ENIGMA: Eccentric, Non-spinning, Inspiral Gaussian-process Merger Approximant for the characterization of eccentric binary black hole mergers

Abstract

We present \(\texttt{ENIGMA}\), a time domain, inspiral-merger-ringdown waveform model that describes non-spinning binary black holes systems that evolve on moderately eccentric orbits. The inspiral evolution is described using a consistent combination of post-Newtonian theory, self-force and black hole perturbation theory. Assuming moderately eccentric binaries that circularize prior to coalescence, we smoothly match the eccentric inspiral with a stand-alone, quasi-circular merger, which is constructed using machine learning algorithms that are trained with quasi-circular numerical relativity waveforms. We show that \(\texttt{ENIGMA}\) reproduces with excellent accuracy the dynamics of quasi-circular compact binaries. We validate \(\texttt{ENIGMA}\) using a set of \(\texttt{Einstein Toolkit}\) eccentric numerical relativity waveforms, which describe eccentric binary black hole mergers with mass-ratios between \(1 \leq q \leq 5.5\), and eccentricities \(e_0 \lesssim 0.2\) ten orbits before merger. We use this model to explore in detail the physics that can be extracted with moderately eccentric, non-spinning binary black hole mergers. In particular, we use \(\texttt{ENIGMA}\) to show that the gravitational wave transients GW150914, GW151226, GW170104 and GW170814 can be effectively recovered with spinning, quasi-circular templates if the eccentricity of these events at a gravitational wave frequency of 10Hz satisfies \(e_0\leq \{0.175,\, 0.125,\,0.175,\,0.175\}\), respectively. We show that if these systems have eccentricities \(e_0\sim 0.1\) at a gravitational wave frequency of 10Hz, they can be misclassified as quasi-circular binaries due to parameter space degeneracies between eccentricity and spin corrections.