Eccentric Pairs: Analytic Gravitational Waves from Binary Black Holes in Elliptic Orbits

Abstract

Gravitational waves (GW) from eccentric binaries have intricate signals encoding important features about the location, creation and evolution of the sources. Eccentricity shortens the merger time, making the emitted GW statistically predominant in the observed data once detectors will reach the required sensitivity. We present a novel implementation of fully analytical GW templates from eccentric binary black hole (BBH) mergers within the \texttt{Wolfram Mathematica} software. We increase the accuracy by identifying and minimizing the possible source of errors. We start with an overview of the physics involved in eccentric mergers, then assemble the strain for the inspiral by employing up to six post-Newtonian (PN) corrections. We complete the eccentric inspiral with the quasi-circular Backwards one Body (BoB) merger model in frequency, amplitude and phase, then we build the hybrid GW strain for the whole evolution of the binary. For low eccentricity we reach coincidence in the overlap, with no ambiguity in the time interval, a remarkable improvement from the usual matching techniques. For high-eccentricity we compensate for the implicit quasi-circular assumption of the BOB approach, by introducing a small rescaling in amplitude. Our streamlined implementation is relevant for the new field of GW astronomy and is straightforward to understand, use and extend, offering researchers in the field a valuable open resource tool.