Population Synthesis in the Blue II. The Spectroscopic Age of 47 Tucanae

Abstract

We develop a new set of models for intermediate-metallicity single stellar populations in the blue/optical region and use those models to determine the spectroscopic age of 47 Tuc. The models are based on a moderately high-resolution (1.8 A FWHM) empirical spectral library, state-of-the-art theoretical isochrones from M. Salaris and the most recent set from the Padova group, and new semi-empirical calibrations between fundamental stellar parameters and observables. We highlight the importance of correctly modeling the luminosity function (LF) of the cluster at the level of the giant branch, in order to achieve a good reproduction of the integrated spectrum; agreement between the spectroscopic age and the age based on the cluster's color-magnitude diagram (CMD) is achieved only if the observed LF is used rather than the theoretical ones, which either do not include AGB stars (Salaris) or underpredict the total number counts of bright giants in the cluster by a factor of two(Padova). After all corrections are made, the CMD and the spectroscopic ages (from Hgamma and Hbeta) are in close agreement: 11--12 Gyrs for Salaris isochrones and about 13 Gyrs for Padova. The difference between the model ages is due to the inclusion of atomic diffusion in the Salaris models. Previously older spectroscopic ages were due to the underestimate of the number of red giants and/or the use of isochrones that neglected the effects of He-diffusion and alpha-enhancement. A similar underestimate in the bright giant LF, if it exists in current super-solar metallicity models, would cause spectroscopic ages of elliptical galaxies inferred from such models to be too high by approximately 30%.