Abstract
We measure equivalent widths (EW) - focussing on two unique features (NaI and
TiO2) of low-mass stars (0.3 Mødot) - 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 IMF. We compare these EWs to those
derived from simple stellar population models computed with different IMFs,
ages,\alpha/Fe, and elemental abundances. We find that models are able to
simultaneously reproduce the observed NaD łambda5895 and NaI łambda8190
features for the lower-mass (~\sigma*) ETGs but deviate increasingly for more
massive ETGs, due do strongly mismatching NaD EWs. The TiO2 łambda6230
feature and the NaI łambda8190 feature, may be a powerful IMF diagnostic,
with age and metallicity effects orthogonal to the effect of IMF on the
feature's strength. We find that both features correlate strongly with galaxy
velocity dispersion. The XLENS ETG (SDSSJ0912+0029) and one SDSS ETG
(SDSSJ0041-0914) appear to require both an extreme dwarf-rich IMFs and a high
sodium enhancement (Na/Fe=+0.4). However, 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 to x~3.0 for ETGs in the range \sigma=200-335
km/s.
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