Comparisons of eccentric binary black hole simulations with post-Newtonian models

We present the first comparison between numerical relativity (NR) simulations of an eccentric binary black hole system with corresponding post-Newtonian (PN) results. We evolve an equal-mass, nonspinning configuration with an initial eccentricity e0. 1 for 21 gravitational wave cycles before merger, and find agreement in the gravitational wave phase with an adiabatic eccentric PN model with 2 PN radiation reaction within 0. 1 radians for 10 cycles. The NR and PN phase difference grows to 0. 7 radians by 5 cycles before merger. We find that these results can be obtained by expanding the eccentric PN expressions in terms of the frequency-related variable x= () ^2/3 with M the total mass of the binary. When using instead the mean motion n=2/P, where P is the orbital period, the comparison leads to significant disagreements with NR.