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

Abstract

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 $M\ensuremath{\omega}=0.1$, 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 ${S}_{i}/{M}_{i}^{2}=0.85$. Finally, our results suggest that the merger waveform will play an important role in estimating the spin from such inspiral waveforms.