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.