Differential stellar population models: how to reliably measure [Fe/H] and [alpha/Fe] in galaxies

We present differential stellar population models, which allow improved determinations of the ages, iron and alpha-element abundances of old stellar populations from spectral fitting. These new models are calibrated at solar abundances using the predictions from classical, semi-empirical stellar population models. We then use the predictive power of fully synthetic models to compute predictions for different [Fe/H] and [alpha/Fe]. We show that these new differential models provide remarkably accurate fits to the integrated optical spectra of the bulge globular clusters NGC 6528 and 6553, and that the inferred [Fe/H] and [alpha/Fe] agree with values derived elsewhere from stellar photometry and spectroscopy. The analysis of a small sample of Sloan Digital Sky Survey early-type galaxies further confirms that our alpha-enhanced models provide a better fit to the spectra of massive ellipticals than the solar-scaled ones. Our approach opens new opportunities for precision measurements of abundance ratios in galaxies.