Satellite-disc interaction in an extended local approximation

This project will investigate a novel approach to the gravitational interaction of a planet with the protoplanetary disc within which it is formed, or physically related problems such as those involving secondary black holes interacting with the disc in a galactic nucleus. A theoretical framework will be explored, which exploits the fact that the disc is typically thin and the interaction is nearly symmetrical inside and outside the satellite's orbit. The hydrodynamic theory of the perturbed disc will be developed systematically beyond the usual local approximation or shearing-sheet model to provide a new understanding of the factors leading to a non-zero torque, and therefore to planetary migration, etc. Both linear and nonlinear regimes will be considered, in both two- and three-dimensional disc models, using a combination of semi-analytical and computational methods. Possible aims of the project include finding an improved understanding of the coorbital torque, gap structure and three-dimensional effects such as internal waves involving buoyancy forces. It is also hoped to apply results from the theory of planetary migration to astrophysical situations involving much thinner discs, such as black holes in galactic nuclei.