The hot intra-cluster medium (ICM) is rich in metals, which are synthesised by supernovae (SNe) and accumulate over time into the deep gravitational potential well of clusters of galaxies. Since most of the elements visible in X-rays are formed by type Ia (SNIa) and/or core-collapse (SNcc) supernovae, measuring their abundances gives us direct information on the nucleosynthesis products of billions of SNe since the epoch of the star formation peak (z 2-3). In this study, we compare the most accurate average X/Fe abundance ratios (compiled in a previous work from XMM-Newton EPIC and RGS observations of 44 galaxy clusters, groups, and ellipticals), representative of the chemical enrichment in the nearby ICM, to various SNIa and SNcc nucleosynthesis models found in the literature. The use of a SNcc model combined to any favoured standard SNIa model (deflagration or delayed-detonation) fails to reproduce our abundance pattern. In particular, the Ca/Fe and Ni/Fe ratios are significantly underestimated by the models. We show that the Ca/Fe ratio can be reproduced better, either by taking a SNIa delayed-detonation model that matches the observations of the Tycho supernova remnant, or by adding a contribution from the “Ca-rich gap transient” SNe, whose material should easily mix into the hot ICM. On the other hand, the Ni/Fe ratio can be reproduced better by assuming that both deflagration and delayed-detonation SNIa contribute in similar proportions to the ICM enrichment. In either case, the fraction of SNIa over the total number of SNe (SNIa+SNcc) contributing to the ICM enrichment ranges within 29-45%. This fraction is found to be systematically higher than the corresponding SNIa/(SNIa+SNcc) fraction contributing to the enrichment of the proto-solar environnement (15-25%). We also discuss and quantify two useful constraints on both SNIa (I.e. the initial metallicity on SNIa progenitors and the fraction of low-mass stars that result in SNIa) and SNcc (I.e. the effect of the IMF and the possible contribution of pair-instability SNe to the enrichment) that can be inferred from the ICM abundance ratios. Finally, we show that detonative sub-Chandrasekhar WD explosions (resulting, for example, from violent WD mergers) cannot be a dominant channel for SNIa progenitors in galaxy clusters.
