What do simulations predict for the galaxy stellar mass function and its evolution in different environments?
We present a comparison between the observed galaxy stellar mass function and the one predicted from the De Lucia & Blaizot (2007) semi-analytic model applied to the Millennium Simulation, for cluster satellites and galaxies in the field (meant as a wide portion of the sky, including all environments), in the local universe (z~0.06) and at intermediate redshift (z~0.6), with the aim to shed light on the processes which regulate the mass distribution in different environments. While the mass functions in the field and in its finer environments (groups, binary and single systems) are well matched in the local universe down to the completeness limit of the observational sample, the model over-predicts the number of low mass galaxies in the field at z~0.6 and in clusters at both redshifts. Above M_*=10^10.25 M_sun, it reproduces the observed similarity of the cluster and field mass functions, but not the observed evolution. Our results point out two shortcomings of the model: an incorrect treatment of cluster-specific environmental effects and an over-efficient galaxy formation at early times (as already found by e.g. Weinmann et al. 2012). Next, we consider only simulations. Using also the Guo et al. (2011) model, we find that the high mass end of the mass functions depends on halo mass: only very massive halos host massive galaxies, with the result that their mass function is flatter. Above M_*=10^9.4 M_sun, simulations show an evolution in the number of the most massive galaxies in all the environments. Mass functions obtained from the two prescriptions are different, however results are qualitatively similar, indicating that the adopted recipes to model the evolution of central and satellite galaxies still have to be better implemented in semi-analytic models.