Cosmological inference using gravitational wave standard sirens: A mock data analysis

The observation of binary neutron star merger GW170817, along with its optical counterpart, provided the first constraint on the Hubble constant ${H}_{0}$ using gravitational wave standard sirens. When no counterpart is identified, a galaxy catalog can be used to provide the necessary redshift information. However, the true host might not be contained in a catalog which is not complete out to the limit of gravitational-wave detectability. These electromagnetic and gravitational-wave selection effects must be accounted for. We describe and implement a method to estimate ${H}_{0}$ using both the counterpart and the galaxy catalog standard siren methods. We perform a series of mock data analyses using binary neutron star mergers to confirm our ability to recover an unbiased estimate of ${H}_{0}$. Our simulations used a simplified universe with no redshift uncertainties or galaxy clustering, but with different magnitude-limited catalogs and assumed host galaxy properties, to test our treatment of both selection effects. We explore how the incompleteness of catalogs affects the final measurement of ${H}_{0}$, as well as the effect of weighting each galaxy's likelihood of being a host by its luminosity. In our most realistic simulation, where the simulated catalog is about three times denser than the density of galaxies in the local universe, we find that a 4.4% measurement precision can be reached using galaxy catalogs with 50% completeness and $\ensuremath{\sim}250$ binary neutron star detections with sensitivity similar to that of Advanced LIGO's second observing run.