We introduce a method to quantify the initial eccentricity , gravitational wave frequency , and mean anomaly of numerical relativity simulations that describe non-spinning 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 \leq 10 and eccentricities e _ { 0 } \leq 0.2 fifteen cycles before merger .
We quantify the circularization rate of a variety of eccentric numerical relativity waveforms introduced in [ ] by computing overlaps with their quasi-circular counterparts , finding that 50 M before merger they attain overlaps { \cal { O } } \geq 0.99 , furnishing evidence for the circularization of moderately eccentric binary black hole mergers with mass-ratios q \leq 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 ( \ell, \abs { m } ) = \ { ( 2 , 2 ) , ( 2 , 1 ) , ( 3 , 3 ) , ( 3 , 2 ) , ( 3 , 1 ) , ( 4 , 4 ) ,% ( 4 , 3 ) , ( 4 , 2 ) , ( 4 , 1 ) \ } and one that only includes the \ell = \abs { m } = 2 mode , we find that the overlap between these two classes of waveforms is as low as { \cal { 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 .