Heating of Intracluster Gas by Jet Activities of AGN: Is the "Preheating" Scenario Realistic?

We investigate the non-gravitational heating of hot gas in clusters of galaxies (intracluster medium; ICM) on the assumption that the gas is heated well before cluster formation ('preheating'). We examine the jet activities of radio galaxies as the sources of excess energy in ICM, and the deformation of the cosmic microwave background (the Sunyaev-Zel'dovich effect) by hot electrons produced at the jet terminal shocks. We show that the observed excess entropy of ICM and {\sl COBE/FIRAS} upper limit for the Compton $y$-parameter are compatible with each other only when the heating by the jets occurred at relatively small redshift ($z\lesssim 3$). Since this result contradicts the assumption of 'preheating', it suggests that the heating occurred simultaneously with or after cluster formation.