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We propose a novel approach to accurately pin down the systematics due to thepeculiar velocities of galaxies in measuring the Hubble constant from nearbygalaxies in current and future gravitational-wave (GW) standard-sirenexperiments. Given the precision that future GW standard-siren experiments aimto achieve, the peculiar velocities of nearby galaxies will be a major sourceof uncertainty. Unlike the conventional backward reconstruction that requiresadditional redshift-independent distance indicators to recover the peculiarvelocity field, we forwardly model the peculiar velocity field by using ahigh-fidelity mock galaxy catalog built from high-resolution dark matter only(DMO) N-body simulations with a physically motivated subhalo abundance matchingtechnique without introducing any free parameters. Our mock galaxy catalog canimpressively well reproduce the observed spectroscopic redshift spacedistortions (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. Basedon this mock galaxy catalog, we accurately, for the first time, measure thepeculiar velocity probability distributions for the SDSS main galaxy samples.We find that the systematics induced by the peculiar velocities of SDSS likegalaxies 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 galaxysurveys.

physical review. d/physical review. d.

An accurate method to determine the systematics due to the peculiar  velocities of galaxies in measuring the Hubble constant from gravitational  wave standard sirens