Stochastic gravitational wave background from binary black hole mergers dynamically assembled in dense star clusters

With about a hundred binary black hole (BBH) mergers detected by LIGO-Virgo-KAGRA, and with several hundreds expected in the current O4 run, gravitational waves (GWs) are revolutionizing our understanding of the Universe. Some BBH sources are too faint to be individually detected, but collectively they may give rise to a stochastic GW background (SGWB). In this paper, we calculate the SGWB associated with BBH mergers dynamically assembled in dense star clusters, using state-of-the-art numerical models. We discuss the role of modeling the evolution of the mass distribution of BBH mergers, which has significant implications for model selection and parameter estimation, and could be used to distinguish between different channels of BBH formation. We demonstrate how the birth properties of star clusters affect the amplitude and frequency spectrum of the SGWB, and show that upcoming observation runs of ground-based GW detectors may be sensitive enough to detect it. Even in the case of a nondetection, we find that GW data can be used to constrain the highly uncertain cluster birth properties, which can complement direct observations of young massive clusters and protostar clusters in the early Universe by The James Webb Space Telescope.