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

The absence of large cooling flows in cool core clusters appears to require self-regulated energy feedback by active galactic nuclei but the exact heating mechanism has not yet been identified. Here, we analyse whether a combination of cosmic ray (CR) heating and thermal conduction can offset radiative cooling. To this end, we compile a large sample of 39 cool core clusters and determine steady state solutions of the hydrodynamic equations that are coupled to the CR energy equation. We find solutions that match the observed density and temperature profiles for all our clusters well. Radiative cooling is balanced by CR heating in the cluster centres and by thermal conduction on larger scales, thus demonstrating the relevance of both heating mechanisms. Our mass deposition rates vary by three orders of magnitude and are linearly correlated to the observed star formation rates. Clusters with large mass deposition rates show larger cooling radii and require a larger radial extent of the CR injection function. Interestingly, our sample shows a continuous sequence in cooling properties: clusters hosting radio mini haloes are characterized by the largest cooling radii, star formation and mass deposition rates in our sample and thus signal the presence of a higher cooling activity. The steady state solutions support the structural differences between clusters hosting a radio mini halo and those that do not.