On the formation and stability of resonant planetary systems

We investigate the dynamics of a pair of massive secondaries pushed towards mean-motion resonance by centripetal migration due to interactions with a planetesimal disc surrounding a common primary. An analytical model of planetary systems evolving towards orbital resonance is developed to the second order in eccentricities, allowing for an assessment of the stability of the resonant equilibrium under disc interactions. Numerical applications to resonant pairs are carried out to visualize the selection of inner secondaries leading to stable resonant states by a specific outer secondary body migrating inwards. The structure of the osculating phase space is analysed and the possibilities of capture and escape from resonance are visualized accordingly. Such steps may help in predicting the evolution of a resonant planetary system and understanding its formation, while giving insights on when the driving planetesimal disc could have dissipated. The underlying method is briefly applied to numerical studies of Europa and Enceladus's migrations towards Jupiter and Saturn, respectively, and to the exoplanetary system of GJ 876.