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 (AGNs) 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 halos
are characterised 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.
