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 ~ 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.
@article{arxiv.0806.1037,
title = {Comparisons of eccentric binary black hole simulations with post-Newtonian models},
author = {Ian Hinder and Frank Herrmann and Pablo Laguna and Deirdre Shoemaker},
journal= {arXiv preprint arXiv:0806.1037},
year = {2014}
}
Comments
15 pages, 7 figures. Replaced extrapolation of fit parameters with values at earliest time - results unchanged. Corrected equation typos in Section IIa. Other minor changes. Corresponds to PRD version