Constraining the origin and models of chemical enrichment in galaxy
  clusters using the Athena X-IFU
  The chemical enrichment of the Universe at all scales is related to stellar
winds and explosive supernovae phenomena. Metals produced by stars and later
spread at the mega-parsec scale through the intra-cluster medium (ICM) become a
fossil record of the chemical enrichment of the Universe and of the dynamical
and feedback mechanisms determining their circulation. As demonstrated by the
results of the soft X-ray spectrometer onboard Hitomi, high resolution X-ray
spectroscopy is the path to to differentiate among the models that consider
different metal production mechanisms, predict the outcoming yields, and are
function of the nature, mass, and/or initial metallicity of their stellar
progenitor. Transformational results shall be achieved through improvements in
the energy resolution and effective area of X-ray observatories to detect rare
metals (e.g. Na, Al) and constrain yet uncertain abundances (e.g. C, Ne, Ca,
Ni). The X-ray Integral Field Unit (X-IFU) instrument onboard the
next-generation European X-ray observatory Athena is expected to deliver such
breakthroughs. Starting from 100 ks of synthetic observations of 12 abundance
ratios in the ICM of four simulated clusters, we demonstrate that the X-IFU
will be capable of recovering the input chemical enrichment models at both low
($z = 0.1$) and high ($z = 1$) redshifts, while statistically excluding more
than 99.5% of all the other tested combinations of models. By fixing the
enrichment models which provide the best fit to the simulated data, we also
show that the X-IFU will constrain the slope of the stellar initial mass
function within $\sim$12%. These constraints will be key ingredients in our
understanding of the chemical enrichment of the Universe and its evolution.
