Eccentric binary black hole inspiral-merger-ringdown gravitational waveform model from numerical relativity and post-Newtonian theory

We present a prescription for computing gravitational waveforms for the inspiral, merger and ringdown of nonspinning moderately eccentric binary black hole systems. The inspiral waveform is computed using the post-Newtonian expansion and the merger waveform is computed by interpolating a small number of quasicircular NR waveforms. The use of circular merger waveforms is possible because binaries with moderate eccentricity circularize in the last few cycles before the merger, which we demonstrate up to mass ratio $q={m}_{1}/{m}_{2}=3$. The complete model is calibrated to 23 numerical relativity (NR) simulations starting $\ensuremath{\approx}20$ cycles before the merger with eccentricities ${e}_{\mathrm{ref}}\ensuremath{\le}0.1$ and mass ratios $q\ensuremath{\le}3$, where ${e}_{\mathrm{ref}}$ is the eccentricity $\ensuremath{\approx}7$ cycles before the merger. The NR waveforms are long enough that they start below 30 Hz (10 Hz) for BBH systems with total mass $M\ensuremath{\ge}80\text{ }\text{ }{M}_{\ensuremath{\bigodot}}$ ($230\text{ }\text{ }{M}_{\ensuremath{\bigodot}}$). We find that, for the sensitivity of advanced LIGO at the time of its first observing run, the eccentric model has a faithfulness with NR of over 97% for systems with total mass $M\ensuremath{\ge}85{M}_{\ensuremath{\bigodot}}$ across the parameter space (${e}_{\mathrm{ref}}\ensuremath{\le}0.1$, $q\ensuremath{\le}3$). For systems with total mass $M\ensuremath{\ge}70{M}_{\ensuremath{\bigodot}}$, the faithfulness is over 97% for ${e}_{\mathrm{ref}}\ensuremath{\lesssim}0.05$ and $q\ensuremath{\le}3$. The NR waveforms and the Mathematica code for the model are publicly available.

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