  We consider non-gravitational heating effects on galaxy clusters on the basis
of the Monte-Carlo modeling of merging trees of dark matter halos combined with
the thermal evolution of gas inside each halo. Under the assumption of
hydrostatic equilibrium and the isothermal gas profiles, our model takes
account of the metallicity evolution, metallicity-dependent cooling of gas,
supernova energy feedback, and heating due to jets of radio galaxies in a
consistent manner. The observed properties of galaxy clusters can be explained
in models with higher non-gravitational heating efficiency than that in the
conventional model. Possibilities include jet heating by the Fanaroff-Riley
Type II radio galaxies, and the enhanced star formation efficiency and/or
supernova energy feedback, especially at high redshifts.
