The final parsec problem: aligning a binary with an external accretion
  disc
  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 J_b, J_d stably counteralign if their
initial orientation is sufficiently retrograde, specifically if the angle theta
between them obeys cos(theta) < -J_d/2J_b, on a time short compared with the
mass gain time of the central accretor(s). The magnitude J_b remains unchanged
in this process. Counteralignment can promote the rapid merger of supermassive
black hole binaries, and possibly the formation of coplanar but retrograde
planets around stars in binary systems.
