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 both these models, and validate the time domain model against numerical waveforms. We further show how to use these individual waveforms to detect a repeated burst source.

Repeated Bursts: Gravitational Waves from Highly Eccentric Binaries

“…Using the balance laws in the quadrupole approximation, one can obtain evolution equations for the semi-latus rectum p and orbital eccentricity e in the adiabatic limit (see Eqs. ( 36)-( 37) in [49]).…”

“…The time-domain quadrupole waveform can then be written purely in terms of ψ and is given in Eq. ( 45) in [49].…”

“…A recent development in pursuit of analytic waveforms for highly eccentric binaries is the effective fly-by (EFB) formalism [49]. The formalism seeks an accurate description of the gravitational wave bursts from individual pericenter passages, which may be strung together to create inspiral waveforms using the timing models described in Sec.…”

“…Replace the Bessel function J k (ke) with it's uniform asymptotic expansion about k → ∞. To leading order J k (ke 26) in [49]). For a comparison of the asymptotic expansion to the exact function, see Fig.…”

Active Galactic Nuclei as Factories for Eccentric Black Hole Mergers

“…mergers have an eccentricity e > 0.1 at f GW > Hz or above. Note that sources forming in band, will generally appear as burst sources 36 , and some will even remain eccentric close to merger.…”