Constraints on peculiar velocity distribution of binary black holes using gravitational waves with GWTC-3

TL;DR

This paper uses hierarchical Bayesian modeling on GWTC-3 data to estimate the peculiar velocity distribution of binary black holes, highlighting potential improvements with future detectors like the Einstein Telescope.

Contribution

It introduces a robust hierarchical Bayesian method to infer binary black hole peculiar velocities from gravitational wave data, considering future detector capabilities.

Findings

Current constraints on velocity distribution are weak.

Next-generation detectors can reduce uncertainty to about 10%.

Method provides a robust framework for future velocity distribution inference.

Abstract

Peculiar velocity encodes rich information about the formation, dynamics, evolution, and merging history of binary black holes. In this work, we employ a hierarchical Bayesian model to infer the peculiar velocity distribution of binary black holes. We use the data from GWTC-3 and assume a Maxwell-Boltzmann distribution for the peculiar velocities, but do not consider the dependence of peculiar velocity on the masses of black hole binaries. The constraint on the peculiar velocity distribution parameter, $v_0$, is weak and uninformative. However, the determination of peculiar velocity distribution can be significantly improved with next-generation ground-based gravitational wave detectors. For the Einstein Telescope, the relative uncertainty of $v_0$ will reduce to $\sim$ 10\% using $10^3$ golden binary black hole events. Our statistical approach thus provides a robust and prospective inference for determining the peculiar velocity distribution.