Protoplanetary Disks and embedded Planets

Abstract

After its formation a planetary embryo of a few earth masses is still surrounded by the protoplanetary disk material. Gravitational interaction of this embedded protoplanet with the disk material leads to a change of its orbital elements, most notably its semi-major axis (the change of which is referred to as migration) and eccentricity. In this contribution we describe the main aspects of these processes. Depending on the mass of the planet and on the properties of the disk it is possible to classify into different types of migration. In the first case, for low planetary masses in laminar disks, the interaction is linear and can be treated by semi-analytical methods. This leads to a simple estimate for the migration rate, so called Type I migration, studied long before the discovery of the first extrasolar planet. In the second case, for large planetary masses, the interaction is non-linear, the planet wake becomes a shock in the vicinity of the planet location and opens an annular gap at the planet orbit. In this regime numerical methods are used to analyse the torques acting on the planet, yielding the so called Type II migration. In this review the setup of such models and the main results of these multi-dimensional numerical hydrodynamic simulations are described and presented. One major observational evidence for the migration scenario are resonant systems. The resonances have been most likely established by converging differential migration of the planets leading to capture into the resonances. A problem with this scenario is that continued migration of the system while it is trapped in the resonances leads to orbital eccentricities that rapidly exceed the observational upper limits for system such as GJ 876. Detailed numerical simulations are described to explain this discrepancy.