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Abstract

The detection of gravitational-wave signals from coalescing eccentric binary
black holes would yield unprecedented information about the formation and
evolution of compact binaries in specific scenarios, such as dynamical
formation in dense stellar clusters and three-body interactions. The
gravitational-wave searches by the ground-based interferometers, LIGO and
Virgo, rely on analytical waveform models for binaries on quasicircular orbits.
Eccentric merger waveform models are less developed, and only few numerical
simulations of eccentric mergers are publicly available, but several eccentric
inspiral models have been developed from the post-Newtonian expansion. Here we
present a novel method to convert the dominant quadrupolar mode of any circular
analytical binary-black-hole model into an eccentric model. First, using
numerical simulations, we examine the additional amplitude and frequency
modulations of eccentric signals that are not present in their circular
counterparts. Subsequently, we identify suitable analytical descriptions of
those modulations and interpolate key parameters from twelve numerical
simulations designated as our training dataset. This allows us to reconstruct
the modulated amplitude and phase of any waveform up to mass ratio 3 and
eccentricity 0.2. We find that the minimum overlap of the new model with
numerical simulations is around 0.98 over all of our test dataset that are
scaled to a 50M$_\odot$ black-hole binary starting at 35 Hz with aLIGO A+
design sensitivity. A Python package \pyrex easily carries out the computation
of this method.