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    Aligned Hierarchical Black Hole Mergers in Active-Galactic-Nuclei Disks Revealed by GWTC-4

    Yin-Jie Li1,*, Yuan-Zhu Wang2,*, Shao-Peng Tang1, and Yi-Zhong Fan1,3,†

    • *These authors contributed equally to this work.
    • †Contact author: yzfan@pmo.ac.cn

    Phys. Rev. Lett. 137, 021407 – Published 7 July, 2026

    DOI: https://doi.org/10.1103/qyfv-wkv1

    Abstract

    The active galactic nucleus (AGN) accretion disks are ideal sites for hierarchical black hole (BH) mergers. To robustly probe such a possibility, we analyze binary black hole mergers in the GWTC-4 with a flexible mixture population model for component masses, spin magnitudes, and spin tilt angles, and identify two distinct subpopulations. In the second subpopulation characterized by high spin magnitudes χ∼0.8 as well as the broad mass distribution up to ≳150M⊙, we find a pronounced preference for spins aligned with the orbital angular momentum: an isotropic tilt distribution is strongly disfavored (logarithmic Bayes factor =4.5). The aligned events account for ∼0.57−0.31+0.23 of the second subpopulation, corresponding to a local rate of ∼0.25−0.16+0.38  Gpc−3 yr−1 (all values reflect central 90% credible intervals). These notable features naturally arise from hierarchical mergers embedded in AGN disks, where gas torques may effectively align spins. Our results suggest that AGN-disk hierarchical assembly may be one important channel for the present gravitational-wave sample, and provide concrete, testable predictions for future detection.

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