The Impact of Peculiar Velocities on the Estimation of the Hubble Constant from Gravitational Wave Standard Sirens

TL;DR

This paper examines how peculiar velocity uncertainties affect Hubble constant estimates from gravitational wave standard sirens, proposing a Bayesian model to mitigate bias and improve robustness in nearby galaxy measurements.

Contribution

It introduces a Bayesian approach that accounts for smoothing scale dependence in peculiar velocity estimates, reducing systematic bias in Hubble constant determination.

Findings

Peculiar velocity bias can lead to a 4 km/s/Mpc error in H0.

The Bayesian model yields H0 = 68.6 km/s/Mpc with large uncertainties.

Marginalizing over smoothing scale removes the need for fixed scale choice.

Abstract

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.