Kavli Affiliate: Daniel E. Holz
| First 5 Authors: Alexandra G. Hanselman, Aditya Vijaykumar, Maya Fishbach, Daniel E. Holz,
| Summary:
The detection of GW170817 and the measurement of its redshift from the
associated electromagnetic counterpart provided the first gravitational wave
determination of the Hubble constant ($H_0$), demonstrating the potential power
of standard-siren cosmology. In contrast to this bright siren approach, 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, weighting them by physically-motivated
properties (e.g., tracing star formation or stellar mass) could improve
convergence. Using mock galaxy catalogs, we explore the impact of these
weightings on the measurement of $H_0$. We find that incorrect weighting
schemes can lead to significant biases due to two effects: the assumption of an
incorrect galaxy redshift distribution, and preferentially weighting incorrect
host galaxies during the inference. The magnitudes of these biases are
influenced by the number of galaxies along each line of sight, the measurement
uncertainty in the gravitational-wave luminosity distance, and correlations in
the parameter space of galaxies. We show that the bias may be overcome from
improved localization constraints in future GW detectors, a strategic choice of
priors or weighting prescription, and by restricting the analysis to a subset
of high-SNR events. We propose the use of hierarchical inference as a
diagnostic of incorrectly-weighted prescriptions. Such approaches can
simultaneously infer the correct weighting scheme and the values of the
cosmological parameters, thereby mitigating the bias in dark siren cosmology
due to incorrect host-galaxy weighting.
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