Simulations of black-hole binaries with unequal masses or nonprecessing spins: Accuracy, physical properties, and comparison with post-Newtonian results

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) is an element of [-0.85, 0.85], and along the unequal-mass branch the mass ratio is q = M-2/M-1 is an element of [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 (l = 2, m = +/- 2) modes is larger than the numerical relativity amplitude by between 2-4%.