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

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 $χ\approx 0.69$, 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.

💡 Research Summary

This paper investigates the presence of a hierarchical sub‑population of binary black hole (BBH) mergers—specifically systems that contain a second‑generation (2G) black hole formed from a previous merger and a first‑generation (1G) companion (2G+1G). The authors exploit a robust theoretical prediction that 2G black holes acquire a dimensionless spin magnitude χ≈0.69 regardless of the number of prior mergers. By imposing a strong prior on the primary spin magnitude, they construct a phenomenological mixture model that separates the hierarchical sub‑population (denoted S) from the main population (denoted M).

The mixture model treats the spin magnitudes of the two components as Gaussian distributions truncated to the physical range