Abstract
In this work, we investigate the implications of the Integrated Galaxy-wide
stellar Initial Mass Function (IGIMF) approach in the framework of the
semi-analytic model GAEA (GAlaxy Evolution and Assembly), which features a
detailed treatment of chemical enrichment and stellar feedback. The IGIMF
provides an analytic description of the dependence of the stellar IMF shape on
the rate of star formation in galaxies. We find that our model with a universal
IMF predicts a rather flat $\alpha$/Fe-stellar mass relation. The model
assuming the IGIMF, instead, is able to reproduce the observed increase of
$\alpha$-enhancement with stellar mass. This is mainly due to the fact that
massive galaxies are characterized by larger SFRs at high-redshift, leading to
stronger $\alpha$-enhancement with respect to low-mass galaxies. At the same
time, the IGIMF hypothesis does not affect significantly the trend for shorter
star formation timescales for more massive galaxies. We argue that in the IGIMF
scenario the $\alpha$/Fe ratios are good tracers of the highest SFR events,
but they do not provide much information on the overall star formation
timescales. The final stellar masses and mass-to-light-ratio of our model
galaxies are larger than those estimated from the synthetic photometry assuming
a universal IMF. This result is in agreement with recent claims of a
bottom-heavier IMF in massive galaxies, based on dynamical analyses of local
early type galaxies.
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