We investigate the optical spectral region of spectra of \sim 1000 stars searching for IMF-sensitive features to constrain the low-mass end of the initial mass function ( IMF ) slope in elliptical galaxies .
The use of indicators bluer than NIR features ( NaI , CaT , Wing-Ford FeH ) is crucial if we want to compare our observations to optical simple stellar population ( SSP ) models .
We use the MILES stellar library ( ) in the wavelength range 3500–7500 Å to select indices that are sensitive to cool dwarf stars and that do not or only weakly depend on age and metallicity .
We find several promising indices of molecular TiO and CaH lines .
In this wavelength range , the response of a change in the effective temperature of the cool red giant ( RGB ) population is similar to the response of a change in the number of dwarf stars in the galaxy .
We therefore investigate the degeneracy between IMF variation and \Delta { T _ { eff,RGB } } and show that it is possible to break this degeneracy with the new IMF indicators defined here .
In particular , we define a CaH1 index around \lambda 6380 Å that arises purely from cool dwarfs , does not strongly depend on age and is anti-correlated with [ \alpha /Fe ] .
This index allows the determination of the low-mass end of the IMF slope from integrated-light measurements when combined with different TiO lines and age- and metallicity-dependent features such as H \beta , Mg b , Fe5270 and Fe5335 .
The use of several indicators is crucial to break degeneracies between IMF variations , age , abundance pattern and effective temperature of the cool red giant ( RGB ) population .
We measure line-index strengths of our new optical IMF indicators in the SSP models and compare these with index strengths of the same spectral features in a sample of stacked Sloan Digital Sky Survey ( SDSS ) early-type galaxy ( ETG ) spectra with varying velocity dispersions .
Using different indicators , we find a clear trend of a steepening IMF with increasing velocity dispersion from 150 to 310 \mathrm { km } \mathrm { s } ^ { -1 } described by the linear equation x = ( 2.3 \pm 0.1 ) \log \sigma _ { 200 } + ( 2.13 \pm 0.15 ) , where x is the IMF slope and \sigma _ { 200 } is the central stellar velocity dispersion measured in units of 200 \mathrm { km } \mathrm { s } ^ { -1 } .
We test the robustness of this relation by repeating the analysis with ten different sets of indicators .
We found that the NaD feature has the largest impact on the IMF slope , if we assume solar [ Na/Fe ] abundance .
By including NaD the slope of the linear relation increases by 0.3 ( 2.6 \pm 0.2 ) .
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 .