Endpoint of the up-down instability in precessing binary black holes

Understand

Binary black holes in which both spins are aligned with the binary's 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 toward precise endpoints.