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The heating of the cooling flow (The feedback effervescent heating model)

The standard cooling flow model has predicted a large amount of cool gas in the clusters of galaxies. The failure of the Chandra and XXM-Newton telescopes to detect cooling gas (below 1-2 keV) in clusters of galaxies has suggested that some heating process must work to suppress the cooling. The most likely heating source is the heating by AGNs. There are many heating mechanisms, but we will adopt the effervescent heating model which is a result of the interaction of the bubbles inflated by AGN with the intra-cluster medium(ICM). 
Using the FLASH code, we have carried out time dependent simulations to investigate the effect of the heating on the suppression of the cooling in cooling flow clusters. We have found that the effervescent heating model can not balance the radiative cooling and it is an artificial model. Furthermore, the effervescent heating is a function of the ICM pressure gradient but the cooling is proportional to the gas density square and square root of the gas temperature.