Characterization of numerical relativity waveforms of eccentric binary black hole mergers

We introduce a method to quantify the initial eccentricity, gravitational wave frequency, and mean anomaly of numerical relativity simulations that describe nonspinning black holes on moderately eccentric orbits. We demonstrate that this method provides a robust characterization of eccentric binary black hole mergers with mass ratios $q\ensuremath{\le}10$ and eccentricities ${e}_{0}\ensuremath{\le}0.2$ fifteen cycles before merger. We quantify the circularization rate of a variety of eccentric numerical relativity waveforms introduced in E. A. Huerta et al. [arXiv:1901.07038] by computing overlaps with their quasicircular counterparts, finding that $50M$ before merger they attain overlaps $\mathcal{O}\ensuremath{\ge}0.99$, furnishing evidence for the circularization of moderately eccentric binary black hole mergers with mass ratios $q\ensuremath{\le}10$. We also quantify the importance of including higher-order waveform modes for the characterization of eccentric binary black hole mergers. Using two types of numerical waveforms, one that includes $(\ensuremath{\ell},|m|)={(2,2),(2,1),(3,3),(3,2),(3,1),(4,4),(4,3),\phantom{\rule{0ex}{0ex}}(4,2),(4,1)}$ and one that only includes the $\ensuremath{\ell}=|m|=2$ mode, we find that the overlap between these two classes of waveforms is as low as $\mathcal{O}=0.89$ for $q=10$ eccentric binary black hole mergers, underscoring the need to include higher-order waveform modes for the description of these gravitational wave sources. We discuss the implications of these findings for future source modeling and gravitational wave detection efforts.