The Impact of Peculiar Velocities on the Estimation of the Hubble
  Constant from Gravitational Wave Standard Sirens
  In this work we investigate the systematic uncertainties that arise from the
calculation of the peculiar velocity when estimating the Hubble constant
($H_0$) 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 $\sim 40 \ {\rm Mpc}$ 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
marginalising 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.
