Unstable spin precession in binary black holes

Binary black holes in which both spins are aligned with the orbital angular momentum do not precess. However, the up-down configuration, in which the spin of the heavier (lighter) black hole is aligned (anti-aligned) with the orbital angular momentum, is unstable to spin precession at small orbital separations. We first cast the spin precession problem in terms of a simple harmonic oscillator and provide a cleaner derivation of the instability onset. Surprisingly, we find that following the instability, up-down binaries do not disperse in the available parameter space but evolve towards precise endpoints. Namely, they approach merger with the two spins co-aligned with each other and equally misaligned with the orbital angular momentum. Merging up-down binaries relevant to LIGO/Virgo and LISA may be detected in these endpoint configurations if the instability onset occurs prior to the sensitivity threshold of the detector. We finally apply these findings to a simple astrophysical population of binary black holes where a formation mechanism aligns the spins without preference for co- or counter-alignment, as might be the case for stellar-mass black holes embedded in the accretion disk of a supermassive black hole. See arXiv:2003.02281.