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

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 ∼ 10% using 103 golden binary black hole events. Our statistical approach thus provides a robust and prospective inference for determining the peculiar velocity distribution.