Gravitational wave energy emission and detection rates of Primordial Black Hole hyperbolic encounters

TL;DR

This paper models gravitational wave bursts from primordial black hole hyperbolic encounters, analyzing their energy emission, frequency range, and detection prospects with LIGO and LISA, providing new formulas and correcting previous results.

Contribution

It offers new exact and approximate formulas for the peak frequency of gravitational wave bursts from PBH hyperbolic encounters and corrects prior power spectrum results in the literature.

Findings

GW bursts occur within LIGO and LISA frequency ranges

New formulas improve understanding of peak emission frequencies

Hyperbolic encounter signals help distinguish PBH properties

Abstract

We describe in detail gravitational wave bursts from Primordial Black Hole (PBH) hyperbolic encounters. The bursts are one-time events, with the bulk of the released energy happening during the closest approach, which can be emitted in frequencies that could be within the range of both LIGO (10-1000Hz) and LISA ($10^{-6}-1$ Hz). Furthermore, we correct the results for the power spectrum of hyperbolic encounters found in the literature and present new exact and approximate expressions for the peak frequency of the emission. Note that these GW bursts from hyperbolic encounters between PBH are complementary to the GW emission from the bounded orbits of BHB mergers detected by LIGO, and help breaking degeneracies in the determination of the PBH mass, spin and spatial distributions.