On the connection between radio mini-halos and gas heating in cool core clusters

In this work, we present a study of the central regions of cool-core clusters hosting radio mini-halos, which are di use synchrotron sources extended on cluster-scales surrounding the radio-loud brightest galaxy. We aim to investigate the interplay between the thermal and non-thermal components in the intracluster medium in order to get more insights into these radio sources, whose nature is still unclear. It has recently been proposed that turbulence plays a role for heating the gas in cool cores. A correlation between the radio luminosity of mini-halos, $\nu P_{\nu}$, and the cooling flow power, $P_{\rm CF}$, is expected in the case that this turbulence also plays a role for the acceleration of the relativistic particles. We carried out a homogeneous re-analysis of X-ray Chandra data of the largest sample of cool-core clusters hosting radio mini-halos currently available ($\sim20$ objects), finding a quasi-linear correlation, $\nu P_{\nu} \propto P_{\rm CF}^{0.8}$. We show that the scenario of a common origin of radio mini-halos and gas heating in cool-core clusters is energetically viable, provided that mini-halos trace regions where the magnetic field strength is $B \gg 0.5 \mu G$.