High-accuracy comparison of numerical relativity simulations with post-Newtonian expansions

TL;DR

This paper compares high-accuracy numerical relativity simulations of binary black holes with post-Newtonian waveforms, validating PN theory early on and highlighting specific approximants that match well near merger.

Contribution

It provides the most precise comparison to date between numerical relativity and post-Newtonian waveforms for binary black holes, identifying the TaylorT4 at 3.5PN order as particularly accurate.

Findings

Excellent agreement within 0.05 radians early in the waveform.

TaylorT4 at 3.5PN order matches numerical phase within 0.05 radians over 30 cycles.

Amplitude agreement improves with higher PN order, with a 3.0PN correction reducing differences to less than 1%."],

Abstract

Numerical simulations of 15 orbits of an equal-mass binary black hole system are presented. Gravitational waveforms from these simulations, covering more than 30 cycles and ending about 1.5 cycles before merger, are compared with those from quasi-circular zero-spin post-Newtonian (PN) formulae. The cumulative phase uncertainty of these comparisons is about 0.05 radians, dominated by effects arising from the small residual spins of the black holes and the small residual orbital eccentricity in the simulations. Matching numerical results to PN waveforms early in the run yields excellent agreement (within 0.05 radians) over the first $\sim 15$ cycles, thus validating the numerical simulation and establishing a regime where PN theory is accurate. In the last 15 cycles to merger, however, {\em generic} time-domain Taylor approximants build up phase differences of several radians. But, apparently by coincidence, one specific post-Newtonian approximant, TaylorT4 at 3.5PN order, agrees much better with the numerical simulations, with accumulated phase differences of less than 0.05 radians over the 30-cycle waveform. Gravitational-wave amplitude comparisons are also done between numerical simulations and post-Newtonian, and the agreement depends on the post-Newtonian order of the amplitude expansion: the amplitude difference is about 6--7% for zeroth order and becomes smaller for increasing order. A newly derived 3.0PN amplitude correction improves agreement significantly ($<1%$ amplitude difference throughout most of the run, increasing to 4% near merger) over the previously known 2.5PN amplitude terms.