High-accuracy numerical simulation of black-hole binaries: Computation of the gravitational-wave energy flux and comparisons with post-Newtonian approximants

Expressions for the gravitational-wave (GW) energy flux and center-of-mass energy of a compact binary are integral building blocks of post-Newtonian (PN) waveforms. In this paper, we compute the GW energy flux and GW frequency derivative from a highly accurate numerical simulation of an equal-mass, nonspinning black-hole binary. We also estimate the (derivative of the) center-of-mass energy from the simulation by assuming energy balance. We compare these quantities with the predictions of various PN approximants [adiabatic Taylor and Padé models; nonadiabatic effective-one-body (EOB) models]. We find that Padé summation of the energy flux does not accelerate the convergence of the flux series; nevertheless, the Padé flux is markedly closer to the numerical result for the whole range of the simulation (about 30 GW cycles). Taylor and Padé models overestimate the increase in flux and frequency derivative close to merger, whereas EOB models reproduce more faithfully the shape of and are closer to the numerical flux, frequency derivative, and derivative of energy. We also compare the GW phase of the numerical simulation with Padé and EOB models. Matching numerical and untuned 3.5 PN order waveforms, we find that the phase difference accumulated until Mω=0.1 is -0.12 radians for Padé approximants, and 0.50 (0.45) radians for an EOB approximant with Keplerian (non-Keplerian) flux. We fit free parameters within the EOB models to minimize the phase difference, and confirm the presence of degeneracies among these parameters. By tuning the pseudo 4PN order coefficients in the radial potential or in the flux, or, if present, the location of the pole in the flux, we find that the accumulated phase difference at Mω=0.1 can be reduced—if desired—to much less than the estimated numerical phase error (0.02 radians).