Correlations of the feedback energy and BCG radio luminosity in galaxy
  clusters
  We study the excess entropy and the corresponding non-gravitational feedback
energy ($E_{feedback}$) in the intra-cluster medium (ICM) by considering a
sample of 38 galaxy clusters using Chandra X-ray and NRAO VLA Sky Survey
(NVSS)/Giant Metrewave Radio Telescope (GMRT) radio observations. We find
moderate correlation of the feedback energy and brightest cluster galaxy (BCG)
radio luminosity ($L_R$) with the various cluster thermal properties. We show
conclusively that the active galactic nucleus (AGN) is more effective in
transferring feedback energy to the ICM in less massive clusters. We find that
within $0.3r_{500}$, the feedback energy correlates with cluster temperature as
$E_{feedback}\propto T_{obs}^{0.98\pm0.37}$. Moreover, for radio detected BCG
sample we find that BCG radio luminosity at 1.4 GHz scales with gas mass as
$L_R\propto m_{g,obs}^{ 1.76\pm0.71}$ and with X-ray luminosity as $L_R\propto
L_{X,obs}^{0.94\pm0.35}$. Finally, we discuss the implications of our results
with regard to feedback in clusters.
