Is the IMF in ellipticals bottom-heavy? Clues from their chemical abundances

We tested the implementation of different initial mass functions (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 catalogue. Abundances in the catalogue were derived from averaged spectra, obtained by stacking individual spectra according to central velocity dispersion, as a proxy of galaxy mass. We tested IMFs 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(switch) = 0.1 Gyr