The Stochastic Gravitational Wave Background from Close Hyperbolic Encounters of Primordial Black Holes in Dense Clusters

The inner part of dense clusters of primordial black holes is an active environment where multiple scattering processes take place. Some of them give rise from time to time to bounded pairs, and the rest ends up with a single scattering event. The former eventually evolves to a binary black hole (BBH) emitting periodic gravitational waves (GWs), while the latter with a short distance, called close hyperbolic encounters (CHE), emits a strong GW burst. We make the first calculation of the stochastic GW background originating from overlapped GWs from CHEs. We find that there is a chance that CHE dominates the BBH contribution in the LISA frequency band. It could also be tested by third-generation ground-based GW detectors such as Einstein Telescope and Cosmic Explorer