Interaction between massive planets on inclined orbits and circumstellar discs

We study the interaction between massive planets and a gas disc with a mass in the range expected for protoplanetary discs. We use smoothed particle hydrodynamics simulations to study the orbital evolution of a massive planet as well as the dynamical response of the disc for planet masses between 1 and 6 M-J and the full range of initial relative orbital inclinations. We find that gap formation can occur for planets in inclined orbits as well as for coplanar orbits as expected. For given planet mass, a threshold relative orbital inclination exists under which a gap forms. This threshold increases with planet mass. Orbital migration manifest through a decreasing semimajor axis is seen in all cases. At high relative inclinations, the inclination decay rate increases for increasing planet mass and decreasing initial relative inclination as is expected from estimates based on dynamical friction between planet and disc. For an initial semimajor axis of 5 au and relative inclination of i(0) = 80 degrees, the times required for the inclination to decay by 10 degrees is similar to 10(6) and similar to 10(5) yr for 1 and 6 M-J, respectively, these times scaling in the usual way for larger initial orbits. For retrograde planets, the inclination always evolves towards coplanarity with the disc, with the rate of evolution being fastest for orbits with i(0) -> 180 degrees. The indication is thus that, without taking account of subsequent operation of phenomena such as the Lidov-Kozai effect, planets with mass 1 M-J initiated in circular orbits with semimajor axis similar to 5 au and i(0) similar to 90 degrees might only just become coplanar, as a result of frictional effects, within the disc lifetime. In other cases highly inclined orbits will survive only if they are formed after the disc has mostly dispersed. Planets on inclined orbits warp the disc by an extent that is negligible for 1 M-J but increases with increasing mass becoming quite significant for a planet of mass 6 M-J. In that case, the disc can gain a total inclination of up to 15 degrees together with a warped inner structure with an inclination of up to similar to 20 degrees relative to the outer part. We also find a solid body precession of both the total disc angular momentum vector and the planet orbital momentum vector about the total angular momentum vector, with the angular velocity of precession decreasing with increasing relative inclination as expected in that case. Our results illustrate that the influence of an inclined massive planet on a protoplanetary disc can lead to significant changes of the disc structure and orientation which can in turn affect the orbital evolution of the planet significantly. A three-dimensional treatment of the disc is then essential in order to capture all relevant dynamical processes in the composite system.