The subcritical baroclinic instability in local accretion disc models^*

Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Centre for Mathematical Sciences, Wilberforce Road, Cambridge CB3 0WA, UK e-mail: g.lesur@damtp.cam.ac.uk

Received: 3 November 2009
Accepted: 13 January 2010

Abstract

Context. The presence of vortices in accretion discs has been debated for more than a decade. Baroclinic instabilities might be a way to generate these vortices in the presence of a radial entropy gradient. However, the nature of these instabilities is still unclear and 3D parametric instabilities can lead to the rapid destruction of these vortices.

Aims. We present new results exhibiting a subcritical baroclinic instability (SBI) in local shearing box models. We describe the 2D and 3D behaviour of this instability using numerical simulations and we present a simple analytical model describing the underlying physical process.

Methods. We investigate the SBI in local shearing boxes, using either the incompressible Boussinesq approximation or a fully compressible model. We explore the parameter space varying several local dimensionless parameters and we isolate the regime relevant for the SBI. 3D shearing boxes are also investigated using high resolution spectral methods to resolve both the SBI and 3D parametric instabilities.

Results. A subcritical baroclinic instability is observed in flows stable for the Solberg-Hoïland criterion using local simulations. This instability is found to be a nonlinear (or subcritical) instability, which cannot be described by ordinary linear approaches. It requires a radial entropy gradient weakly unstable for the Schwartzchild criterion and a strong thermal diffusivity (or equivalently a short cooling time). In compressible simulations, the instability produces density waves which transport angular momentum outward with typically α 3 × 10^-3, the exact value depending on the background temperature profile. Finally, the instability survives in 3D, vortex cores becoming turbulent due to parametric instabilities.

Conclusions. The subcritical baroclinic instability is a robust phenomenon, which can be captured using local simulations. The instability survives in 3D thanks to a balance between the 2D SBI and 3D parametric instabilities. Finally, this instability can lead to a weak outward transport of angular momentum, due to the generation of density waves by the vortices.