The peculiar motions of early-type galaxies in two distant regions – V. The Mg–σ relation, age and metallicity

We have examined the Mg–σ relation for early-type galaxies in the EFAR sample and its dependence on cluster properties. A comprehensive maximum likelihood treatment of the sample selection and measurement errors gives fits to the global Mg–σ relation of Mgb = 0.131 logσ− 0.131 and Mg2 = 0.257 logσ− 0.305. The slope of these relations is 25% steeper than that obtained by most other authors due to the reduced bias of our fitting method. The intrinsic scatter in the global Mg–σ relation is estimated to be 0.016 mag in Mgb and 0.023 mag in Mg2. The Mg–σ relation for cD galaxies has a higher zeropoint than for E and S0 galaxies, implying that cDs are older and/or more metal-rich than other early-type galaxies with the same velocity dispersion. We investigate the variation in the zeropoint of the Mg–σ relation between clusters. We find it is consistent with the number of galaxies observed per cluster and the intrinsic scatter between galaxies in the global Mg–σ relation. We find no significant correlation between the Mg–σ zeropoint and the cluster velocity dispersion, X-ray luminosity or X-ray temperature over a wide range in cluster mass. These results provide constraints for models of the formation of elliptical galaxies. However the Mg–σ relation on its own does not place strong limits on systematic errors in Fundamental Plane distance estimates due to stellar population differences between clusters. We compare the intrinsic scatter in the Mg–σ and Fundamental Plane (FP) relations with stellar population models in order to constrain the dispersion in ages, metallicities and M/L ratios for early-type galaxies at fixed velocity dispersion. We find that variations in age alone or metallicity alone cannot explain the measured intrinsic scatter in both Mg–σ and the FP. We derive the joint constraints on the dispersion in age and metallicity implied by the scatter in the Mg–σ and FP relations for a simple Gaussian model. We find upper limits on the dispersions in age and metallicity at fixed velocity dispersion of 32% in δt/t and 38% in δZ/Z if the variations in age and metallicity are uncorrelated; only strongly anti-correlated variations lead to significantly higher upper limits. The joint distribution of residuals from the Mg–σ and FP relations is only marginally consistent with a model having no correlation between age and metallicity, and is better-matched by a model in which age and metallicity variations are moderately anti-correlated (δt/t≈40%, δZ/Z≈50% and ρ≈−0.5), with younger galaxies being more metal-rich.