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We compute the stochastic gravitational wave (GW) background generated byblack hole-black hole (BH-BH) hyperbolic encounters with eccentricities closeto one and compare them with the respective sensitivity curves of planned GWdetectors. We use the Keplerian potential to model the orbits of the encountersand the quadrupole formula to compute the emitted GWs. We take into accounthyperbolic encounters that take place in clusters up to redshift $5$, with BH'smasses spanning from $5 M_{\odot}$ to $55 M_{\odot}$. We assume the clusters tobe virialized and we study several cluster models with different mass andvirial velocity, and finally, provide an accumulative result to display thebackground in an average sense. Using the maxima and the minima of ouraccumulative result for each frequency, we provide analytical expressions forboth optimistic and pessimistic scenarios. Our results imply that thebackground from these encounters are likely to be detected by the thirdgeneration detectors Cosmic explorer, and Einstein telescope, while the tailsection at lower frequencies intersects with DECIGO -- making it a possiblesource for both ground and space based future GW detectors.

Detectability of gravitational wave stochastic background from weakly hyperbolic encounters