The role of the Initial Mass Function in modelling the Intra-Cluster Medium

The expected metal enrichment of the intra-cluster medium (ICM) and the partition of metals between cluster galaxies and the hot ICM depends on the stellar Initial Mass Function (IMF). The choice of the IMF in simulations of clusters has also important consequences on the "cold fraction", which is a fundamental constraint on cluster physics. We discuss the chemical enrichment and the cold fraction in clusters as predicted with different IMFs, by means of a straightforward approach that is largely independent of the details of chemical evolution models or simulations. We suggest this simple approach as a guideline to select the input parameters and interpret the results of more complex models and hydrodynamical simulations.