The Global Baroclinic Instability in Accretion Disks. II. Local Linear Analysis
Abstract
This paper contains a local linear stability analysis for accretion disks under the influence of a global radial entropy gradient β=-dlogT/dlogr for constant surface density. Numerical simulations suggested the existence of an instability in two- and three-dimensional models of the solar nebula. The present paper tries to clarify, quantify, and explain such a global baroclinic instability for two-dimensional flat accretion disk models. As a result, linear theory predicts a transient linear instability that will amplify perturbations only for a limited time or up to a certain finite amplification. This can be understood as a result of the growth time of the instability being longer than the shear time, which destroys the modes that are able to grow. Thus, only nonlinear effects can lead to a relevant amplification. Nevertheless, a lower limit on the entropy gradient ~β~0.22 for the transient linear instability is derived, which can be tested in future nonlinear simulations. This would help to explain the observed instability in numerical simulations as an ultimate result of the transient linear instability, i.e., the global baroclinic instability.
- Publication:
-
The Astrophysical Journal
- Pub Date:
- May 2004
- DOI:
- 10.1086/383119
- arXiv:
- arXiv:astro-ph/0401449
- Bibcode:
- 2004ApJ...606.1070K
- Keywords:
-
- Accretion;
- Accretion Disks;
- Stars: Circumstellar Matter;
- Hydrodynamics;
- Instabilities;
- Methods: Numerical;
- Turbulence;
- Astrophysics
- E-Print:
- 35 pages, 11 figures