Building Fully Analytic Gravitational Waves from Eccentric Binaries

The first observation of gravitational waves (GW) by the Laser Interferometer Gravitational-Wave Observatory in 2015 marked the beginning of the new field of GW astronomy. All GW detections reported until now come from circularized binaries, because current detectors don't have enough sensitivity to detect eccentricity. As techniques improve, detection of GW from eccentric binaries will become not only possible, but preponderant, because they collide faster. The eccentricity encoded in the GW signal reveals valuable information about the long-time evolution of the binary. To decipher it is essential to have complete, accurate and easily reproducible GW templates for elliptic binaries. GW data analysis libraries contain very few eccentricity methods because they are challenging to build and to describe due to the complex physics involved. In this work we develop and share the knowledge necessary to understand and build fully analytic eccentric GW templates, using published scientific results. We compare various methods used to determine the mass, spin and fundamental quasi-normal resonance mode of the final black hole, highlighting some subtleties regarding the inherent ambiguities that enter in those methods. We employ two related analytic models for generating GW in the strong field of the merger: the Implicit Rotating Source and the Backward one Body methods, and analyze their performance against numerically generated GWs. Our goal is to make all these intricate methods less intimidating and more accessible to a larger audience, which is imperative in training researchers and students into the next generation of GW scientists.