Constraining the AGN formation channel for detected black hole binary mergers up to z=1.5 with the Quaia catalogue

Statistical analyses based on the spatial correlation between the sky maps of Gravitational Wave (GW) events and the positions of potential host environments are a powerful tool to infer the origin of the black hole binary mergers that have been detected by the LIGO, Virgo, and KAGRA instruments. In this paper, we tighten our previous constraints on the fraction of detected GW events that may have originated from Active Galactic Nuclei (AGN). We consider 159 mergers detected not later than June 1st, 2024, and the all-sky quasar catalogue Quaia. We increase by a factor of 5.3 and 114 the number of considered GW sources and AGN respectively, also extending our analysis from redshift $0.3$ to $1.5$. This is possible thanks to the uniformity of the AGN catalogue and its high level of completeness, which we estimate as a function of redshift and luminosity. We find at a 95 per cent credibility level that un-obscured AGN with a bolometric luminosity higher than $10^{44.5}{\rm erg\ s}^{-1}$ ($10^{45}{\rm erg\ s}^{-1}$) do not contribute to more than the 21 (11) per cent of the detected GW events.