The Missing Metal Problem in Galaxy Clusters: Characterizing the Early
  Enrichment Population
  Rich and poor galaxy clusters have the same measured halo metallicity,
0.35-0.4 $Z_\odot$, even though they are an order of magnitude apart in stellar
fraction, $M_*/M_{gas}$. The measured intracluster medium (ICM) metallicity in
high-mass clusters cannot be explained by the visible stellar population as
stars typically make up 3-20% of the total baryon mass. The independence of
metallicity of $M_*/M_{gas}$ suggests an external and universal source of
metals such as an early enrichment population (EEP). Galaxy cluster RX
J1416.4+2315, classified as a fosil system, has a stellar fraction of
$M_*/M_{gas}=0.054\pm0.018$, and here we improve the halo metallicity
determination using archival Chandra and XMM Newton observations. We determine
the ICM metallicity of RXJ1416 to be $0.303\pm0.053$ $Z_\odot$ within
$0.3<R/R_{500}<1$, excluding the central galaxy. We combine this measurement
with other clusters with a wider range of $M_*/M_{gas}$ resulting in the fit of
$Z_{tot}=(0.36\pm0.01)+(0.10\pm 0.17)(M_*/M_{gas})$. This fit is largely
independent of $M_*/M_{gas}$, and shows that for a low $M_*/M_{gas}$ system,
the observed stellar population can make only 10-20% of the total metals. We
quantify the Fe contribution of the EEP further by adopting a standard Fe yield
for visible stellar populations, and find that
$Z_{EEP}=(0.36\pm0.01)-(0.96\pm0.17)(M_*/M_{gas})$. To account for the observed
Fe mass, a supernova (SN) rate of $10\pm5$ SNe yr$^{-1}$ (Type Ia) and
$40\pm19$ SNe yr$^{-1}$ (core collapse) is required over the redshift range
$3<z<10$ for a single galaxy cluster with mass $\sim3\times10^{14}$ $M_\odot$
at z=0. These SNe might be visible in observations of high-redshift clusters
and protoclusters with the James Webb Space Telescope.
