# Gravitational wave bursts from Primordial Black Hole hyperbolic encounters

## TL;DR

This paper models gravitational wave bursts from hyperbolic encounters of primordial black holes in dense clusters, predicting detectable signals for current and future observatories like AdvLIGO and LISA.

## Contribution

It provides analytical expressions for GW emission from PBH hyperbolic encounters and estimates detection rates across different mass and velocity configurations.

## Key findings

- AdvLIGO may detect ~10 events per year per Gpc^3.
- LISA could observe ~1000 events per year per Gpc^3.
- Event durations range from milliseconds to hours depending on the detector.

## Abstract

We propose that Gravitational Wave (GW) bursts with millisecond durations can be explained by the GW emission from the hyperbolic encounters of Primordial Black Holes in dense clusters. These bursts are single events, with the bulk of the released energy happening during the closest approach, and emitted in frequencies within the AdvLIGO sensitivity range. We provide expressions for the shape of the GW emission in terms of the peak frequency and amplitude, and estimate the rates of these events for a variety of mass and velocity configurations. We study the regions of parameter space that will allow detection by both AdvLIGO and, in the future, LISA. We find for realistic configurations, with total mass $M\sim60\,M_\odot$, relative velocities $v\sim 0.01\,c$, and impact parameters $b\sim10^{-3}$ AU, for AdvLIGO an expected event rate is ${\cal O}(10)$ events/yr/Gpc$^3$ with millisecond durations. For LISA, the typical duration is in the range of minutes to hours and the event-rate is ${\cal O}(10^3)$ events/yr/Gpc$^3$ for both $10^3\,M_\odot$ IMBH and $10^6\,M_\odot$ SMBH encounters. We also study the distribution functions of eccentricities, peak frequencies and characteristic timescales that can be expected for a population of scattering PBH with a log-normal distribution in masses, different relative velocities and a flat prior on the impact parameter.