The non-universality of the low-mass end of the IMF is robust against
  the choice of SSP model
  We perform a direct comparison of two state-of-the art single stellar
population (SSP) models that have been used to demonstrate the non-universality
of the low-mass end of the Initial Mass Function (IMF) slope. The two public
versions of the SSP models are restricted to either solar abundance patterns or
solar metallicity, too restrictive if one aims to disentangle elemental
enhancements, metallicity changes and IMF variations in massive early-type
galaxies (ETGs) with star formation histories different from the solar
neighborhood. We define response functions (to metallicity and
\alpha-abundance) to extend the parameter space of each set of models. We
compare these extended models with a sample of Sloan Digital Sky Survey (SDSS)
ETGs spectra with varying velocity dispersions. We measure equivalent widths of
optical IMF-sensitive stellar features to examine the effect of the underlying
model assumptions and ingredients, such as stellar libraries or isochrones, on
the inference of the IMF slope down to ~0.1 solar masses. We demonstrate that
the steepening of the low-mass end of the Initial Mass Function (IMF) based on
a non-degenerate set of spectroscopic optical indicators is robust against the
choice of the stellar population model. Although the models agree in a relative
sense (i.e. both imply more bottom-heavy IMFs for more massive systems), we
find non-negligible differences on the absolute values of the IMF slope
inferred at each velocity dispersion by using the two different models. In
particular, we find large inconsistency in the quantitative predictions of IMF
slope variations and abundance patterns when sodium lines are used. We
investigate the possible reasons for these inconsistencies.
