AGN Feedback and Bimodality in Cluster Core Entropy
  We investigate a series of steady-state models of galaxy clusters, in which
the hot intracluster gas is efficiently heated by active galactic nucleus (AGN)
feedback and thermal conduction, and in which the mass accretion rates are
highly reduced compared to those predicted by the standard cooling flow models.
We perform a global Lagrangian stability analysis. We show for the first time
that the global radial instability in cool core clusters can be suppressed by
the AGN feedback mechanism, provided that the feedback efficiency exceeds a
critical lower limit. Furthermore, our analysis naturally shows that the
clusters can exist in two distinct forms. Globally stable clusters are expected
to have either: 1) cool cores stabilized by both AGN feedback and conduction,
or 2) non-cool cores stabilized primarily by conduction. Intermediate central
temperatures typically lead to globally unstable solutions. This bimodality is
consistent with the recently observed anticorrelation between the flatness of
the temperature profiles and the AGN activity (Dunn & Fabian 2008) and the
observation by Rafferty et al. (2008) that the shorter central cooling times
tend to correspond to significantly younger AGN X-ray cavities.
