The maximum mass ratio of hierarchical binary black hole mergers may cause the $q$-$\chi_{\rm eff}$ correlation

Abstract

Regardless of their initial spins, the merger of two roughly equal mass black holes (BHs) produces a remnant BH of dimensionless spin $0.69$. Such remnants can merge with other BHs in dense stellar environments and produce hierarchical mergers. Analyzing the latest catalog binary black hole (BBH) mergers from the LIGO-Virgo-KAGRA detectors, we identify a subpopulation with primary spins consistent with such hierarchical mergers. Consistent with astrophysical expectations for mergers of second-generation BHs with first-generation BHs, we find that this subpopulation has mass ratios below $0.59^{+0.18}_{-0.23}$. We also infer that $19$-$88\%$ of the BBH population below this mass ratio is consistent with belonging to the hierarchically merged population. Our results offer a natural explanation for the narrowing of the effective inspiral spin distribution with mass ratio observed in other studies.