Improved constraint on the Hubble constant from dark sirens with LIGO/Virgo/KAGRA O4a

Abstract

A new measurement of the Hubble constant $H_0$ is presented using the statistical dark siren method applied to a sample of seven well-localized gravitational-wave (GW) events from the fourth LIGO-Virgo-KAGRA (LVK) observing run and ten additional events from the first three runs. Galaxy catalogs from the DESI Legacy Imaging Survey (LS) are combined with a deep learning model to compute photometric redshift probability density functions. We extend our previous analysis by including the events GW230731_215307 and GW230927_153832, using sky maps from the fourth Gravitational-Wave Transient Catalog (GWTC-4), and introducing key methodological improvements: $r$-band luminosity weighting of host galaxies; an extended GW likelihood that incorporates information from the binary black hole component masses; and a consistent treatment of selection effects that accounts for the incompleteness of the magnitude-limited LS galaxy catalog. Using a total of 17 well-localized dark sirens (seven from the first part of the fourth observing run, O4a), we obtain $H_0 = 78.8^{+14.6}_{-12.2}$ km/s/Mpc without luminosity weighting and $H_0 = 78.2^{+12.0}_{-11.0}$ km/s/Mpc when applying $r$-band luminosity weighting. Finally, we combine the luminosity-weighted dark siren sample with the bright siren GW170817, including constraints on the jet viewing angle and corrections for the host galaxy peculiar velocity, to obtain a final constraint of $H_0 = 69.9^{+4.1}_{-4.0}$ km/s/Mpc, representing an improvement of approximately 11% in the uncertainty relative to the GW170817-only result.

Figures (9)

• Figure 1: Schechter-function fit (gray) to the galaxy luminosity distributions of the LS in the r-band. Different colors correspond to different redshift bins.
• Figure 2: Performance of the photometric redshift estimates as a function of $r$-band magnitude. We compare the publicly available LS DR9 redshifts with those obtained using the MDN. The panels show the photo-$z$ bias, $\sigma_{\rm NMAD}$, and outlier fraction.
• Figure 3: GW and EM selection functions. Top panel: gravitational wave (solid lines) and electromagnetic (dashed lines) detection probabilities as functions of $H_0$ (shown in different colors) computed for an apparent magnitude threshold of $m_{r, \rm{thr}}=21$. Bottom panel: Selection function (as defined in eq. \ref{['fig:selectionfunction']}) computed from GW detection simulations using BAYESTAR. The black curve shows the result including only the GW detection probability (solid lines in the top panel), while the gray curve includes the EM detection probability as well (dashed lines in the top panel).
• Figure 4: Posterior distributions of the Hubble constant inferred from individual gravitational wave events. Solid lines represent the analysis using the full GW likelihood, and dashed lines represent the Gaussian approximation. Blue curves correspond to r-band weighted results, while orange curves are unweighted.
• Figure 5: Left panel: effect of galaxy-catalog weighting, with the full GW likelihood held fixed. The blue curve shows the result with no weighting, the orange curve uses $r$-band luminosity weighting, and the green curve uses $g$-band luminosity weighting. Right panel: effect of the GW likelihood treatment using the unweighted catalog. The solid blue curve corresponds to the full GW likelihood (as defined in eq. \ref{['eq:fullgwlike']}), while the dashed blue curve shows the Gaussian approximation likelihood (see eq. \ref{['eq:gwlike']}). In both panels, shaded regions indicate the 68% CI on $H_0$ from the Planck CMB inference planck18 (pink), the SH0ES distance-ladder measurement Breuval2024 (yellow), and the GWTC-4 dark siren analysis based on 142 events with the FullPop-4.0 population model gwtc4_cosmo (green).