We present a new stellar population synthesis model, which predicts SEDs for single-age single-metallicity stellar populations, SSPs, at resolution 1.5A (FWHM) in the spectral region of the near-IR CaII triplet feature. The main ingredient of the model is a new extensive empirical stellar spectral library presented in Cenarro et al., which is composed of more than 600 stars. Two main products of interest for stellar population analysis are presented. The first is a library of SEDs for SSPs covering a large range of ages, metallicities and different IMF types. They are well suited to model galaxy data, since the SSP spectra, with flux-calibrated response curves, can be smoothed to match the resolution of galaxy data, taking into account the internal velocity dispersion of the galaxy, allowing the user to analyze the observed spectrum in its own system. We also produce integrated absorption line indices for the same SSPs in the form of equivalent widths. We find the following behaviour for the CaII feature in old-aged SSPs: i) the CaII triplet feature does not change much with time for all metallicities for ages larger than ~3 Gyr, ii) this index shows a strong dependence with metallicity for values below [M/H] ~-0.5 and iii) for larger metallicities this feature does not show a significant dependence either on age or on the metallicity, being more sensitive to changes in the slope of power-like IMF shapes. The SSP spectra have been calibrated with measurements for globular clusters. Fitting the models to two early-type galaxies of different luminosities, we find that the CaII measurements cannot be fitted unless a very dwarf-dominated IMF is imposed, or if the Ca abundance is even lower than the Fe abundance.
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