Gap opening criterion in locally isothermal tree-dimensional discs by inclined massive planets

We study the gravitational interaction of a Jupiter mass planet with its gaseous protoplanetary disc. The planet's orbit is circular and inclined relative to the midplane of the disc. We use the impulsive approximation to estimate the gravitational tidal torque between the planet and the disc, and infer the gap profile. In addition, we simulate the disc response to an inclined massive planet using the FARGO3D code. For low-mass discs, we provide a criterion for gap opening when the orbital inclination is less to 30 degrees. This study may be useful to understand the planetary migration of massive planets on inclined orbit.