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Abstract:

A simple variational calculation is presented showing that a uniformly rotating barotropic fluid in an external potential attains a true energy minimum if and only if the rotation profile is everywhere subsonic. If regions of supersonic rotation are present, fluid variations exist that could take the sytem to states of lower energy. In any given system, these states may or may not be dynamically accessible, but their existence is important. It means that extending the degrees of freedom available to the fluid (say by weak magnetic fields) may open a path to fluid instabilities. Whether astrophysical gaseous nebula tend toward states of uniform rotation or toward more Keplerian core-disk systems appears to be largely a matter of whether the rotation profile is transonic or not. The suggestion is made that the length scale associated with coherent molecular cloud cores is related to the requirement that the cores be stable and rotate subsonically.

Abstract:

We analyze the linear stability of a dilute, hot plasma, taking into account the effects of stratification and anisotropic thermal conduction. The work is motivated by attempts to understand the dynamics of the intracluster medium in galaxy clusters. We show that magnetic field configurations that nominally stabilize either the heat-flux driven buoyancy instability (associated with a positive thermal gradient) or the magnetothermal instability (negative thermal gradient) can lead to previously unrecognized g-mode overstabilities. The driving source of the overstability is either radiative cooling (positive temperature gradient) or the heat flux itself (negative temperature gradient). While the implications of these overstabilities have yet to be explored, we speculate that the cold fronts observed in many relaxed galaxy clusters may be related to their nonlinear evolution. © 2010. The American Astronomical Society. All rights reserved.