[Paper Review] Synergy between CSST galaxy survey and gravitational-wave observation: Inferring the Hubble constant from dark standard sirens

Ji-Yu Song, Ling-Feng Wang+5 more|arXiv (Cornell University)|Dec 1, 2022

Radio Astronomy Observations and Technology122 references6 citations

TL;DR

This paper proposes a synergy between the China Space Station Telescope (CSST) galaxy survey and third-generation gravitational-wave (GW) detectors to measure the Hubble constant ($H_0$) using dark standard sirens—GW events without electromagnetic counterparts. By combining CSST’s deep, high-precision photometric and spectroscopic galaxy catalogs with simulated 5-year GW data from ET, CE1, and ET2CE, the study demonstrates that $H_0$ can be constrained to sub-percent precision, reaching 0.53% in the most optimistic scenario, significantly improving cosmological distance measurements.

ABSTRACT

Gravitational waves (GWs) from compact binary coalescences encode the absolute luminosity distances of GW sources. Once the redshifts of GW sources are known, one can use the distance-redshift relation to constrain cosmological parameters. One way to obtain the redshifts is to localize GW sources by GW observations and then use galaxy catalogs to determine redshifts from a statistical analysis of redshift information of the potential host galaxies, commonly referred to as the dark siren method. The third-generation (3G) GW detectors are planned to work in the 2030s and will observe numerous compact binary coalescences. Using these GW events as dark sirens requires high-quality galaxy catalogs from future sky survey projects. The China Space Station Telescope (CSST) will be launched in 2024 and will observe billions of galaxies within a 17500 deg$^2$ survey area with redshift up to $z\sim 4$, providing photometric and spectroscopic galaxy catalogs. In this work, we simulate the CSST galaxy catalogs and the 5-year GW data from the 3G GW detectors and combine them to infer the Hubble constant ($H_0$). Our results show that the measurement precision of $H_0$ could reach the sub-percent level, meeting the standard of precision cosmology. We conclude that the synergy between CSST and the 3G GW detectors is of great significance in measuring the Hubble constant.

Motivation & Objective

• To investigate the potential of combining CSST’s galaxy survey with third-generation gravitational-wave detectors for precise $H_0$ measurement using dark standard sirens.
• To assess how CSST’s high-cadence, deep photometric and spectroscopic redshift catalogs improve the completeness and accuracy of host galaxy identification for GW events.
• To quantify the precision of $H_0$ constraints under realistic observational conditions, including errors from GW distance measurement, lensing, and peculiar velocities.
• To evaluate the performance gain from network configurations like ET2CE compared to single detectors.

Proposed method

• Simulated CSST galaxy catalogs using a Schechter function to model galaxy number counts and redshift distributions up to $z \sim 4$, with photometric and spectroscopic redshifts.
• Generated 5-year GW event catalogs for ET, CE1, and ET2CE based on the BBH population from GWTC-3, including sky localization and distance error estimates.
• Applied Fisher Information Matrix (FIM) analysis to estimate parameter errors, including luminosity distance ($d_{\rm L}$) and redshift ($z$) uncertainties.
• Used 3D localization regions from GW data to search for potential host galaxies in the mock CSST catalog, applying Bayesian inference to estimate $H_0$ from the $d_{\rm L}$–$z$ relation.
• Incorporated errors from instrumental noise, gravitational lensing, and peculiar velocities into the $d_{\rm L}$ uncertainty budget, with peculiar velocity error modeled as $\Delta d_{\rm L}^{\rm pv}(z) = d_{\rm L}(z) \cdot \left[1 + \frac{c(1+z)^2}{H(z)d_{\rm L}(z)} \right] \cdot \frac{\sqrt{\langle v^2 \rangle}}{c}$, assuming $\sqrt{\langle v^2 \rangle} = 500\ \text{km s}^{-1}$.
• Performed Bayesian inference on the $d_{\rm L}$–$z$ relation to constrain $H_0$, comparing results across different detector configurations and redshift catalog qualities.

Experimental results

Research questions

• RQ1 Can the synergy between CSST and third-generation GW detectors achieve sub-percent precision in measuring the Hubble constant using dark sirens?
• RQ2 How does the completeness and redshift accuracy of CSST’s galaxy catalogs improve host galaxy identification for unlensed GW events compared to current catalogs like GLADE+?
• RQ3 What is the impact of peculiar velocity errors on the final $H_0$ uncertainty, and how does it affect the precision of cosmological constraints?
• RQ4 How do network configurations like ET2CE outperform single detectors in $H_0$ measurement precision via enhanced localization and host galaxy identification?

Key findings

• The Hubble constant can be constrained to 0.53% precision in the most optimistic scenario using ET2CE and CSST’s galaxy catalog, meeting the standard of precision cosmology.
• For ET alone, $H_0$ is constrained to 0.62% in the optimistic case and 0.89% in the conservative case, with CE1 improving precision by ~3.3% compared to ET.
• The ET2CE network achieves 0.53% precision (optimistic) and 0.71% (conservative), representing a 17.44% improvement over CE1 alone.
• Including peculiar velocity errors reduces $H_0$ precision by 8%–16%, but even in the worst-case scenario (CE1 conservative), precision remains at 1.00%.
• CSST’s photometric and spectroscopic catalogs contain ~100 and ~10 times more galaxies than GLADE+, respectively, significantly enhancing host galaxy detection completeness.
• The average redshift uncertainty in CSST’s photo-z catalog is ~40% lower than in GLADE+, directly improving $H_0$ measurement precision via the $d_{\rm L}$–$z$ relation.