Velocity correction for Hubble constant measurements from standard sirens

Gravitational wave (GW) sources are an excellent probe of the luminosity distance and offer a novel measure of the Hubble constant, $H_0$. This estimation of $H_0$ from standard sirens requires an accurate estimation of the cosmological redshift of the host galaxy of the GW source, after correcting for its peculiar velocity. Absence of an accurate peculiar velocity correction affects both the precision and accuracy of the measurement of $H_0$, particularly for nearby sources. We propose a framework to incorporate such a peculiar velocity correction for GW sources. A first implementation of our method to the event GW170817 combined with the Very Large Baseline Interferometry (VLBI) observation leads to a revised value of $H_0= 68.3^{+ 4.6}_{-4.5}$ km/s/Mpc. While this revision is minor, it demonstrates that our method makes it possible for obtaining an unbiased and accurate measurements of $H_0$ at the precision required for the standard siren cosmology.