  (Abridged) Existing models invoking AGN activty to resolve the cooling flow
conundrum in galaxy clusters focus exclusively on the role of the central
galaxy. Such models require fine-tuning of highly uncertain microscopic
transport properties to distribute the thermal thermal over the entire cluster
cooling core. We propose that the ICM is instead heated by multiple, spatially
distributed AGNs. There is mounting observational evidence for multiple AGNs in
cluster environments. Active AGNs drive bubbles into the ICM. We identify three
distinct interactions between the bubble and the ICM: (1) Upon injection, the
bubbles expand rapidly in situ to reach pressure equilibrium with their
surroundings, generating shocks and waves whose dissipation is the principal
source of ICM heating. (2) Once inflated, the bubbles rise buoyantly at rate
determined by a balance with the viscous drag force, which itself results in
some additional heating. (3) Rising bubbles expand and compress their
surroundings. This process is adiabatic and does not contribute to any
additional heating; rather, the increased ICM density due to compression
enhances cooling. Our model sidesteps the ``transport'' issue by relying on the
spatially distributed galaxies to heat the cluster core. We include self
regulation in our model by linking AGN activity in a galaxy to cooling
characteristics of the surrounding ICM. We use a spherically symmetric
one-dimensional hydrodynamical code to carry out a preliminary study
illustrating the efficacy of the model. Our self-regulating scenario predicts
that there should be enhanced AGN activity of galaxies inside the cooling
regions compared to galaxies in the outer parts of the cluster. This prediction
remains to be confirmed or refuted by observations.
