The effects of stochastic forces on the evolution of planetary systems and Saturn's rings
The increasing number of discovered extra-solar planets opens a new opportunity for studies of the formation of planetary systems. Their diversity keeps challenging the long-standing theories which were based on data primarily from our own solar system. Resonant planetary systems are of particular interest because their dynamical configuration provides constraints on the otherwise 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 realistically model the convergent migration phase and the capture into resonance. The results indicate that the proto-planetary disc initially has a larger surface density than previously thought. Proto-planets are exposed to stochastic forces, generated by density fluctuations in a turbulent disc. A generic model of both a single planet, and two planets in mean motion resonance, being stochastically forced is presented and applied to the system GJ876. It turns out that GJ876 is stable for reasonable strengths of the stochastic forces, but systems with lighter planets can get disrupted. Even if a resonance is not completely disrupted, stochastic forces create characteristic, observable libration patterns. As a further application, the stochastic migration of small bodies in Saturn’s rings is studied. Analytic predictions of collisional and gravitational interactions of a moonlet with ring particles are compared to realistic three dimensional collisional N-body simulations with up to a million particles. Estimates of both the migration rate and the eccentricity evolution of embedded moonlets are confirmed. The random walk of the moonlet is fast enough to be directly observable by the Cassini spacecraft. Turbulence in the proto-stellar disc also plays an important role during the early phases of the planet formation process. In the core accretion model, small, metre-sized particles are getting concentrated in pressure maxima and will eventually undergo a rapid gravitational collapse to form a gravitationally bound planetesimal. Due to the large separation of scales, this process is very hard to model numerically. A scaled method is presented, that allows for the correct treatment of self-gravity for a marginally collisional system by taking into account the relevant small scale processes. Interestingly, this system is dynamically very similar to Saturn’s rings.