On breaking the age-metallicity degeneracy in early-type galaxies: infall versus star formation efficiency

The correlation between [Mg/Fe] and galaxy mass found in elliptical galaxies imposes a strong constraint on the duration of star formation. Furthermore, the colour-magnitude relation restricts the range of ages and metallicities of the stellar populations. We combine these two constraints with a model of star formation and chemical enrichment including infall and outflow of gas to find that the trend towards supersolar [Mg/Fe] in massive ellipticals excludes a pure metallicity sequence as an explanation of the colour-magnitude relation. An age spread from galaxy to galaxy is thereby required, attributable either to a range of star formation efficiencies (C-eff) or to a range of infall time-scales (tau(f)). We find that the inferred range of stellar ages is compatible with the small scatter and the redshift evolution of the colour-magnitude relation. Two alternative scenarios can explain the data: a fixed tau(f) with a mass-dependent efficiency, C-eff proportional to M; or a fixed C-eff with mass-dependent infall, tau(f) proportional to1/rootM. We conclude that the actual scenario may well involve a combination of these two parameters, with mass dependences that should span the range of those given above.