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

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 $z^{\prime }\gg 1$, that may be made more precise and robust with extended BBH surveys from upcoming LIGO O4-5 observations.

7 pages, 6 figures

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Cited by in corpus (1)

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