Unifying spatial correlation with hierarchical population inference to constrain the AGN channel for binary black hole mergers

The origin of the stellar-mass binary black holes (BBHs) observed in gravitational wave (GW) events by the LIGO-Virgo-KAGRA (LVK) detectors remains uncertain. One promising formation pathway is the active galactic nucleus (AGN) channel, in which BBHs embedded in AGN accretion discs experience enhanced merger rates and may produce rapidly spinning black holes in the upper mass gap. Previous constraints on the AGN contribution to the LVK merger population have relied either on spatial correlations between GW localisations and AGN catalogues or on modelling the intrinsic properties of GW sources. We develop a hierarchical Bayesian framework that unifies these approaches within a single likelihood for the fraction of AGN-hosted GW events, f agn. This framework, combined with the latest gravitational wave transient catalogue GWTC-5.0 and the electromagnetic Quaia AGN catalogue, cannot exclude an AGN contribution to the observed merger rate. For unobscured AGN in the optical and infrared bands with bolometric luminosities L bol at least10 44.5,10 45.5,10 46.5, erg,s-1, we exclude f agn at least 0.52,0.41, 0.61 at the 95 percent credible level under our fiducial model. The methodology and results presented in this work lay down the pathway for combining the full GW posterior with electromagnetic observations to infer the properties of GW populations and AGN discs.