Modeling Gravitational Wave Bias from 3D Power Spectra of Spectroscopic Surveys

We present a framework for relating gravitational wave (GW) sources to the astrophysical properties of spectroscopic galaxy samples. We show how this can enable using clustering measurements of GW sources to infer the relationship between the GW sources and the astrophysical properties of their host galaxies. We accomplish this by creating mock GW catalogs from the spectroscopic Sloan Digital Sky Survey (SDSS) DR7 galaxy survey. We populate the GWs using a joint host-galaxy probability function defined over stellar mass, star formation rate (SFR), and metallicity. This probability is modeled as the product of three broken power-law distributions, each with a turnover point motivated by astrophysical processes governing the relation between current-day galaxy properties and binary black hole (BBH) mergers, such as galaxy quenching and BBH delay time. Given that our analysis is anchored in the specific properties and selection characteristics of the adopted galaxy sample, as well as assumptions regarding the host-galaxy probability functions and BBH merger rate prescriptions, the resulting trends should be regarded as model-dependent. Within this framework, our results show that GW bias is most sensitive to host-galaxy probability dependence on stellar mass, with increases of up to $\sim O (10)\%$ relative to galaxy bias as the stellar mass pivot scale rises. We also find a notable relationship between GW bias and SFR: when the host-galaxy probability favors low-SFR galaxies, the GW bias significantly increases. In contrast, we observe no strong correlation between GW bias and metallicity. These findings suggest that the spatial clustering of GW sources is primarily driven by the stellar mass and SFR of their host galaxies and shows how GW bias measurements can inform models of the host-galaxy probability function.