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-halos, 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-halos. 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 Alfven 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-halos 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.
