RHAPSODY-G simulations II - Baryonic growth and metal enrichment in
  massive galaxy clusters
  We study the evolution of the stellar component and the metallicity of both
the intracluster medium and of stars in massive ($M_{\rm vir}\approx 6\times
10^{14}$ M$_{\odot}/h$) simulated galaxy clusters from the Rhapsody-G suite in
detail and compare them to observational results. The simulations were
performed with the AMR code RAMSES and include the effect of AGN feedback at
the sub-grid level. AGN feedback is required to produce realistic galaxy and
cluster properties and plays a role in mixing material in the central regions
and regulating star formation in the central galaxy. In both our low and high
resolution runs with fiducial stellar yields, we find that stellar and ICM
metallicities are a factor of two lower than in observations. We find that cool
core clusters exhibit steeper metallicity gradients than non-cool core
clusters, in qualitative agreement with observations. We verify that the ICM
metallicities measured in the simulation can be explained by a simple
"regulator" model in which the metallicity is set by a balance of stellar yield
and gas accretion. It is plausible that a combination of higher resolution and
higher metal yield in AMR simulation would allow the metallicity of simulated
clusters to match observed values; however this hypothesis needs to be tested
with future simulations. Comparison to recent literature highlights that
results concerning the metallicity of clusters and cluster galaxies might
depend sensitively on the scheme chosen to solve the hydrodynamics.
