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.
