Eccentric black hole mergers via three-body interactions in young, globular, and nuclear star clusters

Eccentric mergers are a signature of the dynamical formation channel of binary black holes (BBHs) in dense stellar environments and hierarchical triple systems. Here, we investigate the formation of eccentric mergers via binary-single interactions by means of $2.5\times10^{5}$ direct $\textit{N}$-body simulations. Our simulations include post-Newtonian terms up to the 2.5th order and model the typical environment of young (YSCs), globular (GCs), and nuclear star clusters (NSCs). Around $0.6\%$ ($1\%$) of our mergers in NSCs (GCs) have an eccentricity ${>0.1}$ when the emitted gravitational wave frequency is 10 Hz in the source frame, while in YSCs this fraction rises to $1.6\%$. Approximately $\sim63\%$ of these mergers are produced by chaotic, resonant interactions where temporary binaries are continuously formed and destroyed, while $\sim31\%$ arise from an almost direct collision of two black holes (BHs). Lastly, $\sim 6\%$ of these eccentric mergers occur in temporary hierarchical triples. We find that binaries undergoing a flyby generally develop smaller tilt angles with respect to exchanges. This result challenges the idea that perfectly isotropic spin orientations are produced by dynamics. The environment dramatically affects BH retention: $0\%$, $3.1\%$, and $19.9\%$ of all the remnant BHs remain in YSCs, GCs, and NSCs, respectively. The fraction of massive BHs also depends on the host cluster properties, with pair-instability ($60\leq\,$M$_{\rm BH}$/M$_{\odot}\leq$100) and intermediate-mass (M$_{\rm BH}\geq$100$\,$M$_{\odot}$) BHs accounting for approximately $\sim44\%$ and $1.6\%$ of the mergers in YSCs, $\sim33\%$ and $0.7\%$ in GCs, and $\sim28\%$ and $0.4\%$ in NSCs, respectively.