Type III migration in a low-viscosity disc

Abstract

We study the type III migration of Saturn and Jupiter-mass planets in low-viscosity discs. A Saturn-mass planet is found to experience cyclic episodes of rapid decay in orbital radius, each amounting to a few Hill radii. We find this to be due to the scattering of large-scale vortices present in the disc. The origin and role of vortices in the context of type III migration is explored. It is shown through numerical simulations and semi-analytical modelling that spiral shocks induced by a sufficiently massive planet will extend close to the planet's orbital radius as well as being global prominent features. The production of vortensity across shock tips results in thin high vortensity rings with a characteristic width of the local scaleheight. For planets with masses equal to and above that of Saturn, the rings are co-orbital features extending all the way around the orbit. Linear stability analysis shows such vortensity rings are dynamically unstable. There exists unstable modes that are localized about local vortensity minima which coincide with gap edges. Simulations show that vortices are an outcome in the nonlinear regime. We used hydrodynamic simulations to examine vortex-planet interactions. Their effect is present in discs with kinematic viscosity less than about an order of magnitude smaller than the typically adopted value of ν= 10-5Ωprp(0)2, where rp(0) and Ωp are the initial orbital radius and angular velocity of the planet, respectively. We find that the magnitude of viscosity affects the nature of type III migration but not the extent of the orbital decay. The role of vortices as a function of initial disc mass is also explored and it is found that the amount of orbital decay during one episode of vortex-planet interaction is independent of initial disc mass. We incorporate the concept of the co-orbital mass deficit in the analysis of our results and link it to the presence of vortices at gap edges. Similar effects are found to occur for a Jupiter-mass planet but with the extent of the fast migration episodes being larger because of the stronger perturbation on the disc. © 2010 The Authors. Journal compilation © 2010 RAS.