Analysing globular cluster observations : Models and analysis tools for Lick/IDS indices

We have extended our evolutionary synthesis code, GALEV, to include Lick/IDS absorption-line indices for both simple and composite stellar population models (star clusters and galaxies), using polynomial fitting functions. We present a mathematically advanced Lick index analysis tool (LINO) for the determination of the ages and metallicities of globular clusters (CGs). An extensive grid of GALEV models for the evolution of star clusters at various metallicities over a Hubble time is compared to observed sets of Lick indices of varying completeness and precision. A dedicated \chi arrow up -minimisation procedure selects the best model including 1 \sigma uncertainties on age and metallicity. We discuss the age and metallicity sensitivities of individual indices and show that these sensitivities themselves depend on age and metallicity; thus, we extend Wortheys (1994) concept of a "metallicity sensitivity parameter" for an old stellar population at solar metallicity to younger clusters of different metallicities. We find that indices at low metallicity are generally more age sensitive than at high metallicity. Our aim is to provide a robust and reliable tool for the interpretation of star-cluster spectra becoming available from 10 m class telescopes in a large variety of galaxies-metal- rich & metal-poor, starburst, post-burst, and dynamically young. We test our analysis tool using observations from various authors for Galactic and M 31 GCs, for which reliable age and metallicity determinations are available in the literature, and discuss to what extent the observational availability of various subsets of Lick indices affects the results. For M 31 GCs, we discuss the influence of non-solar abundance ratios on our results. All models are accessible from our website, http://www.astro.physik.uni-goettingen.de/ \tildegalev/