By means of a semi-analytic model of galaxy formation, we show how the local observed relation between age and galactic stellar mass is affected by assuming a DM power spectrum with a small-scale cutoff. We compare results obtained by means of both a
Lambda-cold dark matter (LambdaCDM) and a Lambda-warm dark matter (LambdaWDM) power spectrum - suppressed with respect to the LambdaCDM at scales below ~ 1 Mpc. We show that, within a LWDM cosmology with a thermal relic particle mass of 0.75 keV, both the mass-weighted and the luminosity-weighted age-mass relations are steeper than those obtained within a LambdaCDM universe, in better agreement with the observed relations. Moreover, both the observed differential and cumulative age distributions are better reproduced within a LambdaWDM cosmology. In such a scenario, star formation appears globally delayed with respect to the LambdaCDM, in particular in low-mass galaxies. The difficulty of obtaining a full agreement between model results and observations is to be ascribed to our present poor understanding of baryonic physics.
It is well established that the [alpha/Fe] ratios in elliptical galaxies increase with galaxy mass. This relation holds also for early-type dwarf galaxies, although it seems to steepen at low masses. The [alpha/Fe] vs. mass relation can be explained
assuming that smaller galaxies form over longer timescales (downsizing), allowing a larger amount of Fe (mostly produced by long-living Type Ia Supernovae) to be released and incorporated into newly forming stars. Another way to obtain the same result is by using a flatter initial mass function (IMF) in large galaxies, increasing in this way the number of Type II Supernovae and therefore the production rate of alpha-elements. The integrated galactic initial mass function (IGIMF) theory predicts that the higher the star formation rate, the flatter the IMF. We have checked, by means of semi-analytical calculations, that the IGIMF theory, combined with the downsizing effect (i.e. the shorter duration of the star formation in larger galaxies), well reproduces the observed [alpha/Fe] vs. mass relation. In particular, we show a steepening of this relation in dwarf galaxies, in accordance with the available observations.
