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Abstract

We present a simple method to track the precession of a black-hole-binary system during the inspiral, using only information from the gravitational-wave (GW) signal. Our method consists of locating the frame from which the magnitudes of the ($\ensuremath{\ell}=2$, $|m|=2$) modes are maximized, which we denote the ``quadrupole-aligned'' frame. We demonstrate the efficacy of this method when applied to waveforms from numerical simulations. In the test case of an equal-mass nonspinning binary, our method locates the direction of the orbital angular momentum to within $(\ensuremath{\Delta}\ensuremath{\theta},\ensuremath{\Delta}\ensuremath{\varphi})=(0.05\ifmmode^\circ\else\textdegree\fi{},0.2\ifmmode^\circ\else\textdegree\fi{})$. We then apply the method to a $q={M}_{2}/{M}_{1}=3$ binary that exhibits significant precession. In general, a spinning binary's orbital angular momentum $\mathbf{L}$ is not orthogonal to the orbital plane. Evidence that our method locates the direction of $\mathbf{L}$ rather than the normal of the orbital plane is provided by comparison with post-Newtonian results. Also, we observe that it accurately reproduces similar higher-mode amplitudes to a comparable non-precessing binary, and that the frequency of the ($\ensuremath{\ell}=2$, $|m|=2$) modes is consistent with the ``total frequency'' of the binary's motion. The simple form of the quadrupole-aligned waveform may be useful in attempts to analytically model the inspiral-merger-ringdown signal of precessing binaries, and in standardizing the representation of waveforms for studies of accuracy and consistency of source modelling efforts, both numerical and analytical.

Tracking the precession of compact binaries from their gravitational-wave signal

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Abstract

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