The steep redshift evolution of the hierarchical binary black hole merger rate may cause the $z$-${\chi }_{\mathrm{eff}}$ correlation

Abstract

There is growing evidence from gravitational-wave observations that some merging black holes are created from previous mergers. Using the prediction that these hierarchically merged black holes have dimensionless spin magnitudes of $\chi \approx 0.69$, we identify a subpopulation in the gravitational-wave data consistent with a hierarchical-merger origin in dense star clusters. This subpopulation's primary mass distribution peaks at $17.0_{-4.4}^{+18.3},{\mathrm{M}}_{\odot }$, which is approximately twice as large as its secondary mass distribution's mode ($10.5_{-4.7}^{+29.7},{\mathrm{M}}_{\odot }$), and its spin tilt distribution is consistent with isotropy. Our inferred secondary mass distributions imply that isolated binary evolution may still be needed to explain the entirety of the $9{\mathrm{M}}_{\odot }$ peak. Surprisingly, we find that the rate of hierarchical mergers may evolve more steeply with redshift than the rest of the population ($98.0\%$ credibility): the fraction of all binary black holes that are hierarchically formed at $z=0.1$ is $0.03_{-0.02}^{+0.05}$, compared to $0.09_{-0.07}^{+0.11}$ at $z=1$. This provides an explanation for the previously discovered broadening of the effective spin distribution with redshift. Our results have implications for star cluster formation histories, as they suggest the potential existence of a high-redshift population of massive, compact clusters.

9 pages, 4 figures (with appendices: 18 pages, 12 figures). Also see Vijaykumar et al., posted simultaneously. v4 is the journal version

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