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The hot Intra-Cluster Medium (ICM) in clusters of galaxies is a very largerepository of metals produced by supernovae. We aim to accurately measure theabundances in the ICM of many clusters and compare these data with metal yieldsproduced by supernovae. Using the data archive of the XMM-Newton X-rayobservatory, we compile a sample of 22 clusters. We fit spectra extracted fromthe core regions and determine the abundances of silicon, sulfur, argon,alcium, iron, and nickel. The abundances from the spectral fits aresubsequently fitted to supernova yields determined from several supernova typeIa and core-collapse supernova models. We find that the argon and calciumabundances cannot be fitted with currently favoured supernova type Ia models.We obtain a major improvement of the fit, when we use an empirically modifieddelayed-detonation model that is calibrated on the Tycho supernova remnant. Thetwo modified parameters are the density where the sound wave in the supernovaturns into a shock and the ratio of the specific internal energies of ions andelectrons at the shock. Our fits also suggest that the core-collapse supernovaethat contributed to the enrichment of the ICM had progenitors which werealready enriched. The Ar/Ca ratio in clusters is a good touchstone fordetermining the quality of type Ia models. The core-collapse contribution,which is about 50% and not strongly dependent on the IMF or progenitormetallicity, does not have a significant impact on the Ar/Ca ratio. The numberratio between supernova type Ia and core-collapse supernovae suggests thatbinary systems in the appropriate mass range are very efficient (~ 5-16%) ineventually forming supernova type Ia explosions.Comment: 13 pages, 10 figures, accepted for publication in A&

Constraining supernova models using the hot gas in clusters of galaxies