Parameter Distributions of Binary Black Hole Mergers Near Supermassive Black Holes as Seen by Advanced Gravitational Wave Detectors

Abstract: 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 a single advanced gravitational-wave (GW) detector 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 is below ~10%. 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 statistically.