2022ApJ...938...69P

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 the mean mass μ with a Pearson correlation coefficient of r = 0.93 ± 0.06 of secondary to primary masses with a mean mass ratio of $\bar{q}\simeq 0.67$, q = M₂/M₁, 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 μ ≳ 31.4 M_⊙ in the mean binary mass $\mu =\left({M}_{1}+{M}_{2}\right)/2$. Its power-law index of α_B,true = 4.77 ± 0.73 inferred from the tail of the observed mass function is found to approach the upper bound 2α_S = 4.7 of the uncorrelated binary IMF, defined by the Salpeter index α_S = 2.35 of the IMF 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 ${\alpha }_{B}^{{\prime} }\gt {\alpha }_{B}$ in a flat ΛCDM background cosmology. The bound ${\alpha }_{B,\mathrm{true}}^{{\prime} }\lesssim 2{\alpha }_{S}$ hereby precludes early formation at arbitrarily high redshifts ${z}^{{\prime} }\gg 1$, which may be made more precise and robust with extended BBH surveys from upcoming LIGO O4-5 observations.