In a series of papers we have argued that local thermal instability, in an intracluster medium (ICM) in global thermal balance, can explain several properties of X-ray gas in clusters, in particular the cool-core clusters.
Globally the cluster cores appear to be in thermal balance. The hot gas in the ICM is, however, locally linearly thermally unstable; i.e., it likes to condense into a thermally stable phase at cooler (10^4 K) temperatures. Thermal conduction in the hot cluster plasma is expected to be important but it is anisotropic, along the direction of local magentic field. This leads to the condensation of gas aligned along the local magnetic field direction. Thus, because of suppressed conduction to perpendicular to the field line, filaments of cold gas can condense out of the hot gas even when the Field length is larger than the system size!
Gravity affects the nonlinear evolution of local thermal instability (with global thermal balance) in a fundamental way. The ratio of the cooling timescale (more precisely, the thermal instability timescale) and the gravitational free-fall time influences the nonlinear evolution. If this ratio is small (the critical ratio is 1 in Cartesian, plane parallel gravity and 10 in spherical gravity! or so we thought until this paper pointed out otherwise) slightly cooler blobs cool to the stable phase. In the opposite regime, the cooling blob responds to gravity. Gravitationally induced shear between the hot and cold gas leads to the mixing of the cooling blob. The case with tcool/tff>~10 never shows cold gas! This criterion quantitatively matches the observed results that extended multiphase gas is seen only in clusters with a short cooling time.
The condensation of cold gas can lead to enhanced feedback heating from the central AGN and prevents the hot gas from cooling much beyond the tcool/tff~10. This state provides a limit on the density of hot gas in cluster cores. We have formulated simple models based on this criterion and found results for different halo masses which matched observed trends; e.g., smaller/higher gas density/entropy in smaller mass halos, steepening of Lx-Tx relation at low temperatures.
More recently we have carried out the simulations of feedback AGN jets (in which the jet energy is proportional to the mass accretion rate estimated at ~1 kpc). We see cooling and heating cycles in which the cluster core hovers around a threshold value of tcool/tff~10 in the hot phase. Of course, the details are more complicated than the strict thermal balance models. We have also investigated the interplay of turbulence and cooling in idealized periodic boxes.