On the nature of local instabilities in rotating galactic coronae and
  cool cores of galaxy clusters
  A long-standing question is whether radiative cooling can lead to local
condensations of cold gas in the hot atmospheres of galaxies and galaxy
clusters. We address this problem by studying the nature of local instabilities
in rotating, stratified, weakly magnetized, optically thin plasmas in the
presence of radiative cooling and anisotropic thermal conduction. For both
axisymmetric and non-axisymmetric linear perturbations we provide the general
equations that can be applied locally to specific systems to establish whether
they are unstable and, in case of instability, to determine the kind of
evolution (monotonically growing or over-stable) and the growth rates of
unstable modes. We present results for models of rotating plasmas
representative of Milky Way-like galaxy coronae and cool-cores of galaxy
clusters. It is shown that the unstable modes arise from a combination of
thermal, magnetothermal, magnetorotational and heat-flux-driven buoyancy
instabilities. Local condensation of cold clouds tends to be hampered in
cluster cool cores, while it is possible under certain conditions in rotating
galactic coronae. If the magnetic field is sufficiently weak the
magnetorotational instability is dominant even in these pressure supported
systems.
