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

TL;DR

This study compares numerical relativity and post-Newtonian waveforms for spinning binary black holes in the orbital hang-up scenario, assessing phase and amplitude differences to improve gravitational wave modeling.

Contribution

It provides a detailed comparison of NR and PN waveforms for spinning binaries, highlighting phase agreement and amplitude discrepancies related to spin effects.

Findings

Phase disagreement less than 3 radians over ten cycles before merger.

Amplitude disagreement increases with black hole spin, from 6% to 12%.

Merger waveforms are crucial for accurate spin estimation.

Abstract

We compare results from numerical simulations of spinning binaries in the "orbital hangup" case, where the binary completes at least nine orbits before merger, with post-Newtonian results using the approximants TaylorT1, T4 and Et. We find that, over the ten cycles before the gravitational-wave frequency reaches $M\omega = 0.1$, the accumulated phase disagreement between NR and 2.5PN 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.