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

Abstract

The 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 for the first time using GWTC-3 by assuming a Maxwell-Boltzmann distribution for the peculiar velocities. The constraint on the peculiar velocity distribution parameter is rather weak and uninformative with the current GWTC-3 data release. However, the measurement of the peculiar velocity distribution can be significantly improved with the next-generation ground-based gravitational wave detectors. For instance, the uncertainty on the peculiar velocity distribution parameter will be measured within $\sim$ 10\% with $10^3$ golden binary black hole events for the Einstein Telescope. We, therefore, conclude that our statistical approach provides a robust inference for the peculiar velocity distribution.Comment: 15 pages, 2 figures