Second post-Newtonian radiative evolution of the relative orientations of angular momenta in spinning compact binaries

Abstract

The radiative evolution of the relative orientations of the spin and orbital angular momentum vectors ${\mathbf{S}}_1,{\mathbf{S}}_2$ and $\mathbf{L}$, characterizing a binary system on eccentric orbit is studied up to the second post-Newtonian order. As an intermediate result, all Burke-Thorne type instantaneous radiative changes in the spins are shown to average out over a radial period. It is proved that spin-orbit and spin-spin terms contribute to the radiative angular evolution equations, while Newtonian, first and second post-Newtonian terms together with the leading order tail terms do not. In complement to the spin-orbit contribution, given earlier, the spin-spin contribution is computed and split into two-body and self-interaction parts. The latter provide the second post-Newtonian order corrections to the 3/2 order Lense-Thirring description.

8 pages, to appear in Phys. Rev. D

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• The Kepler equation for inspiralling compact binaries
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• Supermassive binary black hole mergers
• Renormalized 2PN spin contributions to the accumulated orbital phase for LISA sources
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• An Efficient Method for the Evaluation of Secular Effects in the Perturbed Keplerian Motion
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• Spin-dominated waveforms for unequal mass compact binaries
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• Renormalized spin coefficients in the accumulated orbital phase for unequal mass black hole binaries