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, non-spinning configuration with an initial eccentricity e approximate to 0: 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 = (omega M)(2/3) with M the total mass of the binary. When using instead the mean motion n = 2 pi/P, where P is the orbital period, the comparison leads to significant disagreements with NR.