Mass Distribution of Binary Black Hole Mergers from Young and Old Dense Star Clusters

Dense star clusters are thought to contribute significantly to the merger rates of stellar-mass binary black holes (BBHs) detected by the LIGO-Virgo-KAGRA collaboration. We combine $N$-body dynamic models of realistic dense star clusters with cluster formation histories to estimate the merger rate distribution as a function of primary mass for merging BBHs formed in these environments. It has been argued that dense star clusters – most notably old globular clusters – predominantly produce BBH mergers with primary masses $M_p\approx 30M_{\odot }$. We show that dense star clusters forming at lower redshifts – and thus having higher metallicities – naturally produce lower-mass BBH mergers. We find that cluster BBH mergers span a wide range of primary mass, from about $6M_{\odot }$ to above $100M_{\odot }$, with a peak near $8M_{\odot }$, reproducing the overall merger rate distribution inferred from gravitational wave detections. Our results show that most low-mass BBH mergers (about $95\mathrm{\%}$ with $M_p\lesssim 20M_{\odot }$) originate in metal-rich ($Z\sim Z_{\odot }$) dense star clusters, while more massive BBH mergers form predominately in metal-poor globular clusters. We also discuss the role of hierarchical mergers in shaping the BBH mass distribution. Gravitational wave detection of dynamically-formed low-mass BBH mergers – potentially identifiable by features such as isotropic spin distributions – may serve as probes of cluster formation histories in metal-rich environments at low redshifts.