Polar alignment of a protoplanetary disc around an eccentric binary III: Effect of disc mass

Abstract: Martin & Lubow (2017) found that an initially sufficiently misaligned low mass protoplanetary disc around an eccentric binary undergoes damped nodal oscillations of tilt angle and longitude of ascending node. Dissipation causes evolution towards a stationary state of polar alignment in which the disc lies perpendicular to the binary orbital plane with angular momentum aligned to the eccentricity vector of the binary. We use hydrodynamic simulations and analytic methods to investigate how the mass of the disc affects this process. The simulations suggest that a disc with nonzero mass settles into a stationary state in the frame of the binary, the generalised polar state, at somewhat lower levels of misalignment with respect to the binary orbital plane, in agreement with the analytic model. Provided that discs settle into this generalised polar state, the observational determination of the misalignment angle and binary properties can be used to determine the mass of a circumbinary disc. We apply this constraint to the circumbinary disc in HD 98800. We obtain analytic criteria for polar alignment of a circumbinary ring with mass that approximately agree with the simulation results. Very broad misaligned discs undergo breaking, but the inner regions at least may still evolve to a polar state. The long term evolution of the disc depends on the evolution of the binary eccentricity that we find tends to decrease. Although the range of parameters required for polar alignment decreases somewhat with increasing disc mass, such alignment appears possible for a broad set of initial conditions expected in protostellar circumbinary discs.