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Feedback processes by active galactic nuclei in the centres of galaxyclusters appear to prevent large-scale cooling flows and impede star formation.However, the detailed heating mechanism remains uncertain. One promisingheating scenario invokes the dissipation of Alfv\'en waves that are generatedby streaming cosmic rays (CRs). In order to study this idea, we usethree-dimensional magneto-hydrodynamical simulations with the AREPO code thatfollow the evolution of jet-inflated bubbles that are filled with CRs in aturbulent cluster atmosphere. We find that a single injection event producesthe CR distribution and heating rate required for a successful CR heatingmodel. As a bubble rises buoyantly, cluster magnetic fields drape around theleading interface and are amplified to strengths that balance the ram pressure.Together with helical magnetic fields in the bubble, this initially confinesthe CRs and suppresses the formation of interface instabilities. But as thebubble continues to rise, bubble-scale eddies significantly amplify radialmagnetic filaments in its wake and enable CR transport from the bubble to thecooling intracluster medium. By varying the jet parameters, we obtain a richand diverse set of jet and bubble morphologies ranging from Fanaroff-Riley typeI-like (FRI) to FRII-like jets. We identify jet energy as the leading orderparameter (keeping the ambient density profiles fixed), whereas jet luminosityis primarily responsible for setting the Mach numbers of shocks aroundFRII-like sources. Our simulations also produce FRI-like jets that inflatebubbles without detectable shocks and show morphologies consistent with clusterobservations.

Simulations of the dynamics of magnetised jets and cosmic rays in galaxy clusters