Dynamical instabilities in stars

Abstract

The linear dynamical instability at the origin of convection in stars is reviewed and shown to depend essentially on the sign of

$$A = \frac{1}{\rho }\frac{{d\rho }}{{dr}} - \frac{1}{{\Gamma _1 p}}\frac{{dp}}{{dr}}$$

which is the usual argument of convection criteria. The case of two or more superadiabatic regions separated by subadiabatic ones might well deserve more detailed attention.

Once this instability is partially removed by the setting in of convection its effects must be balanced by dissipation terms if a stationary state is to result. This yields the value of a Rayleigh number.

If energy generation is included in the non-conservative terms, possibilities are somewhat enriched including a case of dynamical instability in presence of A<O (usually stable) but very small in absolute value.