Revealing the $\chi_{\rm eff}$-$q$ correlation among Coalescing Binary Black Holes and { Tentative} Evidence for AGN-driven Hierarchical Mergers

TL;DR

This study investigates the correlation between effective spin and mass ratio in binary black holes, revealing two distinct subpopulations likely originating from different formation channels, including hierarchical mergers in AGN disks.

Contribution

It provides evidence for two separate spin distributions in BBHs, supporting the existence of hierarchical mergers in AGN disks and other environments.

Findings

Bayesian analysis favors two distinct $oldsymbol{ ext{chi}}_{ m eff}$ distributions over one.

The low-mass subpopulation's $oldsymbol{ ext{chi}}_{ m eff}$ distribution peaks near zero.

The high-mass subpopulation's $oldsymbol{ ext{chi}}_{ m eff}$ peaks around 0.4, consistent with hierarchical mergers.

Abstract

The origin of the correlation between the effective spins ($\chi_{\rm eff}$) 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 $\chi_{\rm eff}-q$ correlation for each subpopulation. Surprisingly, the $\chi_{\rm eff}$-$q$ correlation {either significantly weakens or disappears} for the low-mass subpopulation if we introduce a second $\chi_{\rm eff}$ distribution for the high-mass subpopulation, which likely originates from hierarchical mergers. {This suggests that the $\chi_{\rm eff}$-$q$ correlation in the overall population can be explained by the superposition of two distinct subpopulations.} {We find Bayesian evidence strongly favoring two separate $\chi_{\rm eff}$ distributions over a single mass-ratio-dependent distribution, with Bayes factors $\ln\mathcal{B}>4.2$.} The first subpopulation has a narrow $\chi_{\rm eff}$ distribution peaking at $\sim0.05$, whose primary-mass function {showing a rapid decline beyond} $\sim 40M_{\odot}$, in agreement with first-generation BBHs. The second $\chi_{\rm eff}$ distribution is broad and peaks at $\mu_{\chi,2} \sim 0.4$, aligning with predictions for hierarchical mergers in active galactic nucleus (AGN) disks. {However, we cannot exclude negative $\chi_{\rm eff}$values in the second subpopulation, suggesting hierarchical mergers might occur both in AGN disks and stellar clusters. Furthermore, the inferred second $\chi_{\rm eff}$ distribution might alternatively arise from other formation channels, such as stable mass transfer or chemically homogeneous evolution, if not interpreted as hierarchical mergers.}