How Low Can You Go: Constraining the Effects of Catalog Incompleteness on Dark Siren Cosmology

TL;DR

This paper investigates how galaxy catalog completeness affects dark siren measurements of the Hubble constant, showing that incomplete catalogs can still yield unbiased results if they include the brightest galaxies, especially for well-localized GW events.

Contribution

It quantifies the galaxy catalog completeness needed for unbiased dark siren $H_0$ measurements, highlighting the importance of galaxy clustering and luminosity in the analysis.

Findings

Complete catalogs down to 1% brightest galaxies suffice for unbiased $H_0$ with well-localized events.

Clustering of faint galaxies around bright ones reduces bias in $H_0$ estimation.

Using only the brightest galaxies can bias $H_0$ if clustering is absent or localization is poor.

Abstract

Gravitational waves (GWs) serve as standard sirens by directly encoding the luminosity distance to their source. When the host galaxy redshift is known, for example, through observation of an electromagnetic (EM) counterpart, GW detections can provide an independent measurement of the Hubble constant, $H_0$. However, even in the absence of an EM counterpart, inferring $H_0$ is possible through the dark siren method. In this approach, every galaxy in the GW localization volume is considered a potential host that contributes to a measurement of $H_0$, with redshift information supplied by galaxy catalogs. Using mock galaxy catalogs, we explore the effect of catalog incompleteness on dark siren measurements of $H_0$. We find that in the case of well-localized GW events, if GW hosts are found in all galaxies with host halo masses $M_h > 2 \times10^{11} M_{\odot}h^{-1}$, catalogs only need to be complete down to the 1% brightest magnitude $M_i < -22.43$ to draw an unbiased, informative posterior on H0. We demonstrate that this is a direct result of the clustering of fainter galaxies around brighter and more massive galaxies. For a mock galaxy catalog without clustering, or for GW localization volumes that are too large, using only the brightest galaxies results in a biased $H_0$ posterior. These results are important for informing future dark siren analyses with LIGO-Virgo-KAGRA as well as next-generation detectors.