The Global Baroclinic Instability in Accretion Disks. II: Local Linear Analysis

Hubert Klahr

doi:10.1086/383119

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The Global Baroclinic Instability in Accretion Disks. II: Local Linear Analysis

Hubert Klahr

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Abstract

This paper contains a local linear stability analysis for accretion disks under the influence of a global radial entropy gradient beta = - d log T / d log r 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 which are able to grow. So only non-linear effects can lead to a relevant amplification. Nevertheless, a lower limit on the entropy gradient ~beta = 0.22 for the transient linear instability is derived, which can be tested in future non-linear 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.

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Hubert Klahr. 2004-01-22. The Global Baroclinic Instability in Accretion Disks. II: Local Linear Analysis. https://doi.org/10.1086/383119

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