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 Å, FWHM) empirical spectral library, state-of-the-art theoretical isochrones from M. Salaris and the most recent set from the Padova group, and new semiempirical 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 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 asymptotic giant branch stars (Salaris) or underpredict the total number counts of bright giants in the cluster by a factor of 2 (Padova). After all corrections are made, the CMD and the spectroscopic ages (from Hγ and Hβ) are in close agreement: ~11-12 Gyr for Salaris isochrones and ~13 Gyr 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 α-enhancement. Uncertainties in spectroscopic age determinations of old stellar populations stem from a number of effects, the most important of which are the T_eff 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 T_eff scale of the library giants, -/+0.1 dex in the level of the giant branch LF, and +/-0.1 dex in the assumed [Fe/H] of either the target stellar population or the assumed zero point of the metallicity scale of the stellar library. A similar underestimate in the bright giant LF, if it exists in current supersolar metallicity models, would cause spectroscopic ages of elliptical galaxies inferred from such models to be too high by approximately 30%.