  The intracluster medium (ICM) is a reservoir of heavy elements synthesized by
different supernovae (SNe) types over cosmic history. Different enrichment
mechanisms contribute a different relative metal production, predominantly
caused by different SNe Type dominance. Using spatially resolved X-ray
spectroscopy, one can probe the contribution of each metal enrichment
mechanism. However, a large variety of physically feasible supernova explosion
models make the analysis of the ICM enrichment history more uncertain. This
paper presents a non-parametric PDF analysis to rank different theoretical SNe
yields models by comparing their performance against observations.
Specifically, we apply this new methodology to rank 7192 combinations of
core-collapse SN and Type Ia SN models using 8 abundance ratios from $Suzaku$
observations of 18 galaxy systems (clusters and groups) to test their
predictions. This novel technique can compare many SN models and maximize
spectral information extraction, considering all the individual measurable
abundance ratios and their uncertainties. We find that Type II Supernova with
nonzero initial metallicity progenitors in general performed better than
Pair-Instability SN and Hypernova models and that 3D SNIa models (with the WD
progenitor central density of $2.9\times10^9 \mathrm{g\,cm^{-3}}$) performed
best among all tested SN model pairs.

High Energy Astrophysical Phenomena;Cosmology and Nongalactic Astrophysics;Astrophysics of Galaxies