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Authors: Thibault Damour, Alessandro Nagar

Date: 16 Nov 2007

Abstract: We continue the program of constructing, within the Effective-One-Body (EOB) approach, high accuracy, faithful analytic waveforms describing the gravitational wave signal emitted by inspiralling and coalescing binary black holes (BHs). We present the comparable-mass version of a new, resummed 3PN-accurate EOB quadrupolar waveform recently introduced in the small-mass-ratio limit. We compare the phase and the amplitude of this waveform to the recently published results of a high-accuracy numerical relativity (NR) simulation of 15 orbits of an inspiralling equal-mass binary BHs system performed by the Caltech-Cornell group. We find a remarkable agreement, both in phase and in amplitude, between the new EOB waveform and the published numerical data. More precisely: (i) in the gravitational wave (GW) frequency domain $M\omega <0.08$ where the phase of one of the non-resummed ‘Taylor approximant’ (T4) waveform matches well with the numerical relativity one, we find that the EOB phase fares as well, while (ii) for higher GW frequencies, $0.08<M\omega\lesssim 0.14$, where the TaylorT4 approximant starts to significantly diverge from the NR phase, we show that the EOB phase continues to match well the NR one. We further propose various methods of tuning the two inspiral flexibility parameters, $a_5$ and $v_{\rm pole}$, of the EOB waveform so as to ‘best fit’ EOB predictions to numerical data. We find that the maximal dephasing between EOB and NR can then be reduced below $10ˆ{-3}$ GW cycles over the entire span (30 GW cycles) of the simulation. Our resummed EOB amplitude agrees much better with the NR one than any of the previously considered non-resummed, post-Newtonian one.

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