The Kozai-Lidov Mechanism in Hydrodynamical Disks. III. Effects of Disk Mass and Self-gravity

Previously we showed that a substantially misaligned viscous accretion disk with pressure that orbits around one component of a binary system can undergo global damped Kozai-Lidov (KL) oscillations. These oscillations produce periodic exchanges of the disk eccentricity with inclination. The disk KL mechanism is quite robust and operates over a wide range of binary and disk parameters. However, the effects of self-gravity, which are expected to suppress the KL oscillations for sufficiently massive disks, were ignored. Here, we analyze the effects of disk self-gravity by means of hydrodynamic simulations and compare the results with the expectations of analytic theory. The disk mass required for suppression in the simulations is a few percent of the mass of the central star and this roughly agrees with an analytical estimate. The conditions for suppression of the KL oscillations in the simulations are close to requiring that the disk be gravitationally unstable. We discuss some implications of our results for the dynamics of protoplanetary disks and the related planet formation.