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

TL;DR

Dark siren cosmology can infer $H_0$ using GW distances without EM counterparts by associating them with galaxy catalogs. The authors use a Bayesian framework and a MICECAT-based mock catalog to quantify how catalog incompleteness affects $H_0$, showing that for well-localized events, catalogs complete to the 1% brightest galaxies (e.g., $M_i<-22.43$) are sufficient when GW hosts lie in halos with $M_h>2\times10^{11}\,M_\odot h^{-1}$. This effectiveness arises from galaxy clustering: faint galaxies tend to be near bright ones, so missing faint hosts can be compensated by nearby bright galaxies; removing clustering degrades the inference. The results imply that upcoming detectors with improved localization will benefit from bright-galaxy samples in dark-siren analyses, with limited information gain from adding more bright galaxies beyond ~20–40% and with caveats for poorly localized events and photometric redshift uncertainties.

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.

Figures (7)

• Figure 1: Average number of galaxies per $3\ \mathrm{deg}^2$ LOS for $z\leq0.4$, shown as a function of increasing brightness cutoffs in the $i$-band and $g$-band. The shaded region illustrates the standard deviation over the 200 LOS. There are greater numbers of bright $i$-band galaxies at this redshift range than bright $g$-band galaxies.
• Figure 2: Posterior on $H_0$ for 200 GW events injected along one LOS and reconstructed with only the 10% brightest galaxies in the $i$- and $g$-band with 10%, 20%, and 30% error on GW luminosity distance. In the bottom panels are the normalized redshift distributions and the cumulative density function of the full LOS and the 10% brightest $i$- and $g$-band galaxies.
• Figure 3: KS statistics between the redshift distributions of the 1%, 10%, and 20% brightest galaxies and the full galaxy sample along our 200 LOS for z$\leq$0.4. We also include the KS statistics between the redshift distribution of a random 1% of galaxies with the full LOS for comparison.
• Figure 4: Resulting posteriors on $H_0$ from injecting 1 GW event into each of 200 LOS and reconstructing the LOS redshift distribution with the 1%, 10%, and 20% brightest galaxies in the $i-$ and $g$-band.
• Figure 5: Median KL divergence between posteriors of increasing brightness fractions over 10 realizations of GW events. Here we show only results from posteriors constructed with the bright $i$-band galaxies at our three levels of $d_L$ uncertainty.