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

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, kindly provided by M. Salaris, and new semi-empirical calibrations between fundamental stellar parameters and observables. Model line-strengths include all corrections for deficiencies of the stellar library that are described in Paper I. We highlight the importance of correctly modeling the giant-branch LF of the cluster 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 one, which lacks AGB stars. After all corrections are made, the CMD and the spectroscopic ages (from Hgamma and Hbeta) are both ~ 11 Gyrs. Previously older spectroscopic ages were due to either the omission of AGB stars or the use of isochrones that neglect the effects of He-diffusion and alpha-enhancement. Uncertainties in spectroscopic age determinations of old stellar populations stem from a number of effects, the most important of which are the Teff and Fe/H-scales of the giant stars used in the stellar library, the LF on the upper giant branch, and the assumed metallicity of the target stellar population itself. A +/- 1 Gyr uncertainty in age results from uncertainties of +/- 75 K in the Teff-scale of the library giants, +/- 0.1 dex in their Fe/H-scale and, +/- 0.1 dex in the level of the giant-branch LF, and +/- 0.1 dex in the assumed Fe/H of the target stellar population.