Demographics of Hierarchical Black Hole Mergers in Dense Star Clusters

With about a hundred mergers of binary black holes (BBHs) detected via gravitational waves by the LIGO-Virgo-KAGRA (LVK) Collaboration, our understanding of the darkest objects in the Universe has taken unparalleled steps forward. While most of the events are expected to consist of BHs directly formed from the collapse of massive stars, some may contain the remnants of previous BBH mergers. In the most massive globular clusters and in nuclear star clusters, successive mergers can produce second- (2G) or higher-generation BHs, and even form intermediate-mass BHs. Overall, we predict that up to $\sim 10\%$, $\sim 1\%$ or $\sim 0.1\%$ of the BBH mergers have one component being a 2G, 3G, or 4G BH, respectively. Assuming that $\sim 500$ BBH mergers will be detected in O4 by LVK, this means that $\sim 50$, $\sim 5$, or $\sim 0.5$ events, respectively, will involve a 2G, 3G, or 4G BH, if most sources are produced dynamically in dense star clusters. With their distinctive signatures of higher masses and spins, such hierarchical mergers offer an unprecedented opportunity to learn about the BH populations in the densest stellar systems and to shed light on the elusive intermediate-mass BHs that may form therein.