Non-thermal Emissions from Cool Cores Heated by Cosmic-Rays in Galaxy
  Clusters
  We study non-thermal emissions from cool cores in galaxy clusters. We adopted
a recent model, in which cosmic-rays (CRs) prevail in the cores and stably heat
them through CR streaming. The non-thermal emissions come from the interaction
between CR protons and intracluster medium (ICM). Comparison between the
theoretical predictions and radio observations shows that the overall CR
spectra must be steep, and most of the CRs in the cores are low-energy CRs.
Assuming that the CRs are injected through AGN activities, we study the nature
of the shocks that are responsible for the CR acceleration. The steep CR
spectra are likely to reflect the fact that the shocks travel in hot ICM with
fairly small Much numbers. We also study the dependence on the CR streaming
velocity. The results indicate that synchrotron emissions from secondary
electrons should be observed as radio mini-halos in the cores. In particular,
low-frequency observations (e.g. LOFAR) are promising. On the other hand, the
steepness of the spectra makes it difficult to detect non-thermal X-ray and
gamma-ray emissions from the cores. The low-energy CRs may be heating optical
filaments observed in the cores.
