Origin of central abundances in the hot intra-cluster medium - II.
  Chemical enrichment and supernova yield models
  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/SNe fraction contributing to the enrichment of the
proto-solar environnement (15-25%). We also discuss and quantify two useful
constraints on both SNIa and SNcc that can be inferred from the ICM abundance
ratios.
