Quasi-steady vortices in protoplanetary disks

I. From dwarfs to giants

¹ Max Planck Institut für Astronomie, Königsthul 17, 69117 Heidelberg, Germany
² Institute for Computational Science, University of Zurich, Winterthurerstrasse 190, 8057 Zurich, Switzerland
e-mail: clement.surville@physik.uzh.ch
³ Aix Marseille Université, CNRS, Laboratoire d’Astrophysique de Marseille, UMR 7326, 13388 Marseille, France
e-mail: pierre.barge@lam.fr

Received: 23 July 2014
Accepted: 27 April 2015

Abstract

Aims. We determine the size, structure, and evolution of persistent vortices in 2D and inviscid Keplerian flows.

Methods. A Gaussian model of the vortices is built and compared with numerical solutions issued from non-linear hydrodynamical simulations. Test vortices are also produced using a fiducial method based on the Rossby wave instability to help explore the vortex parameters. Numerical simulations are performed using a second order finite volume method. We assume a perfect-gas law and a non-homentropic adiabatic flow.

Results. The new model nicely fits the numerical vortex solution. In the vortex centre it is consistent with existing models, whereas in the outer regions it enables the vortex to be connected with the background flow. Two families of vortices can be distinguished following the importance of the compressional effects. The model also permitted a new class of vortices to be discovered corresponding to huge perturbations of pressure and density and whose radial sizes are significantly larger than the disk scale height, in contrast with the standard way to define the maximum vortex size.

Conclusions. Our Gaussian model of the vortex solutions of the 2D Euler’s equations is a useful tool for studying vortex properties. Among the large number of vortex solutions, the possible existence of giant vortices could open interesting perspectives in planetary formation, particularly during the building stage of the giant gas planets.