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The discovery of GW170817 provided the first direct gravitational-wave measurement of the Hubble constant, H₀, demonstrating the potential power of standard-siren cosmology. The dark siren approach can be utilized for gravitational-wave sources in the absence of an electromagnetic counterpart: one considers all galaxies contained within the localization volume as potential hosts. When statistically averaging over the potential host galaxies, one can weight them by their luminosities to account for physically-motivated prescriptions (e. g. , tracing star formation or stellar mass). Using mock galaxy catalogs, we explore the impact of these weightings on the measurement of H₀, focusing on the bias in H₀ inference that results from incorrectly-weighted prescriptions. We find that assuming an incorrect galaxy host probability can lead to significant biases in H₀, up to about five times off from typical values inferred by current experiments. These biases are due to inconsistent galaxy weighted redshift distributions as well as preferentially selecting the incorrect host during inference. The magnitudes of these biases are influenced by the galaxy number density along each line of sight, the uncertainty in the measurement of the gravitational-wave luminosity distance, and correlations in the parameter space of galaxies. These biases may be overcome with future GW detectors that contain better GW localization, using a strategic choice of weighting prescription, or with increasing the SNR cut. We propose using hierarchical inference as a diagnosis of incorrectly-weighted prescriptions, which can further be used to simultaneously infer the correct weighting scheme and cosmological parameters.
Hanselman et al. (Thu,) studied this question.