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

TL;DR

This paper identifies a subpopulation of hierarchical binary black hole mergers in gravitational-wave data, showing their rate increases with redshift and suggesting implications for star cluster formation histories.

Contribution

It provides evidence of a redshift-dependent hierarchical merger rate and characterizes the properties of this subpopulation, highlighting their impact on understanding black hole origins.

Findings

Hierarchical mergers have a spin magnitude of approximately 0.69.

The primary mass distribution peaks at about 17 solar masses.

The merger rate increases steeply with redshift, especially for hierarchical mergers.

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 $17.0^{+18.3}_{-4.4},\mathrm{M}_{\odot}$, which is approximately twice as large as its secondary mass distribution's mode ($10.5^{+29.7}_{-4.7},\mathrm{M}_{\odot}$), 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 $0.03^{+0.05}_{-0.02}$, compared to $0.09^{+0.11}_{-0.07}$ 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.