The final parsec problem: Aligning a binary with an external accretion disc

Abstract

We consider the interaction between a binary system (e.g. two supermassive black holes or two stars) and an external accretion disc with misaligned angular momentum. This situation occurs in galaxy merger events involving supermassive black holes, and in the formation of stellar mass binaries in star clusters. We work out the gravitational torque between the binary and disc, and show that their angular momenta stably counteralign if their initial orientation is sufficiently retrograde, specifically if the angle θ between them obeys cosθ