Final spins from the merger of precessing binary black holes

The inspiral of binary black holes is governed by gravitational radiation reaction at binary separations r ≲ 1000M, yet it is too computationally expensive to begin numerical-relativity simulations with initial separations r ≳ 10M. Fortunately, binary evolution between these separations is well described by post-Newtonian equations of motion. We examine how this post-Newtonian evolution affects the distribution of spin orientations at separations r ≃ 10M where numerical-relativity simulations typically begin. Although isotropic spin distributions at r ≃ 1000M remain isotropic at r ≃ 10M, distributions that are initially partially aligned with the orbital angular momentum can be significantly distorted during the post-Newtonian inspiral. Spin precession tends to align (antialign) the binary black hole spins with each other if the spin of the more massive black hole is initially partially aligned (antialigned) with the orbital angular momentum, thus increasing (decreasing) the average final spin. Spin precession is stronger for comparable-mass binaries and could produce significant spin alignment before merger for both supermassive and stellar-mass black hole binaries. We also point out that precession induces an intrinsic accuracy limitation (≲0.03 in the dimensionless spin magnitude, ≲20° in the direction) in predicting the final spin resulting from the merger of widely separated binaries.