High-accuracy waveforms for binary black hole inspiral, merger, and ringdown

The first spectral numerical simulations of 16 orbits, merger, and ringdown of an equal-mass nonspinning binary black hole system are presented. Gravitational waveforms from these simulations have accumulated numerical phase errors through ringdown of $\ensuremath{\lesssim}0.1\text{ }\text{ }\mathrm{radian}$ when measured from the beginning of the simulation, and $\ensuremath{\lesssim}0.02\text{ }\text{ }\mathrm{radian}$ when waveforms are time and phase shifted to agree at the peak amplitude. The waveform seen by an observer at infinity is determined from waveforms computed at finite radii by an extrapolation process accurate to $\ensuremath{\lesssim}0.01\text{ }\text{ }\mathrm{radian}$ in phase. The phase difference between this waveform at infinity and the waveform measured at a finite radius of $r=100M$ is about half a radian. The ratio of final mass to initial mass is ${M}_{f}/M=0.951\text{ }62\ifmmode\pm\else\textpm\fi{}0.000\text{ }02$, and the final black hole spin is ${S}_{f}/{M}_{f}^{2}=0.686\text{ }46\ifmmode\pm\else\textpm\fi{}0.000\text{ }04$.