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

Abstract

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}.

Figures (6)

• Figure 1: Illustration of two BHs with masses $m_i$ and $m_j$ with relative velocity, $v_0$, in a close hyperbolic encounter, where $r_{\rm min}$ is the closest approach to produce GWs in this process.
• Figure 2: Energy loss from GW emission due to binary formation (solid line) and CHEs (dashed line) for the initial PBH population. Stars indicate the onset times of binary formation and CHEs. Vertical dotted lines mark successive epochs, with up to four BH generations forming within a Hubble time.
• Figure 3: Redshift evolution of GW emission from BBHs and CHEs for four initial masses. CHEs appear earlier than BBH formations, and while BBH contributions decrease at lower redshifts, CHEs continue to rise. Vertical dotted lines mark successive epochs in redshift.
• Figure 4: GW emission from BBHs and CHEs for all generated masses, shown from the 2nd epoch ($z = 1.88$) to the present, for an initial PBH mass of $10\,M_{\odot}$.
• Figure 5: GW emission from BBHs and CHEs across all PBH generations for four different initial masses. Results are shown from redshift 5 to the present, focusing on 2G PBHs and beyond. Upper left panel: values in the legend are multiplied by $10\,M_{\odot}$. Upper right panel: values in the legend are multiplied by $1\,M_{\odot}$. Lower left panel: values in the legend are multiplied by $10^{-2}\,M_{\odot}$. Lower right panel: values in the legend are multiplied by $10^{-14}\,M_{\odot}$.