Radio mini-halos and AGN heating in cool core clusters of galaxies
  The brightest cluster galaxy (BCG) in the majority of relaxed, cool core
galaxy clusters is radio loud, showing non-thermal radio jets and lobes ejected
by the central active galactic nucleus (AGN). Such relativistic plasma has been
unambiguously shown to interact with the surrounding thermal intra-cluster
medium (ICM) thanks to spectacular images where the lobe radio emission is
observed to fill the cavities in the X-ray-emitting gas. This `radio-mode AGN
feedback' phenomenon, which is thought to quench cooling flows, is widespread
and is critical to understand the physics of the inner regions of galaxy
clusters and the properties of the central BCG. At the same time,
mechanically-powerful AGN are likely to drive turbulence in the central ICM
which may contribute to gas heating and also play a role for the origin of
non-thermal emission on cluster-scales. Diffuse non-thermal emission has been
observed in a number of cool core clusters in the form of a radio mini-halo
surrounding the radio-loud BCG on scales comparable to that of the cooling
region. This contribution outlines the main points covered by the talk on these
topics. In particular, after summarizing the cooling flow regulation by AGN
heating and the non-thermal emission from cool core clusters, we present a
recent study of the largest collection of known mini-halo clusters (~ 20
objects) which investigated the scenario of a common origin of radio mini-halos
and gas heating. We further discuss the prospects offered by future radio
surveys with the Square Kilometre Array (SKA) for building large (>> 100
objects), unbiased mini-halo samples while probing at the same time the
presence of radio-AGN feedback in the host clusters.
