# Eccentric, nonspinning, inspiral, Gaussian-process merger approximant for the detection and characterization of eccentric binary black hole mergers

arXiv: https://arxiv.org/abs/1711.06276 · HTML: https://mlsanity.com/paper/1711.06276/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 16 Nov 2017.

## Built on by (most cited first, 2 of 2)

- [Advances in Machine and Deep Learning for Modeling and Real-time Detection of Multi-Messenger Sources](https://mlsanity.com/paper/2105.06479/) (2021)
- [Discovery of Interpretable Surrogates via Agentic AI: Application to Gravitational Waves](https://mlsanity.com/paper/2605.11280/) (2026)

## Abstract (arXiv)

We present textttENIGMA, 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 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 textttENIGMA reproduces with excellent accuracy the dynamics of quasi-circular compact binaries. We validate textttENIGMA using a set of textttEinstein Toolkit eccentric numerical relativity waveforms, which describe eccentric binary black hole mergers with mass-ratios between 1 ≤ q ≤ 5.5, and eccentricities e0 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. We use textttENIGMA to show that GW150914, GW151226, GW170104, GW170814 and GW170608 can be effectively recovered with spinning, quasi-circular templates if the eccentricity of these events at a gravitational wave frequency of 10Hz satisfies e0≤ 0.175,, 0.125,,0.175,,0.175,, 0.125, respectively. We show that if these systems have eccentricities e0~ 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. Using our catalog of eccentric numerical relativity simulations, we discuss the importance of including higher-order waveform multipoles in gravitational wave searches of eccentric binary black hole mergers.