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 less than or similar to 1000M, yet it is too computationally expensive to begin numerical-relativity simulations with initial separations r greater than or similar to 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 similar or equal to 10M where numerical-relativity simulations typically begin. Although isotropic spin distributions at r similar or equal to 1000M remain isotropic at r similar or equal to 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 super-massive and stellar-mass black hole binaries. We also point out that precession induces an intrinsic accuracy limitation (less than or similar to 0: 03 in the dimensionless spin magnitude, less than or similar to 20 degrees in the direction) in predicting the final spin resulting from the merger of widely separated binaries.