Connecting The Hierarchically Merging Binary Black Hole Population To Their Host Galaxies

TL;DR

This work addresses whether hierarchically merging BBHs originate predominantly in AGN disks or in dense stellar environments by exploiting angular cross-correlations between gravitational-wave sky localizations and galaxy skymaps. The authors develop a formalism based on the angular power spectrum $C_{\ell}$ and galaxy bias, using two all-sky catalogs (AGN from QUAIA GAIA-unWISE and non-AGN from GLADE+) to compare cross-correlations with GW localizations. They validate a point-estimate approach, demonstrate robustness across mock populations, and extend to mixtures of sources by inferring fractional contributions $f_A$ and $f_N$ with likelihoods and model selection via the Akaike Information Criterion (AIC). The key result is that, with on the order of $\mathcal{O}(5000)$ detections at future A#-class sensitivity, one can statistically distinguish an AGN-dominated hierarchical-merger channel from non-AGN channels, providing a powerful, complementary tool to direct host associations. The method highlights how 2D GW localization data, when combined with comprehensive galaxy catalogs, can shed light on the environments that produce the upper-m mass BBH mergers and inform models of hierarchical formation.

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 disks (AGN), however connecting individual black hole mergers to host galaxies is a challenging endeavor 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 catalog 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.

Figures (7)

• Figure 1: Masked galaxy pixel map from the GLADE+ catalog, where non star forming galaxies (including AGN) are removed.
• Figure 2: QUAIA quasar catalog, with the same mask used for GLADE+.
• Figure 3: An example of $N=100$ GW sky localization posteriors for events with true locations sampled from the QUAIA quasar catalog. The sky localizations are computed using gwbench.
• Figure 4: On the left hand side, we show that when the true BBH locations are sampled from the AGN catalog there is good agreement between the ACC computed between the GW catalog and AGN catalog (GW x AGN), and the autocorrelation of the AGN catalog (AGNxAGN, shown as orange circles, along with its power law best fit and the 90 per cent confidence interval region shaded). On the right hand side, we show that there is no support for the ACC between the GW catalog (with true locations drawn from an AGN catalog) and the non-AGN catalog being consistent with the autocorrelation of the non-AGN galaxy catalog. The $C_\ell$ coefficients plotted are band-averaged over the interval $\left[C_\ell-\Delta \ell/2,C_\ell+\Delta \ell/2 \right]$ with $\Delta \ell=10$; for visual clarity we offset the $N=1000$$C_\ell$ coefficients on the plot. Error bars on the GW cross-correlations and the galaxy auto-correlations are given by Equation \ref{['eq:Covariance_matrix']}.
• Figure 5: Same as Fig. \ref{['fig:Cl_GWAGN_point_estimate']}, but the true BBH locations sampled from locations in the non-AGN catalog. In this case there is greater support for the ACC between the GW catalog and non-AGN being consistent with the non-AGN catalog within statistical uncertainties, as expected.