Dynamics of the inner edge of the dead zone in protoplanetaty disks

¹ Laboratoire AiM, CEA/DSM - CNRS - Universite Paris 7, Irfu/Service d’Astrophysique, CEA-Saclay, 91191 Gif-sur-Yvette, France
² DAMTP, University of Cambridge, CMS Wilberforce Rd, Cambridge CB3 OWA, UK

^a e-mail: julien.faure@cea.fr

Abstract

In protoplanetary disks, the inner boundary between an MRI active and inactive region has recently been suggested to be a promising site for planet formation. A set of numerical simulations has indeed shown that vortex formation mediated by the Rossby wave instability is a natural consequence of the disk dynamics at that location. However, such models have so far considered only the case of an isothermal equation of state, while the more complex thermodynamics of this region may have strong consequences on disk properties because of thermal ionization. Gas is heated by turbulent dissipation and radiatively cools on long timescales because disks are optically thick.

Using a mean field model of the dynamics of that boundary, Latter and Balbus (2012) have shown that this complexity can lead to situations in which the active/dead interface moves systematically inward or outward, depending on the initial conditions. This is because turbulent activity is controlled by ohmic resistivity that is itself a sensitive function of temperature. Such a behavior suggests, as observed in young stellar object, a nonsteady accretion onto the central star.

Using the Godunov code Ramses, we have performed 3D global numerical simulations of protoplanetary disks that relax the isothermal hypothesis in order to check the above scenario. We confirm the existence of such MRI fronts, thus validating the mean field approach described above. As shown by Latter and Balbus (2012), MRI fronts tend to stop at a critical radius. We argue that the typical front velocity crucially depends on turbulent diffusion of temperature. The diffusivity of temperature due to turbulence is measured to be order of H²/Ω where Ω is the local orbital time and H the typical height of the disk.