Flip-flopping binary black holes.

We study binary spinning black holes to display the long term individual spin dynamics. We perform a full numerical simulation starting at an initial proper separation of d≈25M between equal mass holes and evolve them down to merger for nearly 48 orbits, 3 precession cycles, and half of a flip-flop cycle. The simulation lasts for t=20 000M and displays a total change in the orientation of the spin of one of the black holes from an initial alignment with the orbital angular momentum to a complete antialignment after half of a flip-flop cycle. We compare this evolution with an integration of the 3.5 post-Newtonian equations of motion and spin evolution to show that this process continuously flip flops the spin during the lifetime of the binary until merger. We also provide lower order analytic expressions for the maximum flip-flop angle and frequency. We discuss the effects this dynamics may have on spin growth in accreting binaries and on the observational consequences for galactic and supermassive binary black holes.