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In this work, we investigate the implications of the Integrated Galaxy-widestellar Initial Mass Function (IGIMF) approach in the framework of thesemi-analytic model GAEA (GAlaxy Evolution and Assembly), which features adetailed treatment of chemical enrichment and stellar feedback. The IGIMFprovides an analytic description of the dependence of the stellar IMF shape onthe rate of star formation in galaxies. We find that our model with a universalIMF predicts a rather flat [$\alpha$/Fe]-stellar mass relation. The modelassuming the IGIMF, instead, is able to reproduce the observed increase of$\alpha$-enhancement with stellar mass, in agreement with previous studies.This is mainly due to the fact that massive galaxies are characterized bylarger star formation rates at high-redshift, leading to stronger$\alpha$-enhancement with respect to low-mass galaxies. At the same time, theIGIMF hypothesis does not affect significantly the trend for shorter starformation timescales for more massive galaxies. We argue that in the IGIMFscenario the [$\alpha$/Fe] ratios are good tracers of the highest starformation events. The final stellar masses and mass-to-light-ratio of our modelmassive galaxies are larger than those estimated from the synthetic photometryassuming a universal IMF, providing a self-consistent interpretation of similarrecent results, based on dynamical analysis of local early type galaxies.

monthly notices of the royal astronomical society

Variations of the initial mass function in semi-analytical models:  implications for the mass assembly and the chemical enrichment of galaxies in  the GAEA model