Paper detail

The cold mode: A phenomenological model for the evolution of density perturbations in the intracluster medium

Cool cluster cores are in global thermal equilibrium but are locally thermally unstable. We study a nonlinear phenomenological model for the evolution of density perturbations in the ICM due to local thermal instability and gravity. We have analyzed and extended a model for the evolution of an over-dense blob in the ICM. We find two regimes in which the over-dense blobs can cool to thermally stable low temperatures. One for large $t_{\rm {cool}} / t_{\rm {ff}}$ ($t_{\rm {cool}}$ is the cooling time and $t_{\rm {ff}}$ is the free fall time), where a large initial over-density is required for thermal runaway to occur; this is the regime which was previously analyzed in detail. We discover a second regime for $t_{\rm {cool}} / t_{\rm {ff}} \lesssim 1$ (in agreement with Cartesian simulations of local thermal instability in an external gravitational field), where runaway cooling happens for arbitrarily small amplitudes. Numerical simulations have shown that cold gas condenses out more easily in a spherical geometry. We extend the analysis to include geometrical compression in weakly stratified atmospheres such as the ICM. With a single parameter, analogous to the mixing length, we are able to reproduce the results from numerical simulations; namely, small density perturbations lead to the condensation of extended cold filaments only if $t_{\rm {cool}} / t_{\rm {ff}} \lesssim 10$.