We make use of a semi-analytical model of galaxy formation to investigate the origin of the observed correlation between [a/Fe] abundance ratios and stellar mass in elliptical galaxies. We implement a new galaxy-wide stellar initial mass function (To
p Heavy Integrated Galaxy Initial Mass Function, TH-IGIMF) in the semi-analytic model SAG and evaluate its impact on the chemical evolution of galaxies. The SFR-dependence of the slope of the TH-IGIMF is found to be key to reproducing the correct [a/Fe]-stellar mass relation. Massive galaxies reach higher [a/Fe] abundance ratios because they are characterized by more top-heavy IMFs as a result of their higher SFR. As a consequence of our analysis, the value of the minimum embedded star cluster mass and of the slope of the embedded cluster mass function, which are free parameters involved in the TH-IGIMF theory, are found to be as low as 5 solar masses and 2, respectively. A mild downsizing trend is present for galaxies generated assuming either a universal IMF or a variable TH-IGIMF. We find that, regardless of galaxy mass, older galaxies (with formation redshifts > 2) are formed in shorter time-scales (< 2 Gyr), thus achieving larger [a/Fe] values. Hence, the time-scale of galaxy formation alone cannot explain the slope of the [a/Fe]-galaxy mass relation, but is responsible for the big dispersion of [a/Fe] abundance ratios at fixed stellar mass.We further test the hyphothesis of a TH-IGIMF in elliptical galaxies by looking into mass-to-light ratios, and luminosity functions. Models with a TH-IGIMF are also favoured by these constraints. In particular, mass-to-light ratios agree with observed values for massive galaxies while being overpredicted for less massive ones; this overprediction is present regardless of the IMF considered.
We present a study on the origin of the metallicity evolution of the intra-cluster medium (ICM) by applying a semi-analytic model of galaxy formation to N-body/SPH (smoothed particle hydrodynamic) non-radiative numerical simulations of clusters of ga
laxies. The semi-analytic model includes gas cooling, star formation, supernovae feedback and metal enrichment, and is linked to the diffuse gas of the underlying simulations so that the chemical properties of gas particles are dynamically and consistently generated from stars in the galaxies. This hybrid model let us have information on the spatial distribution of metals in the ICM. The results obtained for a set of clusters with virial masses of ~1.5*10^15 h^{-1} M_sun contribute to the theoretical interpretation of recent observational X-ray data, which indicate a decrease of the average iron content of the intra-cluster gas with increasing redshift. We find that this evolution arises mainly as a result of a progressive increase of the iron abundance within ~0.15 R_vir. The clusters have been considerably enriched by z~1 with very low contribution from recent star formation. Low entropy gas that has been enriched at high redshift sinks to the cluster centre contributing to the evolution of the metallicity profiles.
