Comparing effective-one-body gravitational waveforms to accurate numerical data

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, resummed 3 post-Newtonian (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<0. 08 where the phase of one of the nonresummed ``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<M0. 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, a₅ and v₏₎₋₄, 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 <810^-3 cycles). In addition, our resummed EOB amplitude agrees much better with the numerical relativity one than any of the previously considered nonresummed, post-Newtonian one (including a recently derived, nonresummed 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.