Warping a protoplanetary disc with a planet on an inclined orbit

Recent observations of several protoplanetary discs have found evidence of departures from flat, circular motion in the inner regions of the disc. One possible explanation for these observations is a disc warp, which could be induced by a planet on a misaligned orbit. We present three-dimensional numerical simulations of the tidal interaction between a protoplanetary disc and a misaligned planet. For low planet masses, we show that our simulations accurately model the evolution of inclined planet orbit (up to moderate inclinations). For a planet massive enough to carve a gap, the disc is separated into two components and the gas interior and exterior to the planet orbit evolve separately, forming an inner and outer disc. Due to the inclination of the planet, a warp develops across the planet orbit such that there is a relative tilt and twist between these discs. We show that when other parameters are held constant, the relative inclination that develops between the inner and outer disc depends on the outer radius of the total disc modelled. For a given disc mass, our results suggest that the observational relevance of the warp depends more strongly on the mass of the planet rather than the inclination of the orbit.