A Standard Siren Measurement of the Hubble Constant from GW170817 without the Electromagnetic Counterpart

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 redshifts from all of the galaxies with the distance estimate from GW170817 provides an estimate of the Hubble constant, H <SUB>0</SUB>. Considering all galaxies brighter than 0.626{L}<SUB>B</SUB><SUP>\star </SUP> as equally likely to host a binary neutron star merger, we find {H}<SUB>0</SUB>={77}<SUB>-18</SUB><SUP>+37</SUP> km s<SUP>-1</SUP> Mpc<SUP>-1</SUP> (maximum a posteriori and 68.3% highest density posterior interval; assuming a flat H <SUB>0</SUB> prior in the range ≤ft[10,220\right] km s<SUP>-1</SUP> Mpc<SUP>-1</SUP>). We explore the dependence of our results on the thresholds by which galaxies are included in our sample, and we show that weighting the host galaxies by stellar mass or star formation rate provides entirely consistent results with potentially tighter constraints. By applying the method to simulated gravitational-wave events and a realistic galaxy catalog we show that, because of the small localization volume, this statistical standard siren analysis of GW170817 provides an unusually informative (top 10%) constraint. Under optimistic assumptions for galaxy completeness and redshift uncertainty, we find that dark binary neutron star measurements of H <SUB>0</SUB> will converge as 40 % /\sqrt{(N)}, where N is the number of sources. While these statistical estimates are inferior to the value from the counterpart standard siren measurement utilizing NGC 4993 as the unique host, {H}<SUB>0</SUB>={76}<SUB>-13</SUB><SUP>+19</SUP> km s<SUP>-1</SUP> Mpc<SUP>-1</SUP> (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 yr ago.