On the mass-function of GWTC-2 binary black hole systems and their progenitors

TL;DR

This paper analyzes the mass distribution of binary black holes detected by LIGO, revealing a broken power-law shape consistent with stellar initial mass functions and providing insights into their formation and evolution across cosmic time.

Contribution

It introduces a detailed statistical characterization of LIGO BBH mass functions, linking them to stellar initial mass functions and binary evolution processes.

Findings

Mass distribution follows a broken power-law with a tail at high masses.

Mass ratio distribution indicates effective mass transfer prior to BBH formation.

Constraints on progenitor redshift suggest limits on early universe BBH formation.

Abstract

The distribution of LIGO black hole binaries (BBH) shows an intermediate-mass range consistent with the Salpeter Initial Mass Function (IMF) in black hole formation by core-collapse supernovae, subject to preserving binary association. They are effectively parameterized by mean mass $\mu$ with Pearson correlation coefficient $r = 0.93\,\pm\,0.06$ of secondary to primary masses with mean mass-ratio $\bar{q}\simeq 0.67$, $q=M_2/M_1$, consistent with the paucity of intermediate-mass X-ray binaries. The mass-function of LIGO BBHs is well-approximated by a broken power-law with a tail $\mu\gtrsim 31.4M_\odot$ {in the mean binary mass $\mu=\left(M_1+M_2\right)/2$}. Its power-law index $\alpha_{B,true}=4.77\pm 0.73$ inferred from the tail of the observed mass-function is found to approach the upper bound $2\alpha_S=4.7$ of the uncorrelated binary initial mass-function, defined by the Salpeter index $\alpha_S=2.35$ of the Initial Mass Function of stars. The observed low scatter in BBH mass ratio $q$ evidences equalizing mass-transfer in binary evolution prior to BBH formation. At the progenitor redshift $z^\prime$, furthermore, the power-law index satisfies $\alpha_B^\prime>\alpha_B$ in a flat $\Lambda$CDM background cosmology. The bound $\alpha_{B,true}^\prime \lesssim 2\alpha_S$ hereby precludes early formation at arbitrarily high redshift $z^\prime \gg1$, that may be made more precise and robust with extended BBH surveys from upcoming LIGO O4-5 observations.