Radio sirens: inferring $H_0$ with binary black holes and neutral hydrogen in the era of the Einstein Telescope and the SKA Observatory

Technical Summary: Radio Sirens: Inferring $H_0$ with Binary Black Holes and Neutral Hydrogen

Problem Statement
Gravitational wave (GW) cosmology relies on "standard sirens" to measure the expansion rate of the Universe. While GW signals from binary black hole (BBH) mergers provide direct measurements of luminosity distance, extracting cosmological parameters requires independent redshift information. "Bright sirens" (events with electromagnetic counterparts) are rare, having been observed only once to date. Consequently, the field relies on "dark sirens," which infer redshift statistically. Current dark siren methods typically utilize galaxy catalogs to construct line-of-sight (LoS) redshift priors or employ summary statistics like cross-correlation. However, these approaches face challenges regarding catalog completeness, flux limits, and the need for complex modeling of galaxy luminosity functions, particularly at high redshifts. This paper addresses the need for a robust, spectroscopic redshift prior that leverages the large-scale structure (LSS) of the Universe without relying on discrete, potentially incomplete galaxy catalogs.

Methodology
The authors propose a novel framework termed "radio sirens," which synergizes simulated observations from the Einstein Telescope (ET) and the Square Kilometre Array Observatory (SKAO). The methodology employs a hierarchical Bayesian inference (HBI) framework to combine GW data with neutral hydrogen (HI) intensity mapping (IM) data.

1. Simulations:

   • Dark Matter (DM) & HI Maps: Mock LSS maps were constructed using high-resolution Dark Energy and Massive Neutrino Universe (DEMNUni) simulations. These were converted into HI density contrast maps ($\delta_{HI}$) assuming a linear bias relation ($b_{HI}=1$) relative to the DM field. The maps cover a sky area of $20,000 \text{ deg}^2$ up to redshift $z \sim 3$, corresponding to the capabilities of SKA-Mid in single-dish mode.
   • GW Events: $10^4$ BBH merger events were simulated for the ET. The merger rate was modeled as a function of the DM density contrast, assuming GWs trace the underlying matter distribution ($b_{GW}=1, \alpha_{GW}=0$). Events were filtered to include only those with a signal-to-noise ratio (SNR) $> 150$, resulting in $\sim 3,100$ detectable events. Two catalogs were generated: "Clustered GWs" (distributed according to the DM field) and "Isotropic GWs" (uniformly distributed).

2. Inference Framework:

   • The analysis utilizes the icarogw software to perform hierarchical Bayesian analysis.
   • The core innovation is the use of the 3D HI density field to construct a LoS redshift prior for GW events. Instead of assigning probabilities to discrete galaxies, the method uses the continuous HI density contrast to weight the probability of a GW source residing at a specific redshift along a given line of sight.
   • The analysis explicitly excludes source-frame mass information (spectral siren methods) to isolate the constraining power of the HI prior and avoid dependence on specific astrophysical mass models.

Key Contributions

• Radio Sirens Concept: The paper introduces and tests a "radio siren" approach, utilizing HI intensity mapping as a spectroscopic redshift prior for dark sirens. This offers a tomographic view of the LSS that circumvents the completeness issues inherent in flux-limited galaxy catalogs.
• Proof-of-Concept Validation: The study demonstrates that combining ET BBH detections with SKAO HI maps can significantly tighten constraints on cosmological parameters.
• Systematic Risk Identification: The authors rigorously test the method's sensitivity to the assumed clustering model. By comparing clustered versus isotropic GW distributions, they highlight that the method's validity is contingent on the GW population accurately tracing the HI field.

Results

• Constraint on $H_0$: When analyzing the "Clustered GWs" catalog with the HI prior, the Hubble constant is constrained to $H_0 = 65.8^{+4.9}_{-5.2} \text{ km s}^{-1} \text{ Mpc}^{-1}$ at 68% credibility. This represents a precision of $\sim 8\%$.
• Improvement Factor: This result constitutes an improvement of approximately 90% compared to the analysis of the same clustered GW catalog without HI information, where the posterior on $H_0$ was found to be largely uninformative.
• Bias Sensitivity: In the "Isotropic GWs" scenario (where GWs do not trace the HI field), applying the HI prior resulted in a significant bias, overestimating $H_0$. This confirms that the method yields biased results if the assumed clustering relation between GWs and the LSS is incorrect.
• Expansion History: The inclusion of HI data allows for a reconstruction of the late-time expansion history $H(z)$ up to $z \sim 3$. The constraints are tightest at low redshift ($z \lesssim 0.5$) where the HI density contrast is highest, but the method primarily constrains the overall normalization ($H_0$) rather than the detailed shape of the expansion history (e.g., $\Omega_{m,0}$ constraints remain weak).
• Self-Consistency: The framework successfully recovered injected bias parameters ($b_{GW}, \alpha_{GW}$) when allowed to vary, indicating the method is self-consistent for joint cosmological and clustering inference.

Significance and Claims
The paper claims to establish the basic viability of the "radio siren" concept as a powerful, independent route to precision cosmology in the era of third-generation GW detectors and next-generation radio telescopes. The authors emphasize that this approach offers a physically motivated redshift prior that exploits the 3D structure of the Universe without the completeness corrections required by galaxy catalogs.

However, the authors maintain a modest stance regarding the current limitations. They acknowledge that the study is a proof-of-concept based on optimistic assumptions, including:

• Perfect tracing of DM by HI ($b_{HI}=1$) without stochasticity.
• The use of Fisher matrix approximations for GW parameter estimation.
• The neglect of observational systematics such as beam effects, foreground cleaning, and calibration issues in HI maps.
• The exclusion of BBH mass spectrum information.

The paper concludes that while the radio siren method shows promise for constraining $H_0$ to $\sim 8\%$ precision with $\sim 3,000$ high-SNR events, future work must address realistic astrophysical models for BBH environments, observational systematics in IM, and the joint modeling of mass spectra and clustering to fully realize the potential of this technique.