The effects of the IMF on the chemical evolution of elliptical galaxies
  We describe the use of our chemical evolution model to reproduce the
abundance patterns observed in a catalog of elliptical galaxies from the SDSS
DR4. The model assumes ellipticals form by fast gas accretion, and suffer a
strong burst of star formation followed by a galactic wind which quenches star
formation. Models with fixed IMF failed in simultaneously reproducing the
observed trends with the galactic mass. So, we tested a varying IMF; contrary
to the diffused claim that the IMF should become bottom heavier in more massive
galaxies, we find a better agreement with data by assuming an inverse trend,
where the IMF goes from being bottom heavy in less massive galaxies to top
heavy in more massive ones. This naturally produces a downsizing in star
formation, favoring massive stars in largest galaxies. Finally, we tested the
use of the Integrated Galactic IMF, obtained by averaging the canonical IMF
over the mass distribution function of the clusters where star formation is
assumed to take place. We combined two prescriptions, valid for different SFR
regimes, to obtain the IGIMF values along the whole evolution of the galaxies
in our models. Predicted abundance trends reproduce the observed slopes, but
they have an offset relative to the data. We conclude that bottom-heavier IMFs
do not reproduce the properties of the most massive ellipticals, at variance
with previous suggestions. On the other hand, an IMF varying with galactic mass
from bottom-heavier to top-heavier should be preferred
