Average Heating Rate of Hot Atmospheres in Distant Clusters by Radio
  AGN: Evidence for Continuous AGN Heating
  We examine atmospheric heating by radio active galactic nuclei (AGN) in
distant X-ray clusters by cross correlating clusters selected from the 400
Square Degree (400SD) X-ray Cluster survey with radio sources in the NRAO VLA
Sky Survey. Roughly 30% of the clusters show radio emission above a flux
threshold of 3 mJy within a projected radius of 250 kpc. The radio emission is
presumably associated with the brightest cluster galaxy. The mechanical jet
power for each radio source was determined using scaling relations between
radio power and cavity (mechanical) power determined for nearby clusters,
groups, and galaxies with hot atmospheres containing X-ray cavities. The
average jet power of the central radio AGN is approximately $2\times
10^{44}$\ergs. We find no significant correlation between radio power, hence
mechanical jet power, and the X-ray luminosities of clusters in the redshift
range 0.1 -- 0.6. This implies that the mechanical heating rate per particle is
higher in lower mass, lower X-ray luminosity clusters. The jet power averaged
over the sample corresponds to an atmospheric heating of approximately 0.2 keV
per particle within R$_{500}$. Assuming the current AGN heating rate does not
evolve but remains constant to redshifts of 2, the heating rate per particle
would rise by a factor of two. We find that the energy injected from radio AGN
contribute substantially to the excess entropy in hot atmospheres needed to
break self-similarity in cluster scaling relations. The detection frequency of
radio AGN is inconsistent with the presence of strong cooling flows in 400SD
clusters, but does not exclude weak cooling flows. It is unclear whether
central AGN in 400SD clusters are maintained by feedback at the base of a
cooling flow. Atmospheric heating by radio AGN may retard the development of
strong cooling flows at early epochs.
