A Hubble constant estimation with dark standard sirens and galaxy cluster catalogues

TL;DR

This paper demonstrates the first use of galaxy cluster catalogues as redshift support for dark standard siren measurements of the Hubble constant $H_0$, extending GW cosmography to higher redshifts by adapting the gwcosmo pipeline. It introduces a LOS-$z$ prior that combines in-catalogue cluster information (redshifts and masses) with an out-of-catalogue mass-function component, analyzed on GWTC-3 BBHs with PSZ2 and eRASS cluster data. The combined analysis yields $H_0 = 77^{+10}_{-10}$ km s$^{-1}$ Mpc$^{-1}$ (PSZ2) and $H_0 = 81^{+8}_{-8}$ km s$^{-1}$ Mpc$^{-1}$ (eRASS), representing 10% and 38% precision improvements over traditional galaxy catalogues, respectively, and illustrating EM contributions beyond the mass distribution alone. This opens pathways for precise cosmography with distant mergers in upcoming LVK runs and future observatories, while underscoring the need for further systematic studies and end-to-end simulations.

Abstract

In this paper, we explore the possibility of using galaxy cluster catalogues to provide redshift support for a gravitational-wave dark standard siren measurement of the Hubble constant $H_0$. We adapt the cosmology inference pipeline gwcosmo to handle galaxy cluster catalogues. Together with binary black holes from the GWTC-3, we use galaxy cluster data from the PSZ2 and the eRASS catalogues. With these catalogues, we obtain $H_0 = 77^{+10}_{-10}$ and $81^{+8}_{-8}\, \text{km}\, \text{s}^{-1}\, \text{Mpc}^{-1}$ respectively, which demonstrates improvements on precision by factors of 10% and 38% respectively over the traditional galaxy catalogue result. This exploratory work paves the way towards precise and accurate cosmography making use of distant compact binary mergers from upcoming observing runs of the LIGO-Virgo-KAGRA detector network and future gravitational-wave observatories.

Figures (6)

• Figure 1: Mass and redshift data for the galaxy cluster catalogues PSZ2 (top panel) and eRASS (bottom panel), along with the used lower and upper mass limits used in the analysis.
• Figure 2: Completeness fraction of the PSZ2 and eRASS galaxy cluster catalogues and the GLADE+ galaxy catalogue (in the $K$-band) indicating the probability that the catalogue contains the host cluster or galaxy of a GW event, as a function of redshift for $H_0=70\,\text{km} \, \text{s}^{-1} \text{Mpc}^{-1}$ and $\Omega_M = 0.3065$.
• Figure 3: Posterior probability distributions on $H_0$ from individual BBH events (with SNR$>9$) from GWTC-3 and PSZ2 and eRASS galaxy cluster catalogues. The results are compared with the results using the traditional GLADE+ galaxy catalogue and the "empty catalogue" case. The in-catalogue contribution from galaxy cluster catalogues is evident in features such as peaks in the distributions for several of the events.
• Figure 4: Combined posterior probability distribution on $H_0$ from the set of events in Fig. \ref{['fig: event h0 combined fixed populations']}. The galaxy cluster catalogues PSZ2 and eRASS respectively lead to improvements on precision of $10\%$ and $38\%$ over the traditional result from the GLADE+ galaxy catalogue as well as the "empty catalogue" case.
• Figure 5: Sensitivity of the PSZ2 and eRASS results to the $M^*$ parameter (top panel) and galaxy cluster redshift uncertainty (bottom panel). We vary the $M^*$ parameter to the limits of its 1-$\sigma$ confidence region of $M^*=2.6^{+0.8}_{-0.6} \times 10^{14} \, h^{-1}M_\odot$. The results are shown as shaded bands in the top panel. Next we increase all the galaxy cluster redshift uncertainties to and $25\,\text{Mpc}$, corresponding to half of typical inter-cluster separations. The results are shown as dotted lines in the bottom panel. No significant difference is observed compared to when the redshift uncertainties from the galaxy clusters are used.