Inclination-type resonance in two-planet systems

Abstract

Abstract We investigate the inclination-growth mechanisms for two-planet systems during the late protoplanetary disc phase. In previous works, much attention has been directed to the inclination-type resonance, and it has been shown that it asks for high eccentricities to be acquired during the migration of the giant planets. By adopting eccentricity and inclination damping formulae based on hydrodynamical simulations (instead of the K-prescription), we have carried out 20000 numerical simulations, where we vary the initial planetary eccentricities, the migration rate, and the dispersal time of the gas disc. Our results confirm that highly mutually inclined systems are unlikely to be produced by an inclination-type resonance of two migrating giant planets. However, in $\sim 1~\%$ of the simulations, inclination-type resonance is observed, and a dynamical study of the evolutions reveals that the inclination-type resonance mechanism operates in three cases: i) when the inner planet reaches the inner cavity of the disc, ii) at moderate to high eccentricities for faster migration rates, and iii) at low to moderate eccentricities after a phase of orbital destabilization and re-arrangement.