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 $2.5$ direct 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 $$ when the emitted gravitational wave frequency is 10 Hz in the source frame, while in YSCs this fraction rises to $1.6$. Approximately $of these mergers are produced by chaotic, resonant interactions where temporary binaries are continuously formed and destroyed, while$ arise from an almost direct collision of two black holes (BHs). Lastly, $6$ 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 ($60 BH$/M$_ odot and intermediate-mass BH odot$) BHs accounting for approximately $and$1.6$of the mergers in YSCs,$ and $0.7$ in GCs, and $and$0.4$ in NSCs, respectively.