Turbulence in Accretion Disks: Vorticity Generation and Angular Momentum Transport via the Global Baroclinic Instability

Abstract

In this paper we present the global baroclinic instability as a source for vigorous turbulence leading to angular momentum transport in Keplerian accretion disks. We show by analytical considerations and three-dimensional radiation-hydrodynamic simulations that, in particular, protoplanetary disks have a negative radial entropy gradient, which makes them baroclinic. Two-dimensional numerical simulations show that a baroclinic flow is unstable and produces turbulence. These findings are tested for numerical effects by performing a simulation with a barotropic initial condition, which shows that imposed turbulence rapidly decays. The turbulence in baroclinic disks transports angular momentum outward and creates a radially inward-bound accretion of matter. Potential energy is released, and excess kinetic energy is dissipated. Finally, the reheating of the gas supports the radial entropy gradient, forming a self-consistent process. We measure accretion rates in our two-dimensional and three-dimensional simulations of = -10-9 to -10-7 M☉ yr-1 and viscosity parameters of α = 10-4 to 10-2, which fit perfectly together and agree reasonably with observations. The turbulence creates pressure waves, Rossby waves, and vortices in the (R, ϕ)-plane of the disk. We demonstrate in a global simulation that these vortices tend to form out of little background noise and to be long-lasting features, which have already been suggested to lead to the formation of planets.