main M _ sequence and is halfway to the start of the giant branch. Using the new spectra, we present an improved value of the spectroscopic period radial velocity semiamplitude (P \ 2d . 62157^0d . 00015), (K \ 228.2^2.2 km s~1), and mass function [ f (M) \ 3.24^0.09Based on the new spectra of the M _ ]. source and spectra of several MK spectral type standards, we classify the secondary star as F3 IVÈF6 IV. Evolutionary models suggest an average mass transfer rate for such a system of M 0 2 \ 3.4 ] 10~9 g s~1, which is much larger than the average mass transfer rates implied in the M _ yr~1 \ 2.16 ] 1017 other six transient black hole systems but is still barely below the critical mass transfer rate required for stability.