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Preprint

Michael Kesden , Davide Gerosa , Richard O'Shaughnessy , Emanuele Berti , Ulrich Sperhake

2014-11-03

Binary black holes (BBHs) on quasicircular orbits are fully characterized by their total mass \(M\), mass ratio \(q\), spins \(\mathbf{S}_1\) and \(\mathbf{S}_2\), and orbital angular momentum \(\mathbf{L}\). When the binary separation \(r \gg GM/c^2\), the precession timescale is much shorter than the radiation-reaction time on which \(L = |\mathbf{L}|\) decreases due to gravitational-wave (GW) emission. We use conservation of the total angular momentum \(\mathbf{J} = \mathbf{L} + \mathbf{S}_1 + \mathbf{S}_2\) (with magnitude \(J\)) and the projected effective spin \(\xi \equiv M^{-2} [(1+q) \mathbf{S}_1 + (1+q^{-1})\mathbf{S}_2] \cdot \hat{\mathbf{L}}\) on the precession time to derive an effective potential for BBH spin precession. This effective potential allows us to solve the orbit-averaged spin-precession equations analytically for arbitrary mass ratios and spins. These solutions are quasiperiodic functions of time: after a period \(\tau(L, J, \xi)\) the angular momenta return to their initial relative orientations and precess about \(\mathbf{J}\) by an angle \(\alpha(L, J, \xi)\). We classify BBH spin precession into three distinct morphologies between which BBHs can transition during their inspiral. Our new solutions constitute fundamental progress in our understanding of BBH spin precession and also have important astrophysical applications. We derive a precession-averaged evolution equation \(dJ/dL\) that can be numerically integrated on the radiation-reaction time, allowing us to statistically track BBH spins from formation to merger far more efficiently than was possible with previous orbit-averaged precession equations. This will greatly help us predict the signatures of BBH formation in the GWs emitted near merger and the distributions of final spins and gravitational recoils. The solutions may also help efforts to model and interpret GWs from generic BBH mergers.

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Michael Kesden, Emanuele Berti, Ulrich Sperhake (2010)

http://arxiv.org/licenses/nonexclusive-distrib/1.0/