The stellar IMF determined in early-type galaxies from a non-degenerate
  set of optical line indices
  We investigate the optical spectral region of spectra of 1000 stars searching
for IMF-sensitive features to constrain the low-mass end of the initial mass
function (IMF) slope in elliptical galaxies. We use the MILES stellar library
in the wavelength range [3500-7500] {\AA} to select indices that are sensitive
to cool dwarf stars and that only weakly depend on age and metallicity. In this
wavelength range, the response of a change in the effective temperature of the
cool red giant population is similar to the response of a change in the number
of dwarf stars in the galaxy. We investigate the degeneracy between IMF
variation and Teff,RGB and show that it is possible to break it with the new
IMF indicators defined here. In particular, we define a CaH1 index around
{\lambda}6380 {\AA} that arises purely from cool dwarfs, does not strongly
depend on age and is anti-correlated with [a/Fe]. This index allows the
determination of the the IMF slope when combined with TiO lines and age- and
metallicity-dependent features. The use of several indicators is crucial to
break degeneracies between IMF, age, abundance pattern and Teff of the RGB
population. We measure line-index strengths of the optical IMF indicators in
the SSP models and compare these with index strengths of the same features in
stacked SSDSS early-type galaxy spectra with varying velocity dispersions.
Using 10 different indicators, we find a clear trend of a steepening IMF with
increasing velocity dispersion described by the equation
x=(2.3+-0.1)*log{\sigma}200+(2.13+-0.15), where x is the IMF slope and
{\sigma}200 is the central stellar velocity dispersion measured in units of
200km/s. We compute the 'IMF mismatch' parameter as the ratio of stellar
mass-to-light ratio predicted from the x-{\sigma}200 relation to that inferred
from SSP models assuming a Salpeter IMF and find good agreement with
independent published results.
