Measuring age, metallicity and abundance ratios from absorption-line indices

In this study we present detailed calculations of absorption-line indices on the Lick system based on the new stellar models by Salasnich et al. incorporating the enhancement of alpha-elements, both in opacity and in chemical abundances. The models span large ranges of initial masses, chemical compositions and ages, and are calculated for both solar and enhanced abundance ratios [X-el/Fe] of alpha-elements. With these models and the so-called response functions of Tripicco & Bell, we calculate the indices for single stellar populations (SSPs) of different age, metallicity and degree of enhancement. Starting from the widely accepted conviction that H-beta is a good age indicator, that [MgFe] is most sensitive to metallicity and indices such as Mg-b, Mg-2 and others are most sensitive to metallicity and degree of enhancement, we made use of the triplet H-beta, Mg-b and (Fe) and minimum-distance method proposed by Trager et al. to estimate the age, the metallicity and the enhancement degree for the galaxies of the Gonzalez sample and compare the results with those of Trager et al. and Thomas, Maraston & Bender. Because very large differences are found - in particular, as far as age is concerned, ours are systematically older than those of Trager et al. and Thomas et al. - we analyse in a great detail all possible sources of disagreement, going from the stellar models and SSPs to many technical details of the procedure to calculate the indices and finally the pattern of chemical elements (especially when alpha-enhanced mixtures are adopted). Each of the above aspects of the problem bears on the final result: amazingly enough, at increasing complexity of the underlying stellar models and SSPs, the uncertainty increases. However, the key issue of the analysis is that at given metallicity Z and enhancement factor, the specific abundance ratios [X-el/Fe] adopted for some elements (e.g. O, Mg, Ti and probably others) dominate the scene because with the Tripicco & Bell response functions they may strongly affect indices such as H-beta and age in turn. In brief, with the ratio [Ti/Fe] = 0.63 adopted by Salasnich et al., H-beta at old ages turned out to be larger than the mean observational value and therefore the age was forced to very old values in order to recover the observations. In contrast, the results by Trager et al. and Thomas et al. are immediately recovered if their [Ti/Fe] ratios are adopted, i.e. [Ti/Fe] = 0.0 or 0.3, respectively. We have also analysed how the galaxy ages, metallicities and degrees of enhancement vary with the triplets of indices in usage. With this aim in mind we turn to the Trager 'IDS pristine' sample, which contains many more galaxies and a much wider list of indices than the Gonzalez sample. The solution is not unique in reflecting that the poor ability of most indices to be disentangled among the three parameters. Finally, in light of the above results and points of uncertainty, we have made some remarks on the interpretation of the distribution of early-type galaxies in popular two-indices planes, such as H-beta versus [MgFe]. We argue that part of the scatter along the H-beta axis observed in this plane could be attributed to a spread both in the degree of enhancement and some abundance ratios rather than to the age, which is the current explanation. If so, another dimension is added to the problem, i.e. the history of star formation and chemical enrichment in individual galaxies. The main conclusion of this study is that deriving ages, metallicities and the degree of enhancement from line indices is a cumbersome affair where the results are still uncertain.