Where post-Newtonian and numerical-relativity waveforms meet

We analyze numerical-relativity (NR) waveforms that cover nine orbits (18 gravitational-wave cycles) before merger of an equal-mass system with low eccentricity, with numerical uncertainties of 0.25 radians in the phase and 2% in the amplitude; such accuracy allows a direct comparison with post-Newtonian (PN) waveforms. We focus on waveforms predicted by one of the PN approximants that has been proposed for use in gravitational-wave data analysis, restricted 3.5PN TaylorT1, and compare these with a section of the numerical waveform from the second to the eighth orbit, which is about one and a half orbits before merger. This corresponds to a gravitational-wave frequency range of M omega=0.0455 to 0.1 Depending on the method of matching PN and NR waveforms, the accumulated phase disagreement over this frequency range can be within numerical uncertainty. Similar results are found in comparisons with an alternative PN approximant, 3PN TaylorT3. The amplitude disagreement, on the other hand, is around 6%, but roughly constant for all 13 cycles that are compared, suggesting that for the purpose of producing hybrid waveforms, only 4.5 orbits need be simulated to match PN and NR waves with the same accuracy as is possible with nine orbits. If, however, we model the amplitude up to 2.5PN order, numerical and post-Newtonian amplitude disagreement is close to the numerical error of 2%.