Linear Analysis of the Evolution of Nearly Polar Low Mass Circumbinary Discs

Martin & Lubow (2017) showed through simulations that an initially tilted disc around an eccentric binary can evolve to polar alignment in which the disc lies perpendicular to the binary orbital plane. We apply linear theory to show both analytically and numerically that a nearly polar aligned low mass circumbinary disc evolves to polar alignment and determine the alignment timescale. Significant disc evolution towards the polar state around moderately eccentric binaries can occur for typical protostellar disc parameters in less than a typical disc lifetime for binaries with orbital periods of order 100 years or less. Resonant torques are much less effective at truncating the inner parts of circumbinary polar discs than the inner parts of coplanar discs. For polar discs, they vanish for a binary eccentricity of unity. The results agree with the simulations in showing that discs can evolve to a polar state. Circumbinary planets may then form in such discs and reside on polar orbits.