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

TL;DR

This paper compares numerical relativity simulations of an eccentric binary black hole system with post-Newtonian models, showing good phase agreement over several cycles and highlighting the importance of variable choice in modeling.

Contribution

It presents the first detailed comparison between NR and eccentric PN models for binary black holes, emphasizing the impact of variable selection on accuracy.

Findings

NR and PN phases agree within 0.1 radians for 10 cycles

Discrepancies grow to 0.7 radians near merger

Using frequency-related variable x improves model accuracy

Abstract

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.