Gravitational Wave Bias in IllustrisTNG300 from Machine-Learned Population-Synthesis Calibrated Merger Rates

The large scale clustering of gravitational wave (GW) sources offers an independent probe of cosmology and compact-binary astrophysics. Interpreting future GW clustering measurements requires understanding how merger rates depend on host-galaxy properties and environment. We develop a simulation-based framework to model the clustering of binary black hole (BBH) mergers and estimate the corresponding GW bias. We populate IllustrisTNG300 with GW sources using a machine-learning emulator trained on the GALAXYRATE data set, which provides population-synthesis calibrated merger rates linked to galaxy formation histories. This enables physically motivated mock GW catalogs with galaxy-specific BBH merger rates that depend on stellar mass, star formation rate, metallicity, and redshift. We compare this framework to a simpler phenomenological model in which the merger rate depends only on stellar mass. In both approaches, GW sources are more strongly biased than the overall galaxy population, reflecting the preference for BBH mergers to occur in more massive, more strongly clustered halos. The machine-learned model also produces stronger scale dependence in the GW bias than stellar-mass weighting alone, indicating that additional host properties affect GW clustering. We further find that metallicity correlates positively with both GW and galaxy bias. These results highlight the importance of physically motivated merger rate models for GW large scale structure analyses and provide a framework for interpreting future clustering measurements from experiments such as the Einstein Telescope and Cosmic Explorer.