Analytic Waveforms for Eccentric Gravitational Wave Bursts

TL;DR

This paper introduces the first analytic waveforms for highly eccentric binary fly-bys, improving computational efficiency and matching accuracy for gravitational wave burst detection, with potential applications in repeated burst source identification.

Contribution

The authors develop and validate the first analytic effective fly-by waveforms for eccentric binaries, enhancing modeling speed and accuracy over previous numerical methods.

Findings

Time-domain model is twice as fast as numerical quadrupole waveform.

Match with quadrupole waveforms exceeds 0.97, indicating high accuracy.

Match with numerical relativity waveforms is lower due to neglected relativistic effects.

Abstract

We here present the first analytic effective fly-by (EFB) waveforms designed to accurately capture the burst of gravitational radiation from the closest approach of highly eccentric compact binaries. The waveforms are constructed by performing a re-summation procedure on the well-known Fourier series representation of the two-body problem at leading post-Newtonian order. This procedure results in two models: one in the time-domain, and one in the Fourier domain, which makes use of the stationary phase approximation. We discuss the computational efficiency of these models, and find that the time-domain model is roughly twice as fast as a numerical quadrupole waveform. We compare the time-domain model to both numerical, leading post-Newtonian order, quadrupole waveforms and numerical relativity fly-by waveforms using the match statistic. While the match is typically $>0.97$ when compared to the quadrupole waveforms, it is much lower when comparing to the numerical relativity fly-by waveforms, due to neglecting relativistic effects within the model. We further show how to use these individual waveforms to detect a repeated burst source.