LAUSR

We take advantage of our recently published model for Galaxy Evolution and Assembly (GAEA) to study the origin of the observed correlation between [$\alpha$/Fe] and galaxy stellar mass. In particular, we analyse the role of radio mode AGN feedback, that recent work has identified as a crucial ingredient to reproduce observations. In GAEA, this process introduces the observed trend of star formation histories extending over shorter time-scales for more massive galaxies, but does not provide a sufficient condition to reproduce the observed $\alpha$ enhancements of massive galaxies. In the framework of our model, this is possible only assuming that any residual star formation is truncated for galaxies more massive than $10^{10.5}\,{\rm M}_{\odot}$. This results, however, in even shorter star formation time-scales for the most massive galaxies, that translate in total stellar metallicities significantly lower than observed. Our results demonstrate that (i) trends of [$\alpha$/Fe] ratios cannot be simply converted in relative time-scale indicators, and (ii) AGN feedback cannot explain alone the positive correlation between [$\alpha$/Fe] and galaxy mass/velocity dispersion. Reproducing simultaneously the mass-metallicity relation and the $\alpha$ enhancements observed poses a challenge for hierarchical models, unless more exotic solutions are adopted such as metal-rich winds or a variable IMF.