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 those in the solar neighborhood. We define response functions (to metallicity and α-abundance) to extend the parameter space for each set of models. We compare these extended models with a sample of Sloan Digital Sky Survey (SDSS) ETG 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 M⊙. We demonstrate that the steepening of the low-mass end of the 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 in the absolute values of the IMF slope inferred at each velocity dispersion by using the two different models. In particular, we find large inconsistencies in the quantitative predictions of the IMF slope variations and abundance patterns when sodium lines are used. We investigate the possible reasons for these inconsistencies.
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