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

## TL;DR

This paper introduces a new method using high-fidelity mock galaxy catalogs from N-body simulations to accurately model galaxy peculiar velocities, significantly reducing systematics in measuring the Hubble constant with gravitational-wave standard sirens.

## Contribution

The paper presents the first use of a physically motivated, parameter-free mock galaxy catalog to precisely measure peculiar velocity distributions and mitigate their impact on Hubble constant measurements.

## Key findings

- Peculiar velocity systematics can be reduced below 1% for certain redshifts.
- Mock galaxy catalog reproduces observed redshift space distortions in non-linear regimes.
- The method enables more accurate Hubble constant measurements from GW standard sirens.

## Abstract

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.