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Constraining the Hubble Constant using Cross-Correlation of Gravitational Wave Events with Flux-Limited Galaxy Catalog

Tathagata Ghosh, Surhud More

TL;DR

This paper tackles constraining the Hubble constant $H_0$ using gravitational-wave dark sirens that lack electromagnetic redshifts by cross-correlating GW event locations with a flux-limited galaxy catalog. It introduces a Bayesian 3D cross-correlation framework that uses GW luminosity-distance information alongside galaxy clustering, explicitly accounting for flux limits and per-event volume uncertainties. In simulations with 300 GW events distributed within $1\,\mathrm{Gpc}$ at O4 sensitivity, the method achieves a precision of about $9\%$ (90% HDI) on $H_0$. The work also highlights key limitations for real-data application, including depth variations and redshift-dependent GW–galaxy bias, and outlines necessary extensions and marginalizations, suggesting the approach can complement EM-counterpart-based $H_0$ measurements.

Abstract

Gravitational waves (GWs) from the compact binary coalescence provide direct measurement of the luminosity distance to the event. However, unlike binary neutron stars, redshift information is not available from GW observations of binary black holes. Consequently, independent redshift measurements of such GW events are necessary to measure $H_0$. In this study, we demonstrate a novel Bayesian formalism to infer $H_0$ utilizing the $3$D cross-correlation of GW events with galaxies from flux-limited catalog in configuration space. We demonstrate the efficacy of our method with $300$ simulated GW events distributed within $1$ Gpc in colored Gaussian noise of Advanced LIGO and Advanced Virgo detectors operating at O4 sensitivity. We show that such measurements can constrain the Hubble constant with a precision of $\sim 9 \%$ ($90\%$ highest density interval). We highlight the potential improvements that need to be accounted for in further studies before the method can be applied to real data.

Constraining the Hubble Constant using Cross-Correlation of Gravitational Wave Events with Flux-Limited Galaxy Catalog

TL;DR

This paper tackles constraining the Hubble constant using gravitational-wave dark sirens that lack electromagnetic redshifts by cross-correlating GW event locations with a flux-limited galaxy catalog. It introduces a Bayesian 3D cross-correlation framework that uses GW luminosity-distance information alongside galaxy clustering, explicitly accounting for flux limits and per-event volume uncertainties. In simulations with 300 GW events distributed within at O4 sensitivity, the method achieves a precision of about (90% HDI) on . The work also highlights key limitations for real-data application, including depth variations and redshift-dependent GW–galaxy bias, and outlines necessary extensions and marginalizations, suggesting the approach can complement EM-counterpart-based measurements.

Abstract

Gravitational waves (GWs) from the compact binary coalescence provide direct measurement of the luminosity distance to the event. However, unlike binary neutron stars, redshift information is not available from GW observations of binary black holes. Consequently, independent redshift measurements of such GW events are necessary to measure . In this study, we demonstrate a novel Bayesian formalism to infer utilizing the D cross-correlation of GW events with galaxies from flux-limited catalog in configuration space. We demonstrate the efficacy of our method with simulated GW events distributed within Gpc in colored Gaussian noise of Advanced LIGO and Advanced Virgo detectors operating at O4 sensitivity. We show that such measurements can constrain the Hubble constant with a precision of ( highest density interval). We highlight the potential improvements that need to be accounted for in further studies before the method can be applied to real data.
Paper Structure (4 sections, 2 figures)

This paper contains 4 sections, 2 figures.

Table of Contents

  1. Introduction
  2. Method and Simulation
  3. Results
  4. Summary

Figures (2)

  • Figure 1: Left Panel: Comparison of overdensity fluctuation $\sigma_{\delta}$ for the complete and flux-limited galaxy catalog considering $\theta_{\rm max}=0.02$ radian. Right Panel: Galaxy bias, $b_{g}$ as a function of redshift for the complete and flux-limited galaxy catalogs. The solid lines in both panels correspond to the complete galaxy catalog from Ref. Ghosh:2023ksl, and the dashed lines correspond to the flux-limited catalog constructed from it in this work.
  • Figure 2: Comparison of $H_{0}$ posteriors inferred using the complete and flux-limited galaxy catalogs for different numbers of GW events as indicated at the top of the respective plots Ghosh:2023ksl.