ENIGMA: Eccentric, Non-spinning, Inspiral Gaussian-process Merger Approximant for the characterization of eccentric binary black hole mergers
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We present 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 ENIGMA reproduces with excellent accuracy the dynamics of quasi-circular compact binaries. We validate ENIGMA using a set of Einstein Toolkit eccentric numerical relativity waveforms, which describe eccentric binary black hole mergers with mass-ratios between 1 ≤ q ≤ 5.5, and eccentricities e_0 ≲ 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 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≤{0.175, 0.125, 0.175, 0.175}, respectively. We show that if these systems have eccentricities e_0∼ 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.
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