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

A simple model of chemical enrichment in cluster early-type galaxies is presented where the main parameters driving the formation of the stellar component are reduced to four: the infall time-scale (tau(f)), the formation epoch (z(F)), the star formation efficiency (C-eff) and the fraction of gas ejected in outflows (B-out). We find that only variations in B-out or C-eff can account for the colour-magnitude relation, so that the most luminous galaxies had low values of ejected gas and high efficiencies. Less massive galaxies can be related either to a lower star formation efficiency (C-eff sequence) or to an increased outflow rate (B-out sequence). The combination of chemical enrichment tracks with population synthesis models is used to explore the correlation between mass-to-light ratios and masses. A significant slope mismatch is found between stellar and total ML ratios, which cannot be explained by an age spread and implies a non-linear correlation between total and stellar mass: M-TOT proportional to M-ST(1.2). The sequences driven by star formation efficiency (C-eff) and outflows (B-out) are shown to predict different trends at high redshift. The variation with redshift of the slope of the fundamental plane will increase significantly in the efficiency sequence - driven by age - and will slightly decrease in the outflow sequence - driven by metallicity. The evolution of the zero-point is similar in both cases and within the observational errors of current observations. Measurement of the dependence of the tilt of the fundamental plane on redshift will break the degeneracy between outflows and star formation efficiency, which will enable us to determine whether the colour-magnitude relation is controlled by age or metallicity.