A Model-Independent Framework for Gravitational-Wave Reconstruction of Binary Black Hole Hyperbolic Encounters in Ground-Based Interferometers

TL;DR

This work addresses the detectability of binary black hole hyperbolic encounters—short, single-cycle GW bursts—by ground-based interferometers. It adopts a model-agnostic BayesWave framework, using exponential shapelets to reconstruct simulated hyperbolic-waveform injections across a range of mass ratios and detector networks, and compares performance to Morlet-Gabor and chirplet frames. The study finds detectable distances up to $d_L \sim 40-200$ Mpc for a $20\,M_{\odot}$ total-mass system and provides preliminary detection-rate forecasts for LIGO, A+, Cosmic Explorer, and the Einstein Telescope, with CE/ET offering the strongest prospects. The results highlight that shapelets can yield competitive reconstruction fidelity with potentially fewer basis functions, informing search strategies for non-merger GW bursts in current and future detectors.

Abstract

Binary black hole hyperbolic encounters represent a dynamical interaction in which two black holes undergo a close fly-by, emitting gravitational-wave bremsstrahlung in the form of a short-duration, single-cycle transient. These events are expected to occur in dense stellar environments such as globular clusters and both active and quiescent galactic nuclei. In this work, we constrain the detection sensitivity for hyperbolic encounters of black hole pairs with a range of asymmetric masses. We employ BayesWave, a wavelet-based morphology-independent algorithm to characterize hyperbolic encounter waveforms in simulated detector noise; for this study, we explore the use of exponential shapelets. We find that a typical hyperbolic orbit with total mass $20 M_{\odot}$ can be detected up to distance $d_L \sim 40 - 200$ Mpc, and we forecast the possibility of detection by ground-based current and future gravitational wave interferometers.

Figures (9)

• Figure 1: Sensitivity curves for LIGO Cahillane:2022pqm, A+ barsotti2018a+, Cosmic Explorer Reitze:2019iox, and Einstein Telescope Maggiore:2019uih (data fromT1500293). Previous estimates Kocsis:2006hqBini:2023gaj suggest that hyperbolic encounters are most common around $10$Hz. Detectors with improved low-frequency sensitivity, such as Cosmic Explorer and the Einstein Telescope, are better suited to capturing these signals than current-generation instruments like LIGO or even A+.
• Figure 2: Examples of $n=0,1,2,3$ shapelets in the frequency domain (top), and time domain (bottom). For all shapelets, $Q=20$, $f_0=200\mathrm{Hz}$, and $t_0=0\mathrm{s}$.
• Figure 3: Example BayesWave waveform reconstruction of simulated white noise bursts (WNBs) with the three frame function families used in this study. WNBs are unpolarized signals with complicated frequency structure, (due to their localization in time) providing a a good test for the faithfulness of BayesWave's reconstruction.
• Figure 4: Time-domain reconstruction of GW150914, the first GW event, using BayesWave with shapelets and the standard Morlet-Gabor wavelet reconstructions, respectively. This analysis corresponds to LIGO-Hanford.
• Figure 5: Waveforms used for this analysis, from face-on binaries with total mass $20\,{\mathrm{M}_{\odot}}$. Each panel displays is a waveform with plus (solid) and cross (dashed) polarization. This grid spans a parameter space with mass ratios $q = [1, 2, 4, 8, 16]$ (displayed row-wise) and several initial angular momenta, represented column-wise. The waveforms are more narrowly spaced out in time for a larger mass ratio.