The environment surrounding supermassive black holes (SMBHs) in galactic
    nuclei (GNs) is expected to harbour stellar-mass binary black hole (BBH)
    populations. These binaries were suggested to form a hierarchical triple system
    with the SMBH, and gravitational perturbations from the SMBH can enhance the
    mergers of BBHs through Lidov-Kozai (LK) oscillations. Previous studies
    determined the expected binary parameter distribution for this merger channel
    in single GNs. Here we account for the different spatial distribution and mass
    distribution models of BBHs around SMBHs and perform direct high-precision
    regularized N-body simulations, including Post-Newtonian (PN) terms up to order
    PN2.5, to model merging BBH populations in single GNs. We use a full
    inspiral-merger-ringdown waveform model of BBHs with nonzero eccentricities and
    take into account the observational selection effect to determine the parameter
    distributions of LK-induced BBHs detected with single advanced GW detectors
    from all GNs in the Universe. We find that the detected mergers’ total binary
    mass distribution is tilted towards lower masses, and the mass ratio
    distribution is roughly uniform. The redshift distribution peaks between
    ~0.15-0.55, and the vast majority of binaries merge within redshift ~1.1. The
    fraction of binaries entering the LIGO/Virgo/KAGRA band with residual
    eccentricities >0.1 ranges between ~3-12%. We identify a negative correlation
    between residual eccentricity and mass parameters and a negative correlation
    between residual eccentricity and source distance. Our results for the
    parameter distributions and correlations among binary parameters may make it
    possible to disentangle this merger channel from other BBH merger channels

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