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The absence of large cooling flows in cool core clusters appears to requireself-regulated energy feedback by active galactic nuclei (AGNs) but the exactheating mechanism has not yet been identified. Here, we analyse whether acombination of cosmic ray (CR) heating and thermal conduction can offsetradiative cooling. To this end, we compile a large sample of 39 cool coreclusters and determine steady state solutions of the hydrodynamic equationsthat are coupled to the CR energy equation. We find solutions that match theobserved density and temperature profiles for all our clusters well. Radiativecooling is balanced by CR heating in the cluster centres and by thermalconduction on larger scales, thus demonstrating the relevance of both heatingmechanisms. Our mass deposition rates vary by three orders of magnitude and arelinearly correlated to the observed star formation rates. Clusters with largemass deposition rates show larger cooling radii and require a larger radialextent of the CR injection function. Interestingly, our sample shows acontinuous sequence in cooling properties: clusters hosting radio mini halosare characterised by the largest cooling radii, star formation and massdeposition rates in our sample and thus signal the presence of a higher coolingactivity. The steady state solutions support the structural differences betweenclusters hosting a radio mini halo and those that do not.

Cosmic ray heating in cool core clusters - I. Diversity of steady state solutions