**Authors**: Will M. Farr, Niharika Sravan, Andrew Cantrell, Laura Kreidberg, Charles D. Bailyn, Ilya Mandel, Vicky Kalogera

**Date**: 5 Nov 2010

**Abstract**: 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 MCMC 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 by calculating their Bayesian evidence. 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 1% quantile from each black hole mass distribution, M_1%. The best model (the power law) fitted to the low-mass systems gives a distribution 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 minimum black hole mass. 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 underlying mass distribution. The presence of a mass gap remains theoretically unexplained.

1011.1459
(/preprints)

2010-11-08, 11:06
**[edit]**

© M. Vallisneri 2012 — last modified on 2010/01/29

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