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Recent X-ray observations of galaxy clusters show that the distribution ofintra-cluster medium (ICM) metallicity is remarkably uniform in space and time.In this paper, we analyse a large sample of simulated objects, from poor groupsto rich clusters, to study the dependence of the metallicity and relatedquantities on the mass of the systems. The simulations are performed with animproved version of the Smoothed-Particle-Hydrodynamics \texttt{GADGET-3} codeand consider various astrophysical processes including radiative cooling, metalenrichment and feedback from stars and active galactic nuclei (AGN). Thescaling between the metallicity and the temperature obtained in the simulationsagrees well in trend and evolution with the observational results obtained fromtwo data samples characterised by a wide range of masses and a large redshiftcoverage. We find that the iron abundance in the cluster core ($r<0.1R_{500}$)does not correlate with the temperature nor presents a significant evolution.The scale invariance is confirmed when the metallicity is related directly tothe total mass. The slope of the best-fitting relations is shallow($\beta\sim-0.1$) in the innermost regions ($r<0.5R_{500}$) and consistent withzero outside. We investigate the impact of the AGN feedback and find that itplays a key role in producing a constant value of the outskirts metallicityfrom groups to clusters. This finding additionally supports the picture ofearly enrichment.

Mass-Metallicity Relation from Cosmological Hydrodynamical Simulations and X-ray Observations of Galaxy Groups and Clusters