Abstract

(Zanazzi) It is usually assumed that viscous disk torques work to align circumbinary disks with the binary’s orbital plane. However, Martin and Lubow recently used smoothed particle hydrodynamics simulations to show a circumbinary disk may evolve to a configuration perpendicular to the binary’s orbital plane (polar alignment), if the binary is sufficiently eccentric. In this work, we generalize previous dynamical studies of disk warping in circumbinary disks to arbitrary mutual binary-disk inclinations and binary eccentricities, calculating the disk warp profile and dissipative viscous torques acting on the disk. We provide a simple analytic criterion for when a circumbinary disk evolves to be polar with the eccentric binary. We also calculate the probability a disk will evolve to be polar with the binary, given the initial binary disk inclination and binary eccentricity. Due to the ubiquity of order unity binary eccentricities in circumbinary disk systems, this work has important implications on the formation and evolution of circumbinary disks, as well as the inclination distribution of circumbinary planets.