Analytic Waveforms for Eccentric Gravitational Wave Bursts

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.