title: 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.
authors.affiliation: Department of Physics, The University of Texas at Dallas, Richardson, Texas 75080, USA.
authors.forename: Michael
authors.initials: M
authors.lastname: Kesden
authors.affiliation: Department of Applied Mathematics and Theoretical Physics, Centre for Mathematical Sciences, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, United Kingdom.
authors.forename: Davide
authors.initials: D
authors.lastname: Gerosa
authors.affiliation: Center for Computational Relativity and Gravitation, Rochester Institute of Technology, Rochester, New York 14623, USA.
authors.forename: Richard
authors.initials: R
authors.lastname: O'Shaughnessy
authors.affiliation: Department of Physics and Astronomy, The University of Mississippi, University, Mississippi 38677, USA.
authors.forename: Emanuele
authors.initials: E
authors.lastname: Berti
authors.affiliation: Department of Applied Mathematics and Theoretical Physics, Centre for Mathematical Sciences, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, United Kingdom.|Department of Physics and Astronomy, The University of Mississippi, University, Mississippi 38677, USA.|California Institute of Technology, Pasadena, California 91125, USA.
authors.forename: Ulrich
authors.initials: U
authors.lastname: Sperhake