Dependence of peculiar velocity on the host properties of the gravitational wave sources and its impact on the measurement of Hubble constant

Accurate measurement of the Hubble constant from standard sirens such as the gravitational wave (GW) sources with electromagnetic counterparts relies on the robust peculiar velocity correction of the redshift of the host galaxy. We show in this work that the peculiar velocity of the host galaxies exhibits a correlation with the properties of the host galaxy primarily such as its stellar mass and this correlation also evolves with redshift. As the galaxies of higher stellar mass tend to form in galaxies with higher halo masses which are located in spatial regions having a non-linear fluctuation in the density field of the matter distribution, the root mean square (RMS) peculiar velocity of more massive galaxies is higher. As a result, depending on the formation channel of the binary compact objects, the peculiar velocity contamination to the galaxies will be different. The variation in the peculiar velocity of the host galaxies can lead to a significant variation in the estimation of the Hubble constant inferred using sources such as Binary Neutron Stars (BNSs). For the network of GW detectors such as LIGO-Virgo-KAGRA (LVK), LVK+LIGO-India, and Cosmic Explorer+Einstein Telescope, the variation in the precision of Hubble constant inferred from 10 bright siren events can vary from $\sim 5.4 - 6\%$, $\sim 4.5 - 5.3\%$ and $\sim 1.1 - 2.7\%$ respectively. The impact of such a correlation between peculiar velocity and stellar mass on the inference of the Hubble constant is not only limited to GW sources but also applicable to type-Ia supernovae.