Revealing the $\ddot{I}{‡}_{\mathrm{eff}}$-$q$ Correlation among Coalescing Binary Black Holes and Tentative Evidence for AGN-driven Hierarchical Mergers

Abstract

The origin of the correlation between the effective spins ($\ddot{I}{‡}_{\mathrm{eff}}$) 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 $\ddot{I}{‡}_{\mathrm{eff}}-q$ correlation for each subpopulation. Surprisingly, the $\ddot{I}{‡}_{\mathrm{eff}}$-$q$ correlation {either significantly weakens or disappears} for the low-mass subpopulation if we introduce a second $\ddot{I}{‡}_{\mathrm{eff}}$ distribution for the high-mass subpopulation, which likely originates from hierarchical mergers. {This suggests that the $\ddot{I}{‡}_{\mathrm{eff}}$-$q$ correlation in the overall population can be explained by the superposition of two distinct subpopulations.} {We find Bayesian evidence strongly favoring two separate $\ddot{I}{‡}_{\mathrm{eff}}$ distributions over a single mass-ratio-dependent distribution, with Bayes factors $\ln \mathcal{B}>4.2$.} The first subpopulation has a narrow $\ddot{I}{‡}_{\mathrm{eff}}$ distribution peaking at $\sim 0.05$, whose primary-mass function {showing a rapid decline beyond} $\sim 40M_{\odot }$, in agreement with first-generation BBHs. The second $\ddot{I}{‡}_{\mathrm{eff}}$ distribution is broad and peaks at $\hat{I}{¼}_{\ddot{I}‡,2}\sim 0.4$, aligning with predictions for hierarchical mergers in active galactic nucleus (AGN) disks. {However, we cannot exclude negative $\ddot{I}{‡}_{\mathrm{eff}}$values in the second subpopulation, suggesting hierarchical mergers might occur both in AGN disks and stellar clusters. Furthermore, the inferred second $\ddot{I}{‡}_{\mathrm{eff}}$ distribution might alternatively arise from other formation channels, such as stable mass transfer or chemically homogeneous evolution, if not interpreted as hierarchical mergers.}

14 pages, 9 figures, ApJ Accepted

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Cited by in corpus (1)

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