On the orbital evolution of a pair of giant planets in mean motion resonance

Abstract

Pairs of extrasolar giant planets in a mean motion commensurability are common with 2:1resonance occurring most frequently. Disc-planet interaction provides a mechanism for theirorigin. However, the time-scale on which this could operate in particular cases is unclear.We perform 2D and 3D numerical simulations of pairs of giant planets in a protoplanetarydisc as they form and maintain a mean motion commensurability. We consider systems withcurrent parameters similar to those of HD 155358, 24 Sextantis and HD 60532, and discmodels of varying mass, decreasing mass corresponding to increasing age. For the lowestmass discs, systems with planets in the Jovian mass range migrate inwards maintaining a 2:1commensurability. Systems with the inner planet currently at around 1 au from the centralstar could have originated at a few au and migrated inwards on a time-scale comparableto protoplanetary disc lifetimes. Systems of larger mass planets such as HD 60532 attain 3:1resonance as observed. For a given mass accretion rate, results are insensitive to the disc modelfor the range of viscosity prescriptions adopted, there being good agreement between 2D and3D simulations. However, in a higher mass disc a pair of Jovian mass planets passes through2:1 resonance before attaining a temporary phase lasting a few thousand orbits in an unstable5:3 resonance prior to undergoing a scattering. Thus, finding systems in this commensurabilityis unlikely.