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

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

2010-12-13

arxiv.org/abs/1012.2879v1

Phys.Rev.D84:024046,2011

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

11 pages, 12 figures, 1 table

Scientific paper

10.1103/PhysRevD.84.024046

We present a simple method to track the precession of a black-hole-binary system, using only information from the gravitational-wave (GW) signal. Our method consists of locating the frame from which the magnitude of the $(\ell=2,|m|=2)$ modes is 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 $(\Delta \theta, \Delta \phi) = (0.05^{\circ},0.2^{\circ})$. 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 \emph{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 (PN) results. Also, we observe that it accurately reproduces similar higher-mode amplitudes to a comparable non-spinning (and therefore non-precessing) binary, and that the frequency of the $(\ell=2,|m|=2)$ modes is consistent with the "total frequency" of the binary's motion. The simple form of the quadrupole-aligned waveform will be useful in attempts to analytically model the inspiral-merger-ringdown (IMR) 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.

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