Chemo-Archaeological Downsizing in a Hierarchical Universe: Impact of a
  Top Heavy IGIMF
  We make use of a semi-analytical model of galaxy formation to investigate the
origin of the observed correlation between [a/Fe] abundance ratios and stellar
mass in elliptical galaxies. We implement a new galaxy-wide stellar initial
mass function (Top Heavy Integrated Galaxy Initial Mass Function, TH-IGIMF) in
the semi-analytic model SAG and evaluate its impact on the chemical evolution
of galaxies. The SFR-dependence of the slope of the TH-IGIMF is found to be key
to reproducing the correct [a/Fe]-stellar mass relation. Massive galaxies reach
higher [a/Fe] abundance ratios because they are characterized by more top-heavy
IMFs as a result of their higher SFR. As a consequence of our analysis, the
value of the minimum embedded star cluster mass and of the slope of the
embedded cluster mass function, which are free parameters involved in the
TH-IGIMF theory, are found to be as low as 5 solar masses and 2, respectively.
A mild downsizing trend is present for galaxies generated assuming either a
universal IMF or a variable TH-IGIMF. We find that, regardless of galaxy mass,
older galaxies (with formation redshifts > 2) are formed in shorter time-scales
(< 2 Gyr), thus achieving larger [a/Fe] values. Hence, the time-scale of galaxy
formation alone cannot explain the slope of the [a/Fe]-galaxy mass relation,
but is responsible for the big dispersion of [a/Fe] abundance ratios at fixed
stellar mass.We further test the hyphothesis of a TH-IGIMF in elliptical
galaxies by looking into mass-to-light ratios, and luminosity functions. Models
with a TH-IGIMF are also favoured by these constraints. In particular,
mass-to-light ratios agree with observed values for massive galaxies while
being overpredicted for less massive ones; this overprediction is present
regardless of the IMF considered.
