Comparison between numerical-relativity and post-Newtonian waveforms from spinning binaries: The orbital hang-up case

We compare results from numerical simulations of spinning binaries in the ``orbital hang-up'' case, where the binary completes at least nine orbits before merger, with post-Newtonian results using the approximants Taylor T1, T4, and Et. We find that, over the ten cycles before the gravitational-wave frequency reaches M=0. 1, the accumulated phase disagreement between numerical relativity (NR) and 2. 5 post-Newtonian (PN) results is less than three radians, and is less than 2. 5 radians when using 3. 5PN results. The amplitude disagreement between NR and restricted PN results increases with the black holes' spin, from about 6% in the equal-mass case to 12% when the black holes' spins are S₈/M₈^2=0. 85. Finally, our results suggest that the merger waveform will play an important role in estimating the spin from such inspiral waveforms.