Revealing the χ eff–q Correlation among Coalescing Binary Black Holes and Tentative Evidence for AGN-driven Hierarchical Mergers

The origin of the correlation between the effective spins ( χ eff ) and mass ratios ( q ) of LIGO–Virgo–KAGRA’s binary black holes (BBHs) is still an open question. Motivated by the recent identification of two subpopulations of the BBHs, in this work we investigate the potential χ eff – q correlation for each subpopulation. Surprisingly, the χ eff – q correlation either significantly weakens or disappears for the low-mass subpopulation if we introduce a second χ eff distribution for the high-mass subpopulation, which likely originates from hierarchical mergers. This suggests that the χ eff – q correlation in the overall population can be explained by the superposition of two distinct subpopulations. We find Bayesian evidence strongly favoring two separate χ eff distributions over a single mass ratio–dependent distribution, with Bayes factors ln B > 4.2 . The first subpopulation has a narrow χ eff distribution peaking at ∼0.05, whose primary mass function shows a rapid decline beyond ∼40 M ⊙ , in agreement with first-generation BBHs. The second χ eff distribution is broad and peaks at μ χ ,2 ∼ 0.4, aligning with predictions for hierarchical mergers in active galactic nucleus (AGN) disks. However, we cannot exclude negative χ eff values in the second subpopulation, suggesting that hierarchical mergers might occur both in AGN disks and stellar clusters. Furthermore, the inferred second χ eff distribution might alternatively arise from other formation channels, such as stable mass transfer or chemically homogeneous evolution, if not interpreted as hierarchical mergers.