The Gravitational Wave Bias Parameter: Bridging Between Galaxies and Binary Black Holes

          @misc{ pirsa_PIRSA:25100190,
            doi = {10.48660/25100190},
            url = {https://pirsa.org/25100190},
            author = {Sadat Hosseini Khajouei, Dorsa},
            keywords = {},
            language = {en},
            title = {The Gravitational Wave Bias Parameter: Bridging Between Galaxies and Binary Black Holes},
            publisher = {Perimeter Institute},
            year = {2025},
            month = {oct},
            note = {PIRSA:25100190 see, \url{https://pirsa.org}}
          }
          

Abstract

This study presents the modelling of the gravitational wave (GW) bias parameter by bridging between simulated GW sources and galaxies in low redshift galaxy surveys 2MPZ, WISExSCOS (WISC) and SDSS DR7. We study this connection by creating a mock host catalog for GW events and populating galaxy surveys with binary black holes (BBHs) for different scenarios of the GW host-galaxy probability as a function of the galaxy stellar mass, SFR and metallicity. For 2MPZ, WISExSCOS (WISC) galaxy surveys with only stellar mass information, we consider a phenomenological broken power law model for the host-galaxy probability function, with a potential turnover where the star formation efficiency begins to drop. We vary the parameters of the GW host-galaxy probability function and find that generically the GW bias increases as the turnover point increases. The change in the GW bias parameter shows a maximum change of about 30% for different scenarios explored in this work in comparison to the galaxy bias. For the SDSS DR7 survey with stellar mass, SFR and metallicity information, we use a joint host-galaxy probability function defined over stellar mass, star formation rate (SFR), and metallicity. This probability is modelled 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 BBH mergers, such as galaxy quenching and BBH delay time. In this case, our results show that GW bias is most sensitive to host-galaxy probability dependence on stellar mass, with increases of up to ∼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.