A Fourier Domain Waveform for Non-Spinning Binaries with Arbitrary Eccentricity

Although the gravitational waves observed by advanced LIGO and Virgo are consistent with compact binaries in a quasi-circular inspiral prior to coalescence, eccentric inspirals are also expected to occur in Nature. Due to their complexity, we currently lack ready-to-use, analytic waveforms in the Fourier domain valid for sufficiently high eccentricity, and such models are crucial to coherently extract weak signals from the noise. We here take the first steps to derive and properly validate an analytic waveform model in the Fourier domain that is valid for inspirals of arbitrary orbital eccentricity. As a proof-of-concept, we build this model to leading post-Newtonian order by combining the stationary phase approximation, a truncated sum of harmonics, and an analytic representation of hypergeometric functions. Through comparisons with numerical post-Newtonian waveforms, we determine how many harmonics are required for a faithful (matches above 99%) representation of the signal up to orbital eccentricities as large as 0.9. As a first byproduct of this analysis, we present a novel technique to maximize the match of eccentric signals over time of coalescence and phase at coalescence. As a second byproduct, we determine which of the different approximations we employ leads to the largest loss in match, which could be used to systematically improve the model because of our analytic control. The future extension of this model to higher post-Newtonian order will allow for an accurate and fast phenomenological hybrid that can account for arbitrary eccentricity inspirals and mergers.