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Interaction of a giant planet in an inclined orbit with a circum-stellar disk

We investigate the dynamical evolution of a Jovian--mass planet injected into an orbit highly inclined with respect to its nesting gaseous disk. Planet--planet scattering induced by convergent planetary migration and mean motion resonances may push a planet into such an out of plane configuration with inclinations as large as $20^\circ-30^\circ$. In this scenario the tidal interaction of the planet with the disk is more complex and, in addition to the usual Lindblad and corotation resonances, it involves also inclination resonances responsible of bending waves. We have performed three--dimensional hydrodynamic simulations of the disk and of its interactions with the planet with a Smoothed Particle Hydrodynamics (SPH) code. A main result is that the initial large eccentricity and inclination of the planetary orbit are rapidly damped on a timescale of the order of $10^3$ yrs, almost independently of the initial semimajor axis and eccentricity of the planet. The disk is warped in response to the planet perturbations and it precesses. Inward migration occurs also when the planet is inclined and it has a drift rate which is intermediate between type I and type II migration. The planet is not able to open a gap until its inclination becomes lower than $\sim 10^\circ$ when it also begins to accrete a significant amount of mass from the disk.