Gravitational Waves from Hyperbolic Encounters of Primordial Black Holes in Dwarf Galaxies

We investigate the stochastic gravitational wave background (SGWB) generated by primordial black holes (PBHs) in the dense cores of dwarf galaxies (DGs), considering both hierarchical binary black hole (BBH) mergers and close hyperbolic encounters (CHEs). Extending our previous merger framework, we incorporate up to four successive generations of PBHs within a Hubble time and quantify the GW emission from both channels. Our results show that while BBHs dominate the total emission, CHEs occur earlier, provide the first GW signals, and contribute a continuous though subdominant background that becomes relatively more significant once the initial PBH population is depleted and binary formation is suppressed. We compute the resulting SGWB spectra, demonstrating that BBHs and CHEs imprint distinct frequency dependencies consistent with analytical expectations. We then compare the predicted signals with the sensitivity of observatories such as LISA, DECIGO, ET, IPTA, and SKA. The numerical implementation is publicly available at \href{https://github.com/TadeoDGAguilar/PBHs_and_GWs_into_DG}.