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