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 condensation 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 nonaxisymmetric linear perturbations, we provide general equations which 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 overstable) and the growth rates of the unstable modes. We present results for models of rotating plasmas representative of Milky-Way-like galaxy coronae and cool-cores of galaxy clusters. We show 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, then the magnetorotational instability is dominant even in these pressure-supported systems.