Effective Potentials and Morphological Transitions for Binary Black Hole Spin Precession

Abstract

We derive an effective potential for binary black hole (BBH) spin precession at second post-Newtonian order. 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 fixed period, the BBH spins return to their initial relative orientations and jointly precess about the total angular momentum by a fixed angle. Using these solutions, we classify BBH spin precession into three distinct morphologies between which BBHs can transition during their inspiral. We also derive a precession-averaged evolution equation for the total angular momentum that can be integrated on the radiation-reaction time and identify a new class of spin-orbit resonances that can tilt the direction of the total angular momentum during the inspiral. Our new results will help efforts to model and interpret gravitational waves from generic BBH mergers and predict the distributions of final spins and gravitational recoils.

Additional Information

© 2015 American Physical Society. Received 2 November 2014; published 24 February 2015. We thank Antoine Klein, Tyson Littenberg, and Daniele Trifirò for discussions. D. G. is supported by the UK STFC and the Isaac Newton Studentship of the University of Cambridge. R. O'S. is supported by NSF Grants No. PHY-0970074 and No. PHY-1307429. E. B. is supported by NSF CAREER Grant No. PHY-1055103. U.S. is supported by FP7-PEOPLE-2011-CIG Grant No. 293412, FP7-PEOPLE-2011-IRSES Grant No. 295189, SDSC and TACC through XSEDE Grant No. PHY-090003 by the NSF, Finis Terrae through Grant No. ICTS-CESGA-249, STFC Consolidator Grant No. ST/L000636/1, and DiRAC's Cosmos Shared Memory system through BIS Grant No. ST/J005673/1 and STFC Grants No. ST/H008586/1 and No. ST/K00333X/1. The figures were generated using the PYTHON-based MATPLOTLIB package [42].

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Submitted - 1411.0674v2.pdf

Published - PhysRevLett.114.081103.pdf

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