A Flexible Gaussian Process Reconstruction Method and the Mass Function of the Coalescing Binary Black Hole Systems

Abstract

Abstract We develop a new method based on Gaussian processes to reconstruct the mass distribution of binary black holes (BBHs). Instead of prespecifying the formalisms of mass distribution, we introduce a more flexible and nonparametric model with which the distribution can be mainly determined by the observed data. We first test our method with simulated data and find that it can well recover the injected distribution. Then, we apply this method to analyze the data of BBHs’ observations from LIGO-Virgo Gravitational-Wave Transient Catalog 2. By reconstructing the chirp mass distribution, we find that there is a peak or a platform located at 20–30 M ⊙ rather than a single-power-law-like decrease from low mass to high mass. Moreover, one or two peaks in the chirp mass range of  < 20 M ⊙ may be favored by the data. Assuming a mass-independent mass ratio distribution of p(q) ∝ q 1.4, we further obtain a distribution of primary mass and find that there is a feature located in the range of (30, 40) M ⊙, which can be related to Broken Power Law and Power Law + Peak distributions described in Collaboration et al. Besides, the merger rate of BBHs is estimated to be  = 26.29 − 8.96 + 14.21 Gpc − 3 yr − 1 , supposing that there is no redshift evolution.