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Abstract We outline the “dark siren” galaxy catalog method for cosmological inference using gravitational wave (GW) standard sirens, clarifying some common misconceptions in the implementation of this method. When a confident transient electromagnetic counterpart to a GW event is unavailable, the identification of a unique host galaxy is in general challenging. Instead, as originally proposed by Schutz, one can consult a galaxy catalog and implement a dark siren statistical approach incorporating all potential host galaxies within the localization volume. Trott & Huterer recently claimed that this approach results in a biased estimate of the Hubble constant, H 0 , when implemented on mock data, even if optimistic assumptions are made. We demonstrate explicitly that, as previously shown by multiple independent groups, the dark siren statistical method leads to an unbiased posterior when the method is applied to the data correctly. We highlight common sources of error possible to make in the generation of mock data and implementation of the statistical framework, including the mismodeling of selection effects and inconsistent implementations of the Bayesian framework, which can lead to a spurious bias.
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Gravitational-wave Dark Siren Cosmology Systematics from Galaxy Weighting
Abstract The detection of GW170817 and the measurement of its redshift from the associated electromagnetic counterpart provided the first gravitational-wave (GW) determination of the Hubble constant (H0), demonstrating the potential power of standard siren cosmology. In contrast to this “bright siren” approach, the “dark siren” approach can be utilized for GW 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 ofH0. 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 GW 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-signal-to-noise ratio 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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- PAR ID:
- 10566197
- Publisher / Repository:
- DOI PREFIX: 10.3847
- Date Published:
- Journal Name:
- The Astrophysical Journal
- Volume:
- 979
- Issue:
- 1
- ISSN:
- 0004-637X
- Format(s):
- Medium: X Size: Article No. 9
- Size(s):
- Article No. 9
- Sponsoring Org:
- National Science Foundation
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