The impact of peculiar velocities on the estimation of the Hubble constant from gravitational wave standard sirens

ABSTRACT In this work, we investigate the systematic uncertainties that arise from the calculation of the peculiar velocity when estimating the Hubble constant (H0) from gravitational wave standard sirens. We study the GW170817 event and the estimation of the peculiar velocity of its host galaxy, NGC 4993, when using Gaussian smoothing over nearby galaxies. NGC 4993 being a relatively nearby galaxy, at ∼40 Mpc away, is subject to a significant effect of peculiar velocities. We demonstrate a direct dependence of the estimated peculiar velocity value on the choice of smoothing scale. We show that when not accounting for this systematic, a bias of ${\sim }200~{\rm km\, s^{-1}}$ in the peculiar velocity incurs a bias of ${\sim }4~{\rm km\, s^{-1}\, Mpc^{-1}}$ on the Hubble constant. We formulate a Bayesian model that accounts for the dependence of the peculiar velocity on the smoothing scale and by marginalizing over this parameter we remove the need for a choice of smoothing scale. The proposed model yields $H_0 = 68.6 ^{+14.0} _{-8.5}~{\rm km\, s^{-1}\, Mpc^{-1}}$. We demonstrate that under this model a more robust unbiased estimate of the Hubble constant from nearby GW sources is obtained.