Title:Stability Analysis for Cosmic-Ray Heating of Cool Cores in Galaxy Clusters

Abstract:We study the heating of the cool cores in galaxy clusters by cosmic-rays (CRs) accelerated by the central active galactic nuclei (AGNs). We especially focus on the stability of the heating. The CRs stream with Alfvén waves in the intracluster medium (ICM) and heat the ICM. First, assuming that the heating and radiative cooling is balanced, we search steady state solutions for the ICM and CR profiles of clusters by solving a boundary value problem. The boundary conditions are set so that the solutions are consistent with observations of clusters. We find steady state solutions if the magnetic fields are strong enough and the association between the magnetic fields and the ICM is relatively weak. Then, we analyse the stability of the solutions via a Lagrangian perturbation analysis and find that the solutions are globally stable. We confirm the results by numerical simulations. Using the steady state solutions as the initial conditions, we follow the evolution of the profiles for 100 Gyr. We find that the profiles do not evolve on time scales much larger than cluster lifetimes. These results, as well as consistency with observations of radio mini-halos, suggest that the CR heating is a promising mechanism to solve the so-called "cooling flow problem".