Population Synthesis in the Blue. I. Synthesis of the Integrated Spectrum of 47 Tucanae from Its Color-Magnitude Diagram

We perform an empirical synthesis of the blue integrated spectrum of the metal-rich globular cluster 47 Tucanae, based directly on the color-magnitude diagram of the cluster coupled to a moderately high resolution spectral library. Freed from any significant dependence on theory, we are able to perform a fundamental test of the adequacy of the spectral library and its associated stellar parameters. Excellent fits are achieved for almost all absorption-line indices studied, provided the computations are corrected for two limitations of the spectral library, namely, the lack of a representative set of metal-poor giants and the absence of CN-strong stars. The latter effect is corrected by means of spectrum synthesis from model photospheres, considering the abundance pattern of CN-strong and CN-normal stars. We also need to perform a slight correction of the metallicity of the cluster (by -0.05 dex in relation to the standard value [Fe/H]=-0.7) in order to match the metal line index measurements in the cluster spectrum. After these relatively small adjustments, the overall spectral agreement is good. Good fits are achieved for Hβ, Hγ, Mg b, , Ca λ4227, and Fe λ4383, and only Hδ_F is overpredicted. Thus, ages inferred from Hδ_F are slightly older than the ages based on the other Balmer lines, by ~3 Gyr. The success of this exercise suggests that previous failures to synthesize the spectrum of 47 Tuc must have arisen from inadequacies in the theoretical evolutionary isochrones and/or luminosity functions. Such a possibility is considered in a companion paper.