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 $t_{{\rm {cool}}} /
t_{\rm {ff}} \lesssim 10$.
