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 sets 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 is required, attributable either to a range of star formation efficiencies or to a range of infall timescales. 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: fixed infall with an efficiency which is linearly dependent on mass, or a fixed efficiency with a mass-dependent infall timescale t~1/sqrt(M). We conclude that the actual scenario may well involve a combination of these two parameters, with mass dependencies which should span the range of those given above.