An accurate method to determine the systematics due to the peculiar
  velocities of galaxies in measuring the Hubble constant from gravitational
  wave standard sirens
  We propose a novel approach to accurately pin down the systematics due to the
peculiar velocities of galaxies in measuring the Hubble constant from nearby
galaxies in current and future gravitational-wave (GW) standard-siren
experiments. Given the precision that future GW standard-siren experiments aim
to achieve, the peculiar velocities of nearby galaxies will be a major source
of uncertainty. Unlike the conventional backward reconstruction that requires
additional redshift-independent distance indicators to recover the peculiar
velocity field, we forwardly model the peculiar velocity field by using a
high-fidelity mock galaxy catalog built from high-resolution dark matter only
(DMO) N-body simulations with a physically motivated subhalo abundance matching
technique without introducing any free parameters. Our mock galaxy catalog can
impressively well reproduce the observed spectroscopic redshift space
distortions (RSDs) in highly non-linear regimes down to very small scales,
which is a robust test of the velocity field of our mock galaxy catalog. Based
on this mock galaxy catalog, we accurately, for the first time, measure the
peculiar velocity probability distributions for the SDSS main galaxy samples.
We find that the systematics induced by the peculiar velocities of SDSS like
galaxies on the measured Hubble constant can be reduced to below
$1\%$($1\sigma$) for GW host galaxies with a Hubble flow redshift just above
$0.13$, a distance that can be well probed by future GW experiments and galaxy
surveys.
