Where angular momentum goes in a precessing black-hole binary

We evolve a set of 32 equal-mass black-hole binaries with collinear spins (with intrinsic spin magnitudes vertical bar(S) over right arrow (1,2)/m(1,2)(2) = 0.8) to study the effects of precession in the highly nonlinear plunge and merger regimes. We compare the direction of the instantaneous radiated angular momentum, (delta J) over cap (rad)(t) to the directions of the total angular momentum, (J) over cap (t), and the orbital angular momentum, (L) over cap (t). We find that (delta J) over cap (rad)(t) approximately follows (L) over cap throughout the evolution. During the orbital evolution and merger, we observe that the angle between (L) over right arrow and total spin (S) over right arrow is approximately conserved to within 1 degrees, which allows us to propose and test models for the merger remnant's mass and spin. For instance, we verify that the hang-up effect is the dominant effect and largely explains the observed total energy and angular momentum radiated by these precessing systems. We also verify that the total angular momentum, which significantly decreases in magnitude during the inspiral, varies in direction by less than similar to 5 degrees. The maximum variation in the direction of (J) over right arrow occurs when the spins are nearly antialigned with the orbital angular momentum. Based on our results, we conjecture that transitional precession, which would lead to large variations in the direction of (J) over right arrow, is not possible for similar-mass binaries and would require a mass ratio m(1) = m(2) less than or similar to 1/4.