Comparing effective-one-body gravitational waveforms to accurate numerical data
Thibault Damour and Alessandro Nagar

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. We present the comparable-mass version of a new, {\it resummed} 3~PN-accurate EOB quadrupolar waveform that we 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 simulation of 15 orbits of an inspiralling equal-mass binary black hole 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 $M\omega &lt0.08$ 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, $0.08&ltM\omega\lesssim 0.14$, where the Taylor~T4 approximant starts to significantly diverge from the numerical relativity phase, we show that the EOB phase continues to match well the numerical relativity 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 numerical relativity can then be reduced below $10^{-3}$ GW cycles over the entire span (30 GW cycles) of the simulation (while, without tuning them, the dephasing is $&lt8\times 10^{-3}$ cycles). In addition, our resummed EOB amplitude agrees much better with the numerical relativity one than any of the previously considered non-resummed, post-Newtonian one (including a recently derived, non-resummed 3~PN-accurate one). We think that the present work, taken in conjunction with other recent works on the EOB-numerical-relativity comparison confirms the ability of the EOB formalism (especially in its recently improved avatars) to faithfully capture the ``real'' general relativistic waveforms.

© 2008 The American Physical Society.