Golden and Silver Dark Sirens for precise H0 measurement with HETDEX

TL;DR

This work presents a Bayesian dark-siren framework to measure the local Hubble constant $H_0$ by combining GW detections with spectroscopic galaxy catalogs from HETDEX/VIRUS for $z\le 0.2$. It introduces golden and silver dark sirens to categorize host-galaxy ambiguity and assesses EM follow-up feasibility across GW detector networks upgraded to A$^+$ and A$^\#$, showing that a few dozen events can yield percent-level $H_0$ precision when complemented by nearly complete redshift catalogs. The analysis integrates population modeling (BBH mass/spin distributions and redshift evolution), full Bayesian parameter estimation for the selected sirens, and a robust treatment of selection effects through $\beta(H_0)$, demonstrating practical path to high-precision, independent cosmology with dark sirens. The results underscore the crucial role of wide-field, deep spectroscopic surveys like HETDEX in enabling precise local measurements of $H_0$ and addressing the Hubble tension through a fully independent standard-siren approach.

Abstract

Gravitational waves (GWs) from compact binary coalescences are standard sirens that provide a direct measure of the source's luminosity distance, enabling an independent measurement of the Hubble constant (H0). While a bright siren -- a GW event with an identified electromagnetic (EM) counterpart -- provided the first such constraint, most detections, currently dominated by black hole mergers, lack EM signatures. A measurement of H0 is still possible with these dark sirens by statistically associating GW events with galaxies in existing catalogs based on the sky localization. In this work, we explore the potential of two subsets of sirens: rare golden dark sirens, for which a single galaxy dominates the H0 posterior, and silver dark sirens, which are far more common but have a larger set of plausible host galaxies. Using the fifth internal data release of the Hobby-Eberly Telescope Dark Energy Experiment (HETDEX), we assess the suitability of the Visible Integral-field Replicable Unit Spectrograph (VIRUS) for spectroscopic follow-up of dark sirens. VIRUS exposures of the standard HETDEX depth provide precise redshifts and exquisite completeness within z = 0.2. After a single year of observations with the upgraded LIGO-A# network, the combined sample of golden and silver dark sirens with z < 0.2 and follow-up VIRUS observations can potentially yield a few-percent constraint on H0. Our predictions suggest that spectroscopic redshift surveys such as HETDEX can play a key role in realizing high-precision cosmology with dark sirens in the near future. Standard-siren distance measurements offer a critical, fully independent path to the local value of H0 to resolve the Hubble tension.

Figures (10)

• Figure 1: Numerically computed selection function for HLI# and HLV$+$, where G represents golden dark sirens with $\Delta \Omega_{90}\leq 0.1$ deg$^2$ and S represents silver dark sirens with $\Delta \Omega_{90}\leq 1$ deg$^2$.
• Figure 2: The distribution of galaxies in the COSMOS field. The blue points display those galaxies in the area selected for our mock data challenge with $z\leq0.2$ and apparent magnitude $g\leq22$. In the region shown, the HETDEX fill-factor is close to unity.
• Figure 3: The distribution of galaxies in the HETDEX fall survey area. The blue points represent galaxies the SHELA field with $z\leq0.2$ and apparent magnitude $g\leq22$. The large void-like regions in the map are due to unobserved fields. SHELA provides a complementary data set to COSMOS in our mock data challenge: it is $\gtrsim 30$ larger area minimizes the effect of cosmic variance on our analysis, but its much lower fill-factor reduces the number of host galaxy candidates by a factor of $\sim 4.6$.
• Figure 4: The $g$-band galaxy luminosity function derived from the HETDEX catalog compared to that found from the SDSS SDSS:2002vxn. The orange points are derived solely from galaxies in the COSMOS field; the blue points represent galaxies from the full $79~\mathrm{deg}^2$ of the HETDEX DR5 catalog. The apparent magnitude limit is taken conservatively as $g\sim22$. The steep increase in the number of galaxies fainter than $M_g \sim -17$ is also seen in the DESI DR2 data moore2025desidr2galaxyluminosity.
• Figure 5: The expected number of GW events detected by the HLV$+$, HLI$+$, and HLI$\#$ networks as a function of their 90% credible sky area.