Mass function of stellar black holes as revealed by the LIGO-Virgo-KAGRA observations

TL;DR

This study analyzes the mass distribution and density evolution of stellar black holes using gravitational wave data from LIGO-Virgo-KAGRA, revealing a broken power-law distribution and a redshift-dependent density decline.

Contribution

It provides the first statistical analysis of pre- and post-merger black hole samples, deriving their mass functions and redshift evolution from gravitational wave observations.

Findings

Black hole mass distribution follows a broken power-law.

High-mass power-law index is similar for pre- and post-merger samples.

Black hole number density decreases with redshift as z^{-2.06} to z^{-2.12}.

Abstract

Ninety gravitational wave events have been detected by the LIGO-Virgo-KAGRA network and are released in the Gravitational-Wave Transient Catalog. Among these events, 83 cases are definitely binary black hole mergers since the masses of all the objects involved significantly exceed the upper limit of neutron stars. The black holes in these merger events naturally form two interesting samples, a pre-merger sample that includes all the black holes before the mergers and a post-merger sample that consists of the black holes generated during the merging processes. The former represents black holes that once existed in the Universe, while the latter represents newly born black holes. Here we present a statistical analysis on these two samples. The non-parametric $\tau$ statistic method is adopted to correct for the observational selection effect. The Lynden-Bell's $C^{-}$ method is further applied to derive the mass distribution and density function of black holes. It is found that the mass distribution can be expressed as a broken power-law function. More interestingly, the power-law index in the high mass region is comparable for the two samples. The number density of black holes is found to depend on redshift as $\rho(z) \propto z^{-2.06}$ -- $z^{-2.12}$ based on the two samples. Implications of these findings on the origin of black holes are discussed.