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 less than or similar to 0.1 radian when measured from the beginning of the simulation, and less than or similar to 0.02 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 less than or similar to 0.01 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 62 +/- 0.000 02, and the final black hole spin is S-f/M-f(2)=0.686 46 +/- 0.000 04.