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We measure equivalent widths (EW) - focussing on two unique features (NaI and TiO2) of low-mass stars (<0. 3M) - for luminous red galaxy spectra from the the Sloan Digital Sky Survey (SDSS) and X-Shooter Lens Survey (XLENS) in order to study the low-mass end of the initial mass function (IMF). We compare these EWs to those derived from simple stellar population models computed with different IMFs, ages, /Fe, and elemental abundances. We find that models are able to simultaneously reproduce the observed NaD 5895 and Na I 8190 features for lower-mass () early-type galaxies (ETGs) but deviate increasingly for more massive ETGs, due do strongly mismatching NaD EWs. The TiO2 6230 and the Na I 8190 features together appear to be a powerful IMF diagnostic, with age and metallicity effects orthogonal to the effect of IMF. We find that both features correlate strongly with galaxy velocity dispersion. The XLENS ETG (SDSSJ0912+0029) and an SDSS ETG (SDSSJ0041-0914) appear to require both an extreme dwarf-rich IMF and a high sodium enhancement (Na/Fe = +0. 4). In addition, lensing constraints on the total mass of the XLENS system within its Einstein radius limit a bottom-heavy IMF with a power-law slope to x 3. 0 at the 90% C. L. We conclude that NaI and TiO features, in comparison with state-of-the-art SSP models, suggest a mildly steepening IMF from Salpeter (dn/dm m-x with x = 2. 35) to x 3. 0 for ETGs in the range = 200 - 335 km s-1.
Spiniello et al. (Thu,) studied this question.