The stellar IMF in early-type galaxies from a non-degenerate set of optical line indices

We investigate the optical spectral region of spectra of similar to 1000 stars searching for initial mass function (IMF)-sensitive features to constrain the low-mass end of the IMF slope in elliptical galaxies. The use of indicators bluer than near-infrared 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 (Sanchez-Blazquez et al.) in the wavelength range 3500-7500 angstrom 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 angstrom that arises purely from cool dwarfs, does not strongly depend on age and is anticorrelated 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, Mgb, 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 Conroy & van Dokkum SSP models and compare these with index strengths of the same spectral features in a sample of stacked Sloan Digital Sky Survey early-type galaxy 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 km s(-1) described by the linear 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 200 km s(-1). We test the robustness of this relation by repeating the analysis with 10 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 +/- 0.2). We compute the ` IMF mismatch' parameter as the ratio of stellar mass-to-light ratio predicted from the x-s200 relation to that inferred from SSP models assuming a Salpeter IMF and find good agreement with independent published results.