Type III migration in a low viscosity disc

Abstract

We study the type III migration of a Saturn mass planet in low viscosity discs. The 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 orbital radius. The production of vortensity across shock tips results in thin high vortensity rings with a characteristic width of the local scale height. For planets with masses equal to and above that of Saturn, the rings are co-orbital features extending the entire azimuth. Linear stability analysis show there exists unstable modes that are localised about local vortensity minima which coincide with gap edges. Simulations show that vortices are non-linear a outcome. 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^{-5}Ω_pr_p(0)^2, where r_p(0) and Ω_p 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.