The role of disc torques in forming resonant planetary systems

Abstract

The most accurate method for modelling planetary migration and hence the formation of resonant systems is using hydrodynamical simulations. Usually, the force (torque) acting on a planet is calculated using the forces from the gas disc and the star, while the gas accelerations are computed using the pressure gradient, the star, and the planet's gravity, ignoring its own gravity. For the non-migrating the neglect of the disc gravity results in a consistent torque calculation while for the migrating case it is inconsistent. We aim to study how much this inconsistent torque calculation can affect the final configuration of a two-planet system. Our focus will be on low-mass planets because most of the multi-planetary systems, discovered by the Kepler survey, have masses around 10 Earth masses. Performing hydrodynamical simulations of planet-disc interaction, we measure the torques on non-migrating and migrating planets for various disc masses as well as density and temperature slopes with and without considering the disc self-gravity. Using this data, we find a relation that quantifies the inconsistency, use it in an N-body code, and perform an extended parameter study modelling the migration of a planetary system with different planet mass ratios and disc surface densities, in order to investigate the impact of the torque inconsistency on the architecture of the planetary system. Not considering disc self-gravity produces an artificially larger torque on the migrating planet that can result in tighter planetary systems. The deviation of this torque from the correct value is larger in discs with steeper surface density profiles. In hydrodynamical modelling of multi-planetary systems, it is crucial to account for the torque correction, otherwise the results favour more packed systems.