Connecting the hierarchically merging binary black hole population to their host galaxies

ABSTRACT The detection of gravitational waves from merging black holes with masses ${\sim} \, 80{\!-\!}150\, \mathrm{M_\odot }$ suggests that some proportion of black hole binary systems form hierarchically in dense astrophysical environments, as most stellar evolution models cannot explain the origin of these massive black holes through isolated binary evolution. A significant fraction of such mergers could occur in Active Galactic Nuclei (AGN) discs, however connecting individual black hole mergers to host galaxies is a challenging endeavour due to large localization uncertainties. We assess the feasibility of determining the fraction of hierarchically merging black hole binaries by computing the angular cross-correlation between gravitational wave localization posteriors and galaxy catalogue skymaps. We forecast when the clustering of gravitational wave sky localizations can be measured accurately enough to distinguish the AGN origin scenario from hierarchical mergers in galaxies that do not host AGN. We find that if the observed merging population is dominated by binaries formed dynamically in AGN, then this could be determined with $\mathcal {O}(5000)$ mergers detected at the sensitivity that is projected for the upcoming A# gravitational wave detectors.