Is the IMF in ellipticals bottom-heavy? Clues from their chemical
  abundances
  We tested the implementation of different IMFs in our model for the chemical
evolution of ellipticals, with the aim of reproducing the observed relations of
[Fe/H] and [Mg/Fe] abundances with galaxy mass in a sample of early-type
galaxies selected from the SPIDER-SDSS catalog. Abundances in the catalog were
derived from averaged spectra, obtained by stacking individual spectra
according to central velocity dispersion, as a proxy of galaxy mass. We tested
initial mass functions already used in a previous work, as well as two new
models, based on low-mass tapered ("bimodal") IMFs, where the IMF becomes
either (1) bottom-heavy in more massive galaxies, or (2) is time-dependent,
switching from top-heavy to bottom-heavy in the course of galactic evolution.
We found that observations could only be reproduced by models assuming either a
constant, Salpeter IMF, or a time-dependent distribution, as other IMFs failed.
We further tested the models by calculating their M/L ratios. We conclude that
a constant, time-independent bottom-heavy IMF does not reproduce the data,
especially the increase of the $[\alpha/Fe]$ ratio with galactic stellar mass,
whereas a variable IMF, switching from top to bottom-heavy, can match
observations. For the latter models, the IMF switch always occurs at the
earliest possible considered time, i.e. $t_{\text{switch}}= 0.1$ Gyr.
