The high metallicity of the intra-cluster medium (ICM) is generally
interpreted on the base of the galactic wind scenario for elliptical galaxies.
In this framework, we develop a toy-model to follow the chemical evolution of
the ICM, formulated in analogy to chemical models for individual galaxies. The
model computes the galaxy formation history (GFH) of cluster galaxies,
connecting the final luminosity function (LF) to the corresponding metal
enrichment history of the ICM. The observed LF can be reproduced with a smooth,
Madau-plot like GFH peaking at z~ 1-2, plus a "burst" of formation of dwarf
galaxies at high redshift. The model is used to test the response of the
predicted metal content and abundance evolution of the ICM to varying input
galactic models. The chemical enrichment is computed from "galactic yields"
based on models of elliptical galaxies with a variable initial mass function
(IMF), favouring the formation of massive stars at high redshift and/or in more
massive galaxies. For a given final galactic luminosity, these model
ellipticals eject into the ICM a larger quantity of gas and of metals than do
standard models based on the Salpeter IMF. However, a scenario in which the IMF
varies with redshift as a consequence of the effect of the the cosmic
background temperature on the Jeans mass scale, appears to be too mild to
account for the observed metal production in clusters. The high
iron-mass-to-luminosity-ratio of the ICM can be reproduced only by assuming a
more dramatic variation of the typical stellar mass, in line with other recent
findings. The mass in the wind-ejected gas is predicted to exceed the mass in
galaxies by a factor of 1.5-2 and to constitute roughly half of the
intra-cluster gas.Comment: 25 pages, 17 figures, accepted for publication in A&
