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Abstract

We perform a statistical standard siren analysis of GW170817. Our analysis
does not utilize knowledge of NGC 4993 as the unique host galaxy of the optical
counterpart to GW170817. Instead, we consider each galaxy within the GW170817
localization region as a potential host; combining the redshift from each
galaxy with the distance estimate from GW170817 provides an estimate of the
Hubble constant, $H_0$. We then combine the $H_0$ values from all the galaxies
to provide a final measurement of $H_0$. We explore the dependence of our
results on the thresholds by which galaxies are included in our sample, as well
as the impact of weighting the galaxies by stellar mass and star-formation
rate. Considering all galaxies brighter than $0.01 L^\star_B$ as equally likely
to host a BNS merger, we find $H_0= 76^{+48}_{-23}$ km s$^{-1}$ Mpc$^{-1}$
(maximum a posteriori and 68.3% highest density posterior interval; assuming a
flat $H_0$ prior in the range $\left[ 10, 220 \right]$ km s$^{-1}$ Mpc$^{-1}$).
Restricting only to galaxies brighter than $0.626 L^\star_B$ tightens the
measurement to $H_0= 77^{+37}_{-18}$ km s$^{-1}$ Mpc$^{-1}$. We show that
weighting the host galaxies by stellar mass or star-formation rate provides
entirely consistent results with potentially tighter constraints. While these
statistical estimates are inferior to the value from the counterpart standard
siren measurement utilizing NGC 4993 as the unique host, $H_0=76^{+19}_{-13}$
km s$^{-1}$ Mpc$^{-1}$ (determined from the same publicly available data), our
analysis is a proof-of-principle demonstration of the statistical approach
first proposed by Bernard Schutz over 30 years ago.