Talk Title: Measuring age, metallicity and abundance ratios from abosorption line indices
Abstract: In this study we present detailed calculations of absorption line indices on the Lick System, e.g. Hb, Mgb, Mg2, <Fe>, NaD, and C4668, based on the new stellar models by Salasnich et al. (2000) that incorporate the enhancement of alpha-elements both in the opacity and in the chemical abundances. The stellar models span large ranges of initial masses, chemical compositions, and ages. They are followed from the zero age main sequence till the end of the asymptotic giant branch phase or carbon ignition as appropriate, and are calculated for both solar-scaled and alpha-eenhanced abundance patterns. Using these models and the calibration by Tripicco \& Bell (1995), we calculate the integrated indices of Single Stellar Populations (SSPs) of different age, metallicity and degree of enhancement in the alpha-elements. Finally, with the aid of the triplet Hb, Mgb and <Fe>, and the Minimum-Distance Method proposed by Trager et al. (2000), we derive the age, metallicity and enhancement degree for the galaxies of the Gonzalez (1993) sample and compare the results with those by Trager et al. (2000). Since very large differences are found, we analyze in a great detail all possible sources of disagreement, going from the stellar models and SSPs in use to the pattern of chemical elements (especially when alpha-enhanced mixtures are adopted), and the technical procedure used to extend grids of existing theoretical indices. We find that each of the above aspects of the problem bears very much on the final result. Amazingly enough, at increasing complexity of the underlying stellar models and SSPs, the uncertainty of the whole procedure and final results increases. We also analyze how the determinations of age, metallicity and degree of enhancement change at varying the indices under considerations. To this aim we turn to the Trager "IDS Pristine" sample which contains many more galaxies and a much wider list of indices than in the Gonzalez sample. The solutions (age, metallicity, degree of enhancement) we find using different triplets of indices are not unique in that reflecting the poor ability of most indices to disentangle age from metallicity. We also try to better constrain the result by simultaneously using six indices (Hb, Mgb, Mg2, <Fe>, NaD and C4668). Finally, starting from the hint that C4668 and NaD, seem to depend strongly on the metallicity and degree of enhancement and weakly on the age, we propose a new method, i.e. the "Recursive Minimum-Distance Method", to break the age-metallicity degeneracy and to stabilize the solution for age, metallicity, and degree of enhancement. We also make some remarks on the popular two-indices diagnostic. The main conclusion of this study is that deriving ages, metallicities and degree of enhancement from line indices is a cumbersome affair whose results are uncertain. The difficulty may be perhaps overcome only if special care is paid to the quality of the underlying stellar models and the solving procedure.
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