The system contains a Jupiter mass planet that opens a gap in a surrounding gaseous disk. Secular interactions are characterized by a low frequency nodal precession of the system. Formally, the disk contains secular resonances. However, the disk responds in a global manner that cannot be described by standard disk resonance theory. The analysis includes the effects of gas pressure, self-gravity, and turbulent viscosity.
All nontrivial modes damp for sufficiently high turbulent disk parameter alpha.
We determine a stability criterion and the damping timescale.