The effects of stochastic forces on the evolution of planetary systems and Saturn's rings

Abstract

The increasing number of extra-solar planets opens a new opportunity for studies of the formation of planetary systems. Resonant systems are of particular interest because their dynamical configuration provides constraints on the unobservable formation and migration phase. In this thesis, formation scenarios for the planetary systems HD128311 and HD45364 are presented. N-body simulations of two planets and two dimensional hydrodynamical simulations of proto-planetary discs are used to model the migration phase and the capture into resonance. The results indicate that the proto-planetary disc has a larger surface density than previously thought. Proto-planets are exposed to stochastic forces, generated by density fluctuations in the disc. A generic model of both a single planet, and two planets in resonance, being stochastically forced is presented. The system GJ876, for example, is stable for reasonable strengths of the stochastic forces, but systems with lighter planets can get disrupted. Even if they are not disrupted completely, stochastic forces create characteristic, observable libration patterns. Turbulence plays also an important role during the early phases of the planet formation process. Due to the large separation of scales, the gravitational collapse in the core accretion model is very hard to model numerically. A scaled method is presented, that allows for the correct treatment of self-gravity in a marginally collisional system by taking into account the relevant small scale processes. Interestingly, this system is dynamically very similar to Saturn's rings. The stochastic migration of small bodies in Saturn's rings is also studied. Analytic predictions of the interactions of a moonlet/propeller with ring particles are compared to collisional N-body simulations with up to a million particles. The random walk is fast enough to be directly observable by the Cassini spacecraft.