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 α-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 [α/Fe] ratios than classical IMFs and lower [hydrostatic/explosive] α-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 cut-off 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.