Could AGN outbursts transform cool core clusters?

The origin of the bimodality in cluster core entropy is still unknown. At the same time, recent work has shown that thermal conduction in clusters is likely a time-variable phenomenon. We consider if time-variable conduction and active galactic nuclei (AGN) outbursts could be responsible for the cool-core (CC), non-cool-core (NCC) dichotomy. We show that strong AGN heating can bring a CC cluster to an NCC state, which can be stably maintained by conductive heating from the cluster outskirts. On the other hand, if conduction is shut off by the heat-flux-driven buoyancy instability, then the cluster will cool to the CC state again, where it is stabilized by low-level AGN heating. Thus, the cluster cycles between CC and NCC states. In contrast with massive clusters, we predict the CC/NCC bimodality should vanish in groups, due to the lesser role of conductive heating there. We find tentative support from the distribution of central entropy in groups, though firm conclusions require a larger sample carefully controlled for selection effects.