A standard siren measurement of the Hubble constant using gravitational wave events from the first three LIGO/Virgo observing runs and the DESI Legacy Survey

We present a new constraint on the Hubble constant $H_0$ using a sample of well-localized gravitational wave (GW) events detected during the first three LIGO/Virgo observing runs as dark standard sirens. In the case of dark standard sirens, a unique host galaxy is not identified, and the redshift information comes from the distribution of potential host galaxies. From the third LIGO/Virgo observing run detections, we add the asymmetric-mass binary black hole GW190412, the high-confidence GW candidates S191204r, S200129m, and S200311bg to the sample of dark standard sirens analyzed. Our sample contains the top $20\%$ (based on localization) GW events and candidates to date with significant coverage by the Dark Energy Spectroscopic Instrument (DESI) Legacy Survey. We combine the $H_0$ posterior for eight dark siren events, finding $H_0 = 79.8^{+19.1}_{-12.8}~{\rm km~s^{-1}~Mpc^{-1}}$ ($68\%$ Highest Density Interval) for a prior in $H_0$ uniform between $[20,140]~{\rm km~s^{-1}~Mpc^{-1}}$. This result shows that a combination of 8 well-localized dark sirens combined with an appropriate galaxy catalog is able to provide an $H_0$ constraint that is competitive ($\sim 20\%$ versus $18\%$ precision) with a single bright standard siren analysis (i.e. assuming the electromagnetic counterpart) using GW170817. When combining the posterior with that from GW170817, we obtain $H_0 = 72.77^{+11.0}_{-7.55}~{\rm km~s^{-1}~Mpc^{-1}}$. This result is broadly consistent with recent $H_0$ estimates from both the Cosmic Microwave Background and Supernovae.