We present gravitational waveforms for the last orbits and merger of black-hole-binary systems along two branches of the black-hole-binary parameter space: equal-mass binaries with equal nonprecessing spins, and nonspinning unequal-mass binaries. The waveforms are calculated from numerical solutions of Einstein’s equations for black-hole binaries that complete between six and ten orbits before merger. Along the equal-mass spinning branch, the spin parameter of each black hole is ${\chi }_i=S_i/M_i^2\in [-0.85,0.85]$, and along the unequal-mass branch the mass ratio is $q=M_2/M_1\in [1,4]$. We discuss the construction of low-eccentricity puncture initial data for these cases, the properties of the final merged black hole, and compare the last 8–10 gravitational-wave cycles up to $M\omega =0.1$ with the phase and amplitude predicted by standard post-Newtonian (PN) approximants. As in previous studies, we find that the phase from the 3.5PN TaylorT4 approximant is most accurate for nonspinning binaries. For equal-mass spinning binaries the 3.5PN TaylorT1 approximant (including spin terms up to only 2.5PN order) gives the most robust performance, but it is possible to treat TaylorT4 in such a way that it gives the best accuracy for spins ${\chi }_i>-0.75$. When high-order amplitude corrections are included, the PN amplitude of the $(\ell =2,m=\pm 2)$ modes is larger than the numerical relativity amplitude by between 2–4%.

• Received 12 August 2010

DOI:https://doi.org/10.1103/PhysRevD.82.124008