# Black Holes: The Next Generation -- Repeated Mergers in Dense Star Clusters and their Gravitational-Wave Properties

## TL;DR

This study models how repeated black hole mergers in dense star clusters produce distinctive gravitational-wave signals, with the likelihood and properties of second-generation mergers highly dependent on initial black hole spins.

## Contribution

It introduces a comprehensive set of dynamical models and cosmological simulations to predict the properties and frequencies of second-generation black hole mergers in dense star clusters.

## Key findings

- Over 10% of mergers involve second-generation black holes if initial spins are zero.
- Approximately 7% of detectable mergers have black holes in the mass gap region.
- The contribution of second-generation mergers decreases significantly with higher initial black hole spins.

## Abstract

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, $\chi_{\rm birth}$, of 0.0, 0.1, 0.2, or 0.5. We show that if all stellar-born black holes are non-spinning ($\chi_{\rm birth} = 0.0$), 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 $\gtrsim 55M_{\odot}$, placing them 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 $\chi_{\rm birth} = 0.5$. 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.