Using gravitational wave dark sirens to choose between host galaxy weighting models

Binary black hole (BBH) mergers,, an important source of gravitational-waves(GWs), are assumed to be hosted in galaxies. The probability of a galaxy to host a BBH is related to its properties, for example stellar mass and star formation rate. These properties can be estimated from observables, such as the luminosity in certain observation bands. We refer to this description of host galaxy properties as host galaxy weighting models. However, the host galaxy weighting model for BBHs has yet to be accurately determined. Population synthesis has provided a variety of host galaxy weighting models. Here we investigate whether it is possible to distinguish different host galaxy weighting models using a data driven approach. We use the GW cosmology tool gwcosmo with a simulated IGO-Virgo-KAGRA (LVK) fifth observing run (O5)-like observing scenario. We also construct a mock spectroscopic galaxy catalogue from MICECATv2. Our analysis compares the Bayes factors among three simple luminosity weighting models, r-band, g-band, and uniform weighting. The Bayes factors among different host galaxy weighting models show a minor preference for the true model for a ~200-detection case, and a decisive preference for the true model over the uniform model for a ~1000-detection case, which is strongly driven by a small number of well-localised events.