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 x 10(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 >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 similar to 63% of these mergers are produced by chaotic, resonant interactions where temporary binaries are continuously formed and destroyed, while similar to 31% arise from an almost direct collision of two black holes (BHs). Lastly, similar to 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 <= M-BH/M-circle star <= 100) and intermediate-mass (M-BH >= 100 M-circle star) BHs accounting for approximately similar to 44% and 1.6% of the mergers in YSCs, similar to 33% and 0.7% in GCs, and similar to 28% and 0.4% in NSCs, respectively