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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 SPH 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 $6\ \rmn{M_J}$ and the full range of initial relative orbital inclinations. Gap formation can occur for planets in inclined orbits. For given planet mass, a threshold relative orbital inclination exists under which a gap forms. At high relative inclinations, the inclination decay rate increases for increasing planet mass and decreasing initial relative inclination. For an initial semi-major axis of 5 AU and relative inclination of $i_0=80^\circ,$ the times required for the inclination to decay by $10^\circ$ is $\sim10^{6}\ \rmn{yr}$ and $\sim10^{5}\ \rmn{yr}$ for $1\ \rmn{M_J}$ and $6\ \rmn{M_J}$. Planets on inclined orbits warp the disc by an extent that is negligible for $1\ \rmn{M_J}$ but increases with increasing mass becoming quite significant for a planet of mass $6\ \rmn{M_J}$. 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. 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.