We describe two-dimensional gasdynamical models of jets that carry mass as well as energy to the hot gas in galaxy clusters. These flows have many attractive attributes for solving the galaxy cluster cooling flow problem: why the hot gas temperature and density profiles resemble cooling flows but show no spectral evidence of cooling to low temperatures. Using an approximate model for the cluster A1795, we show that mass-carrying jets can reduce the overall cooling rate to or below the low values implied by X-ray spectra. Biconical subrelativistic jets, described by several ad hoc parameters, are assumed to be activated when gas flows toward or cools near a central supermassive black hole. As the jets proceed out from the center, they entrain more and more ambient gas. The jets lose internal pressure by expansion and are compressed by the ambient cluster gas, becoming rather difficult to observe. For a wide variety of initial jet parameters and several feedback scenarios, the global cooling can be suppressed for many gigayears while maintaining cluster temperature profiles similar to those observed. The intermittency of the feedback generates multiple generations of X-ray cavities similar to those observed in the Perseus Cluster and elsewhere.
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