The Mass Distribution of Stellar-Mass Black Holes (1011.1459v2)

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 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).

• The paper employs a comprehensive Bayesian analysis using both parametric and non-parametric models to characterize the stellar-mass black hole distribution.
• It confirms a mass gap with minimum black hole masses exceeding 4.3 M☉, challenging existing models of stellar evolution.
• The findings influence gravitational wave research by refining predictions for merger rates and guiding future observational strategies.

Analyzing the Mass Distribution of Stellar-Mass Black Holes

In the paper "The Mass Distribution of Stellar-Mass Black Holes," the authors undertake an extensive Bayesian analysis to explore the mass distribution of stellar-mass black holes. This exploration is essential for understanding the remnants of massive stars and has implications for gravitational wave studies, where the mass distribution of black holes affects the predicted rates of coalescing events detectable by observatories like LIGO.

Methodology

The paper uses observed masses from a sample of 15 low-mass X-ray binary systems and 5 high-mass, wind-fed systems. To model the black hole mass distribution, the researchers employed a range of approaches:

• Parametric Models: These include power law, exponential, Gaussian, two-Gaussian, and log-normal distributions, each offering a different perspective on how these masses might be distributed based on astrophysical reasoning.
• Non-Parametric Models: Histograms with different numbers of bins offered a more flexible way to represent the mass distribution without assuming a specific shape in advance.

The Bayesian framework, particularly utilizing Markov Chain Monte Carlo (MCMC) methods, allowed the authors to estimate posterior distributions for model parameters and evaluate the relative Bayesian evidence for each model.

Findings

For the low-mass systems, the power-law model emerged as the most likely representation of the underlying mass distribution. Conversely, when considering the combined sample of low- and high-mass systems, the exponential model was favored, hinting at distinct distribution characteristics across different populations.

The paper robustly confirms the presence of a "mass gap" — a dearth of detected black holes with masses between the maximum neutron star mass (around 3 M☉) and the least massive black holes in the paper's sample. The minimum black hole mass with high confidence exceeds 4.3 M☉ for the low-mass sample and 4.5 M☉ for the combined sample, supporting previous findings of an apparent mass gap in black hole observations.

Implications

The findings of this paper have several implications:

1. Astrophysical Models: The presence of a mass gap challenges astrophysical models of stellar evolution and supernova explosions, which traditionally predict a more continuous mass distribution.
2. Gravitational Waves: Understanding the black hole mass distribution is critical for predicting and interpreting gravitational wave signals. The results might influence the expected rates and characteristics of neutron star-black hole mergers versus black hole-black hole mergers.
3. Future Observational Strategies: The confirmation of mass gap phenomena may guide future observational strategies in both electromagnetic and gravitational wave astronomy, focusing efforts to gather more data around the mass boundary regions.

Future Research Directions

The theoretical and observational community will benefit from further exploration into the processes that produce the observed mass gap. Scenarios involving supernova energetics, fallback mechanisms, and binary interaction dynamics warrant higher resolution modeling. Additionally, large-scale population synthesis studies could offer insights into the prevalence and characteristics of low-mass black hole systems that might have been missed due to selection biases.

In conclusion, the paper significantly contributes to our understanding of stellar-mass black holes. The rigorous statistical framework and extensive model comparison approach provide a strong foundation for future theoretical and observational inquiries into black hole formation and evolution.