Radio Mini-Halo Emission from Cosmic Rays in Galaxy Clusters and Heating of the Cool Cores

ABSTRACT It has been proposed that the cool cores of galaxy clusters are stably heated by cosmicrays (CRs). If this is the case, radio mini-halos, which are often found in the centralregions of cool core clusters, may be attributed to the synchrotron emission from theCRs. Based on this idea, we investigate the radial profiles of the mini-halos. First, us-ing numerical simulations, we confirm that it is appropriate to assume that radiativecooling of the intracluster medium (ICM) is balanced with the heating by CR stream-ing. In these simulations, we assume that the streaming velocity of the CRs is thesound velocity of the ICM, and indicate that the heating is even more stable than thecase where the streaming velocity is the Alfv´en velocity. Then, actually assuming thebalance between cooling and heating, we estimate the radial profiles of CR pressurein six clusters only from X-ray observations. Since the CR protons interact with theICM protons, we can predict the radial profiles of the resultant synchrotron radiation.We compare the predictions with the observed radial profiles of the mini-halos in thesix clusters and find that they are consistent if the momentum spectra of the CRs aresteep. These results may indicate that the cores are actually being heated by the CRs.We also predict broad-band spectra of the six clusters, and show that the non-thermalfluxes from the clusters are small in hard X-ray and gamma-ray bands.Key words: cosmic rays — galaxies: clusters: general — cooling flows — radia-tion mechanisms: nonthermal — galaxies: clusters: individual: A1835, A2029, A2390,Perseus, RXJ1347.5-1145, Ophiuchus