Synthesis of H-alpha absorption in old stellar systems: Formation of the cluster red sequence by "Downsizing"

We compute population synthesis models for the variation of H-alpha absorption indices (HaA and HaF), as a function of age and metallicity in old stellar systems. The models are based on the STELIB spectral library, and defined at resolution of 3 Angstrom FWHM. The indices are found to be highly sensitive to age variation, with only moderate response to metallicity. For galaxies uncontaminated by nebular emission, our HaA index is more powerful in breaking the age/metallicity degeneracy than H-beta or H-gamma_F. Using a sample of red cluster galaxies carefully selected to exclude objects with emission, we find a steep decline of HaA with velocity dispersion (slope -0.75 +/- 0.07 Angstrom/dex). The slope can be translated to constraints on age and metallicity scaling relations, incorporating measurement and model errors. If the HaA-sigma slope is due only to age, we obtain Age proportional to sigma^{0.95 +/- 0.12}. Because HaA depends quite weakly on [Fe/H], a metallicity interpretation would require Fe/H proportional to sigma^1.2 or steeper. The HaA-sigma slope is consistent with the combined age and metallicity scaling relations reported by Nelan et al. from classical Lick indices. The relations obtained by Thomas et al. significantly under-predict the observed slope. The discrepancy could arise from differences in the sample compositions.We discuss in detail the effects of emission contamination on the results, and conclude that these are unlikely to yield the observed behaviour in the Ha-sigma relations. The steep age--mass relation supports a "downsizing" formation scenario: fainter red-sequence galaxies became quiescent at lower redshifts, z < 0.5. This picture accords with recent observations of truncated red sequences in clusters at z ~ 0.7.