Dynamics of Convergent Migration and Mean Motion Resonances in Planetary Systems.

Abstract

Recent observations of solar systems orbiting other stars show that exoplanets display an enormous range of physical properties and that planetary systems display a diverse set of architectures, which motivate further studies in planetary dynamics. Part of the richness of this dynamical problem arises from the intrinsic complexity of $N$-body systems, even in the absence of additional forces. The realm of physical behavior experienced by such systems is enormous, and includes mean motion resonances (MMR), secular interactions, and sensitive dependence on the initial conditions (chaos). Additional complications arise from other forces that are often present: During the early stages of evolution, circumstellar disks provide torques that influence orbital elements, and turbulent fluctuations act on young planets. Over longer time scales, solar systems are affected by tidal forces from both stars and planets, and by general relativistic corrections that lead to orbital precession. This thesis addresses a subset of these dynamical problems, including the capture rates of planets into MMR, collision probabilities for migrating rocky planets interacting with Jovian planets, and the exploration of the ``nodding'' phenomenon (where systems move in and out of MMR). This latter effect can have important implications for interpreting transit timing variations (TTV), a method to detect smaller planets due to their interaction with larger transiting bodies.