Measurement of the Hubble constant using the Dark Energy Survey Year 6 Gold galaxy catalog and the fourth Gravitational-Wave Transient Catalog

TL;DR

This work measures the Hubble constant $H_0$ using dark sirens from 142 CBCs in GWTC-4.0 and the DES Year 6 Gold galaxy catalog within a Bayesian gwcosmo framework, treating GW170817 as a bright siren. It introduces a galaxy-catalog LOS redshift prior built from a Schechter-function-informed luminosity distribution and accounts for catalog incompleteness via an out-of-catalog term, while propagating GW-selection effects. Key advances include GPU-accelerated likelihood evaluations, careful redshift-catalog cuts to preserve a uniform comoving-volume prior, and a joint inference of cosmology and CBC populations under FullPop-4.0. The resulting $H_0$ constraints, $70.9^{+22.3}_{-18.6}$ km s$^{-1}$ Mpc$^{-1}$ from dark sirens and $73.1^{+11.7}_{-8.6}$ km s$^{-1}$ Mpc$^{-1}$ when combined with GW170817, demonstrate the potential of deep galaxy catalogs for next-generation GW cosmology, while highlighting challenges posed by redshift distribution features and selection effects.

Abstract

Gravitational wave standard sirens enable independent measurements of the Hubble constant $H_0$. In the absence of electromagnetic counterparts, the "dark siren" method statistically correlates GW events with potential host galaxies. We present a measurement of $H_0$ using 142 compact binary coalescences from the fourth Gravitational-Wave Transient Catalog (GWTC-4.0) combined with the Dark Energy Survey Year 6 Gold photometric galaxy catalog. Using the gwcosmo pipeline, we jointly infer cosmological and GW population parameters. We analyze the impact of galaxy catalog properties on the inference, identifying significant features in the galaxy redshift distribution which can introduce biases. By restricting the galaxy catalog to $0.05<z<0.35$ to maintain consistency with a uniform in comoving volume galaxy distribution, we obtain a result of $H_0 = 70.9^{+22.3}_{-18.6}\;\text{km}\;\text{s}^{-1}\;\text{Mpc}^{-1}$ from dark sirens and $H_0=73.1^{+11.7}_{-8.6}\;\text{km}\;\text{s}^{-1}\;\text{Mpc}^{-1}$ when combined with the bright siren GW170817. This study demonstrates the adaptation of deep galaxy catalogs for GW cosmology, highlighting key challenges and methodologies essential for maximizing the potential of next-generation galaxy surveys.

Figures (7)

• Figure 1: Top: GW event candidate 50% and 90% probability contours included in our analysis which have more than 50% probability to be within the DES Y6 Gold survey footprint (shown in blue). Bottom: The photometric redshift distribution of galaxies $\text{d}N/\text{d}z$ in DES Y6 Gold (red) compared to a uniform in comoving volume distribution (dotted black), scaled to have the same total number of galaxies. More discussion can be found in Section \ref{['sec:meth_prior_validation']}. On the same x-axis are shown redshift measurements (90% confidence interval) for the events, converted from luminosity distance and ordered by increasing localization volume.
• Figure 2: Left: Luminosity function with $1\sigma$ errors and corresponding Schechter function fit in the example redshift range $0.325<z<0.35$. $M_\text{min}$ and $M_\text{max}$ are shown in red. Right: $r$-band Schechter function parameters as a function of redshift and their linear evolution fits. Results from the literature are shown for comparison with evolution when included, typically measured using $z_0=0.1$SDSS:2002vxnMonteroDorta2009Hill2010Loveday2011. The vertical blue lines indicate the different values of $z_\text{median}$, given in the second column of Table \ref{['tab:sch']}.
• Figure 3: Top: LOS redshift priors averaged over the footprint of the DES survey, calculated for different choices of upper redshift cut. For the regions $z<z_{\text{min}}$ and $z>z_{\text{max}}$, the prior reverts to the default uniform in comoving volume "Empty" catalog assumption. The y-axis is the ratio between the catalog prior and the empty catalog. The chosen values of $z_{\text{max}}$ and $z_{\text{min}}$ are shown as blue vertical lines, as in Figure \ref{['fig:footprint']}. The average LOS redshift prior for GLADE+ $K$-band is shown in green for comparison. The effect of applying a cut at $z_{\text{min}}$ is shown for $z_{\text{max}}=0.35$ with a dashed line at low redshift. If there is no cut, the prior dramatically decreases at low redshift due to the saturation selection effect. Bottom: $1\sigma$ average redshift prior comparison for $z_\text{max}=0.35, 0.50$. For $z_\text{max}\leq0.35$, each prior is entirely within $1\sigma$ of the empty catalog. All $z_\text{max}\geq0.40$ exceed $1\sigma$ at some point.
• Figure 4: Posterior distributions for different choices of $z_\text{max}$. The result for the dark siren analysis using GLADE+ $K$-band is shown in green. The "empty catalog" spectral siren result is shown with a dotted line. $1\sigma$ regions for early- and late- universe $H_0$ measurements are shown in red and blue, respectively Planck2018Riess2022.
• Figure 5: Posterior distributions with and without the use of $z_\text{min}$, shown for $z_\text{max}=0.20, 0.35, 0.50$ as example. $1\sigma$ regions for early- and late- universe $H_0$ measurements are again shown in red and blue.