  We present results from a new set of 30 cosmological simulations of galaxy
clusters, including the effects of radiative cooling, star formation, supernova
feedback, black hole growth and AGN feedback. We first demonstrate that our AGN
model is capable of reproducing the observed cluster pressure profile at
redshift, z~0, once the AGN heating temperature of the targeted particles is
made to scale with the final virial temperature of the halo. This allows the
ejected gas to reach larger radii in higher-mass clusters than would be
possible had a fixed heating temperature been used. Such a model also
successfully reduces the star formation rate in brightest cluster galaxies and
broadly reproduces a number of other observational properties at low redshift,
including baryon, gas and star fractions; entropy profiles outside the core;
and the X-ray luminosity-mass relation. Our results are consistent with the
notion that the excess entropy is generated via selective removal of the
densest material through radiative cooling; supernova and AGN feedback largely
serve as regulation mechanisms, moving heated gas out of galaxies and away from
cluster cores. However, our simulations fail to address a number of serious
issues; for example, they are incapable of reproducing the shape and diversity
of the observed entropy profiles within the core region. We also show that the
stellar and black hole masses are sensitive to numerical resolution,
particularly the gravitational softening length; a smaller value leads to more
efficient black hole growth at early times and a smaller central galaxy.
