The study of the metal enrichment of the intra-cluster and inter-galactic media (ICM and IGM) represents a direct means to reconstruct the past history of star formation, the role of feedback processes and the gas-dynamical processes which determine the evolution of the cosmic baryons. In this paper we review the approaches that have been followed so far to model the enrichment of the ICM in a cosmological context. While our presentation will be focused on the role played by hydrodynamical simulations, we will also discuss other approaches based on semi-analytical models of galaxy formation, also critically discussing pros and cons of the different methods. We will first review the concept of the model of chemical evolution to be implemented in any chemo-dynamical description. We will emphasise how the predictions of this model critically depend on the choice of the stellar initial mass function, on the stellar life-times and on the stellar yields. We will then overview the 2 comparisons presented so far between X-ray observations of the ICM enrichment and model predictions. We will show how the most recent chemo-dynamical models are able to capture the basic features of the observed metal content of the ICM and its evolution. We will conclude by highlighting the open questions in this study and the direction of improvements for cosmological chemo-dynamical models of the next generation.
IntroductionClusters of galaxies are the ideal cosmological signposts to trace the past history of the inter-galactic medium (IGM), thanks to the high density and temperature reached by the cosmic baryons trapped in their gravitational potential wells (Rosati et al. 2002;Voit 2005; Diaferio et al. 2008 -Chapter 2, this volume). Observations in the X-ray band with the Chandra and XMM-Newton satellites are providing invaluable information on the thermodynamical properties of the intra-cluster medium (ICM) (Kaastra et al. 2008 -Chapter 9, this volume). These observations highlight that non-gravitational sources of energy, such as energy feedback from supernovae (SNe) and Active Galactic Nuclei (AGN) have played an important role in determining the ICM physical properties. Spatially resolved X-ray spectroscopy permits to measure the equivalent width of emission lines associated to transitions of heavily ionised elements and, therefore, to trace the pattern of chemical enrichment (e.g., Mushotzky 2004 for a review). In turn, this information is inextricably linked to the history of formation and evolution of the galaxy population (e.g., Renzini 1997 and references therein), as inferred from observations in the optical/near-IR band. For instance, De Grandi et al. (2004) have first shown that cool core clusters are characterised by a significant central enhancement of the iron abundance, which closely correlates with the magnitude of the Brightest Cluster Galaxies (BCGs). This demonstrates that a fully coherent description of the evolution of cosmic baryons in the condensed stellar phase and in the diffuse hot phase requires properly ...