Stars formed in galaxy cluster potential wells must be responsible for the
high level of enrichment measured in the intracluster medium (ICM); however,
there is increasing tension between this truism and the parsimonious assumption
that the stars in the generally old population studied optically in cluster
galaxies emerged from the same formation sites at the same epochs. We construct
a phenomenological cluster enrichment model to demonstrate that ICM elemental
abundances are underestimated by a factor >2 for standard assumptions about the
stellar population -- a discrepancy we term the "cluster elemental abundance
paradox". Recent evidence of an elliptical galaxy IMF skewed to low masses
deepens the paradox. We quantify the adjustments to the star formation
efficiency and initial mass function (IMF), and SNIa production efficiency,
required to resolve this while being consistent with the observed ICM abundance
pattern. The necessary enhancement in metal enrichment may, in principle,
originate in the observed stellar population if a larger fraction of stars in
the supernova-progenitor mass range form from an initial mass function (IMF)
that is either bottom-light or top-heavy, with the latter in some conflict with
observed ICM abundance ratios. Other alternatives that imply more modest
revisions to the IMF, mass return and remnant fractions, and primordial
fraction, posit an increase in the fraction of 3-8 solar mass stars that
explode as SNIa or assume that there are more stars than conventionally thought
-- although the latter implies a high star formation efficiency. We discuss the
feasibility of these various solutions and the implications for the diversity
of star formation in the universe, the process of elliptical galaxy formation,
and the origin of this "hidden" source of ICM metal enrichment.Comment: 22 pages, 24 figures; uses emulateapj.cls; moderate revisions
following referee feedback (now includes author's name!); now ApJ in pres
