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

TL;DR

This paper investigates how the gravitational interaction between a binary system and a misaligned external accretion disc can lead to stable counteralignment, influencing merger processes and planetary formation.

Contribution

It provides a detailed analysis of the conditions under which binary and disc angular momenta counteralign, highlighting implications for black hole mergers and planetary system development.

Findings

Counteralignment occurs if cos(theta) < -J_d/2J_b for sufficiently retrograde initial angles.

Counteralignment can accelerate supermassive black hole mergers.

Retrograde planetary orbits may form around stars in binary systems.

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 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.