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Register a new userBlack Hole Mass Function of Coalescing Binary Black Hole Systems: Is There a Pulsational Pair Instability Mass Cutoff?
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Yuan-Zhu Wang
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We analyze the LIGO/Virgo GWTC-2 catalog to study the primary mass distribution of the merging black holes. We perform hierarchical Bayesian analysis, and examine whether the mass distribution has a sharp cutoff for primary black hole masses below $65 M_odot$, as predicted in pulsational pair instability supernova model. We construct two empirical mass functions. One is a piece-wise function with two power-law segments jointed by a sudden drop. The other consists of a main truncated power-law component, a Gaussian component, and a third very massive component. Both models can reasonably fit the data and a sharp drop of the mass distribution is found at $sim 50M_odot$, suggesting that the majority of the observed black holes can be explained by the stellar evolution scenarios in which the pulsational pair-instability process takes place. On the other hand, the very massive sub-population, which accounts for at most several percents of the total, may be formed through hierarchical mergers or other processes.
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With the black hole mass function (BHMF; assuming an exponential cutoff at a mass of $sim 40,M_odot$) of coalescing binary black hole systems constructed with the events detected in the O1 run of the advanced LIGO/Virgo network, Liang et al.(2017) predicted that the birth of the lightest intermediate mass black holes (LIMBHs; with a final mass of $gtrsim 100,M_odot$) is very likely to be caught by the advanced LIGO/Virgo detectors in their O3 run. The O1 and O2 observation run data, however, strongly favor a cutoff of the BHMF much sharper than the exponential one. In this work we show that a power-law function followed by a sudden drop at $sim 40,M_odot$ by a factor of $sim $a few tens and then a new power-law component extending to $geq 100M_odot$ are consistent with the O1 and O2 observation run data. With this new BHMF, quite a few LIMBH events can be detected in the O3 observation run of advanced LIGO/Virgo. The first LIMBH born in GW190521, an event detected in the early stage of the O3 run of advanced LIGO/Virgo network, provides additional motivation for our hypothesis.
We develop a new method based on Gaussian process 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 locating at $20-30,M_{odot}$ 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 $mathcal{M}<20,M_{odot}$ may be favored by the data. Assuming a mass-independent mass ratio distribution of $p(q)propto q^{1.4}$, we further obtain a distribution of primary mass, and find that there is a feature locating in the range of $(30, 40),M_{odot}$, which can be related to textsc{Broken Power Law} and textsc{Power Law + Peak} distributions described in The LIGO Scientific Collaboration et al. (2020). Besides, the merger rate of BBHs is estimated to $mathcal{R} = 26.29^{+14.21}_{-8.96}~{rm Gpc^{-3}~yr^{-1}}$ supposing there is no redshift evolution.
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