Radio mini-halo emission from cosmic rays in galaxy clusters and heating of the cool cores

It has been proposed that the cool cores of galaxy clusters are stably heated by cosmic rays (CRs). If this is the case, radio mini-haloes, which are often found in the central regions of cool core clusters, may be attributed to the synchrotron emission from the CRs. Based on this idea, we investigate the radial profiles of the mini-haloes. First, using numerical simulations, we confirm that it is appropriate to assume that radiative cooling of the intracluster medium (ICM) is balanced with the heating by CR streaming. In these simulations, we assume that the streaming velocity of the CRs is the sound velocity of the ICM and indicate that the heating is even more stable than the case where the streaming velocity is the Alfvén velocity. Then, actually assuming the balance between cooling and heating, we estimate the radial profiles of CR pressure in six clusters only from X-ray observations. Since the CR protons interact with the ICM protons, we can predict the radial profiles of the resultant synchrotron radiation. We compare the predictions with the observed radial profiles of the mini-haloes in the six clusters and find that they are consistent if the momentum spectra of the CRs are steep. 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-thermal fluxes from the clusters are small in hard X-ray and gamma-ray bands.