Population Synthesis in the Blue III. The Integrated Spectrum of M67 and the Spectroscopic Age of M32

We construct an integrated spectrum of the intermediate age, solar metallicity Galactic cluster M67, from individual spectra of cluster members. The integrated spectrum is used as a template to test our stellar population synthesis (SPS) models, in an age and [Fe/H] regime where such models remain largely untested. We show that our models predict a spectroscopic age of 3.5 +/- 0.5 Gyr for M67, in excellent agreement with the age we derive from the color-magnitude diagram of the cluster. The same age is obtained when using Hbeta, Hgamma or Hdelta as the age indicator. Our models predict the abundances of Fe, Mg, C and N in agreement with detailed abundance analyses of cluster stars, to within 0.1 dex. Encouraged by the high degree of consistency of our models, we apply them to the study of the integrated spectrum of the central 3 arcsec of the compact elliptical galaxy M32. The resulting luminosity-weighted age of the galaxy ranges between 2 and 3.5 Gyr, depending on the Balmer line used. According to our models, the center of M32 seems to have a super-solar light-weighted Fe abundance, ranging between [Fe/H] ~ +0.1 and +0.3, depending on the Fe line adopted. Light-weighted abundance ratios found for the center of M32 are as follows: [Mg/Fe] ~ -0.1 -- -0.2, [C/Fe] and [N/Fe] ~ 0. We find that single SPS models with a solar-scaled abundance pattern cannot fit all the Balmer and metal lines in the integrated spectrum of M32. There is a systematic trend in the sense that bluer absorption lines indicate a younger age and a higher [Fe/H]. This slight inconsistency can be due either to (unaccounted for) abundance ratio effects on blue iron and Balmer line indices, or to a spread of the ages of the stellar populations in M32. Current stellar population models cannot break this degeneracy at the level of accuracy required to address this problem.