Black holes: The next generation—repeated mergers in dense star clusters and their gravitational-wave properties

When two black holes merge in a dense star cluster, they form a new black hole with a well-defined mass and spin. If that ``second-generation'' black hole remains in the cluster, it will continue to participate in dynamical encounters, form binaries, and potentially merge again. Using a grid of 96 dynamical models of dense star clusters and a cosmological model of cluster formation, we explore the production of binary black hole mergers where at least one component of the binary was forged in a previous merger. We create four hypothetical universes where every black hole born in the collapse of a massive star has a dimensionless Kerr spin parameter, ${\ensuremath{\chi}}_{\text{birth}}$, of 0.0, 0.1, 0.2, or 0.5. We show that if all stellar-born black holes are nonspinning (${\ensuremath{\chi}}_{\text{birth}}=0.0$), then more than 10% of merging binary black holes from clusters have components formed from previous mergers, accounting for more than 20% of the mergers from globular clusters detectable by LIGO/Virgo. Furthermore, nearly 7% of detectable mergers would have a component with a mass $\ensuremath{\gtrsim}55\text{ }\text{ }{M}_{\ensuremath{\bigodot}}$, placing it clearly in the mass ``gap'' region where black holes cannot form from isolated collapsing stars due to the pulsational-pair instability mechanism. On the other hand, if black holes are born spinning, then the contribution from these second-generation mergers decreases, making up as little as 1% of all detections from globular clusters when ${\ensuremath{\chi}}_{\text{birth}}=0.5$. We make quantitative predictions for the detected masses, mass ratios, and spin properties of first- and second-generation mergers from dense star clusters, and show how these distributions are highly sensitive to the birth spins of black holes.