Synthesis of Hα absorption in old stellar systems: formation of the cluster red sequence by ‘downsizing’

We compute population synthesis models for the variation of Hα absorption indices ( Hα A and Hα F ), as a function of age and metallicity in old stellar systems. The models are based on the STELIB spectral library of Le Borgne et al., and defined at a resolution of 3 Å full width at half‐maximum. Errors in the age and metallicity responses are derived by bootstrap resampling the input measurements on the stellar library. The indices are found to be highly sensitive to age variation, with only moderate response to metallicity. For galaxies uncontaminated by nebular emission, our Hα A index is more powerful in breaking the age–metallicity degeneracy than Hβ or Hγ F . Using a sample of red cluster galaxies from Nelan et al., carefully selected to exclude objects with emission, we find a steep decline of Hα A with velocity dispersion (slope −0.75 ± 0.07 Å dex −1 ). The slope can be translated to constraints on age and metallicity scaling relations, incorporating measurement errors and also the model errors determined from the bootstrap method. If the Hα A –σ slope is due only to age, we obtain Age ∝σ 0.95±0.12 . Because Hα A depends quite weakly on [Fe/H], a metallicity interpretation would require Fe/H ∝σ 1.2 or steeper. The Hα A –σ 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 underpredict the observed slope. The discrepancy could arise from differences in the sample selection. In particular, our sample probes a lower mass range, is not explicitly selected on morphological criteria, and excludes objects significantly bluer than the red sequence. We discuss in detail the impact of emission contamination on the results, and conclude that this effect is unlikely to yield the observed behaviour in the Hα–σ relations. Indeed, similar results are obtained using Hα F , despite its different sensitivity to Hα and [N  ii ] emission lines. 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 .