The IGIMF and other IMFs in dSphs: the case of Sagittarius
  We have studied the effects of various initial mass functions (IMFs) on the
chemical evolution of the Sagittarius dwarf galaxy (Sgr). In particular, we
tested the effects of the integrated galactic initial mass function (IGIMF) on
various predicted abundance patterns. The IGIMF depends on the star formation
rate and metallicity and predicts less massive stars in a regime of low star
formation, as it is the case in dwarf spheroidals. We adopted a detailed
chemical evolution model following the evolution of $\alpha$-elements, Fe and
Eu, and assuming the currently best set of stellar yields. We also explored
different yield prescriptions for the Eu, including production from neutron
star mergers. Although the uncertainties still present in the stellar yields
and data prevent us from drawing firm conclusions, our results suggest that the
IGIMF applied to Sgr predicts lower [$\alpha$/Fe] ratios than classical IMFs
and lower [hydrostatic/explosive] $\alpha$-element ratios, in qualitative
agreement with observations. In our model, the observed high [Eu/O] ratios in
Sgr is due to reduced O production, resulting from the IGIMF mass cutoff of the
massive oxygen-producing stars, as well as to the Eu yield produced in neutron
star mergers, a more promising site than core-collapse supernovae, although
many uncertainties are still present in the Eu nucleosynthesis. We find that a
model, similar to our previous calculations, based on the late addition of iron
from the Type Ia supernova time-delay (necessary to reproduce the shape of
[X/Fe] versus [Fe/H] relations) but also including the reduction of massive
stars due to the IGIMF, better reproduces the observed abundance ratios in Sgr
than models without the IGIMF.
