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

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.