Gas and iron content of galaxy clusters

Up to now, many theoretical studies aimed at reproducing the total amount o f iron and gas in the intra-cluster medium meet the embarrassing situation, in which if the iron content is reproduced, the gas is not. More precisely , at given iron mass, too little gas and too high Fe abundance in turn are obtained as compared to the observational data. Large dilution by primordia l gas is then invoked to get rid of the difficulty. In this paper we presen t a new approach to this problem. Basic ingredients of the present analysis are: (i) The adoption of multi-zone models of elliptical galaxies in the f ramework of the super-nova driven galactic wind scheme. They yield a more r ealistic description of the galactic ejecta in which the effects of gradien ts in star formation and chemical enrichment are taken into account. (ii) T he stellar initial mass function is let vary with the physical conditions o f the star forming medium. More precisely, the typical mass scale of the in itial mass function increases with the gas temperature. Since no cooling pr ocess exists decreasing the temperature of a galaxy's gas below the limit s et by the current value of the cosmic background radiation, it immediately follows that the stellar initial mass function of proto-galaxies whose stel lar activity began at high red-shift (when the CBR temperature was higher t han the present-day mean temperature of molecular clouds) is different from the one in galaxies which did the same but at lower red-shift. Because of this, at given galaxy mass the ejecta are expected to depend on the red-shi ft. (iii) Finally, the basic assumption is made that at any time (red-shift ) the mass distribution of protogalaxies follows the Press-Schechter law ho lding for Dark Matter, however with masses comprised between suitable minim um and maximum values, M-L(min) and M-L* respectively, that are also varyin g with time and/or red-shift. This is equivalent to assume a sort of contin uously varying mass function for galaxies as well. When the same input phys ics (stellar initial mass function and galactic ejecta) is adopted, the new method recovers previous results in literature. However, when the above th ree ingredients are let work simultaneously the total amount of iron and ga s are reasonably matched, a point of major difficulty in previous studies. The absolute abundance of Fe and abundance ratio [O/Fe] are fully compatibl e with the observational determinations. However, even in this case some di lution (up to about 20%) by primordial gas (never cycled through galaxies) seems to be required. This is less than the older estimates of 65% to 90%. Finally, a simple model for the evolution of the intra-cluster medium abund ances as a function of the red-shift is presented and compared with the obs ervational data for clusters at high red-shift (up to z similar or equal to 0.5).