We estimate the average radio-AGN ( mechanical ) power deposited into the hot atmospheres of galaxy clusters over more than three quarters of the age of the Universe .
Our sample was drawn from eight major X-ray cluster surveys , and includes 685 clusters in the redshift range 0.1 < z < 0.6 that overlap the area covered by the NVSS .
The radio-AGN mechanical power was estimated from the radio luminosity of central NVSS sources , using the relation of Cavagnolo et al .
( 13 ) that is based on mechanical powers determined from the enthalpies of X-ray cavities .
We find only a weak correlation between radio luminosity and cluster X-ray luminosity , although the most powerful radio sources resides in luminous clusters .
The average AGN mechanical power of 3 \times 10 ^ { 44 } erg s ^ { -1 } exceeds the X-ray luminosity of 44 \% of the clusters , indicating that the accumulation of radio-AGN energy is significant in these clusters .
Integrating the AGN mechanical power to redshift z = 2.0 , using simple models for its evolution and disregarding the hierarchical growth of clusters , we find that the AGN energy accumulated per particle in low luminosity X-ray clusters exceeds 1 keV per particle .
This result represents a conservative lower limit to the accumulated thermal energy .
The estimate is comparable to the level of energy needed to “ preheat ” clusters , indicating that continual outbursts from radio-AGN are a significant source of gas energy in hot atmospheres .
Assuming an average mass conversion efficiency of \eta = 0.1 , our result implies that the supermassive black holes that released this energy did so by accreting an average of \sim 10 ^ { 9 } M _ { \odot } over time , which is comparable to the level of growth expected during the quasar era .