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

We have examined the Mg-sigma 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-sigma relation of Mgb' = 0.131 log sigma - 0.131 and Mg-2 = 0.257 log sigma - 0.305. The slope of these relations is 25 per cent steeper than that obtained by most other authors owing to the reduced bias of our fitting method. The intrinsic scatter in the global Mg-sigma relation is estimated to be 0.016 mag in Mgb' and 0.023 mag in Mg-2. The Mg-sigma relation for cD galaxies has a higher zero-point than for E and SO galaxies, implying that cDs ape older and/or more metal-rich than other early-type galaxies with the same velocity dispersion. We investigate the variation in the zero-point of the Mg-sigma relation between clusters. We find that it is consistent with the number of galaxies observed per cluster and the intrinsic scatter between galaxies in the global Mg-sigma relation. We find no significant correlation between the Mg-sigma zero-point 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-sigma relation on its own does not place strong limits on systematic errors in Fundamental Plane (FP) distance estimates resulting from stellar population differences between clusters. We compare the intrinsic scatter in the Mg-sigma and Fundamental Plane relations with stellar population models in order to constrain the dispersion in ages, metallicities and MIL ratios for early-type galaxies at fixed velocity dispersion, We find that variations in age or metallicity alone cannot explain the measured intrinsic scatter in both Mg-sigma and the FP. We derive the joint constraints on the dispersion in age and metallicity implied by the scatter in the Mg-sigma 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 per cent in delta t/t and 38 per cent in delta Z/Z if the variations in age and metallicity are uncorrelated; only strongly anticorrelated variations lead to significantly higher upper limits, The joint distribution of residuals from the Mg-sigma 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 anticorrelated (delta t/t approximate to 40 per cent, delta Z/Z approximate to 50 per cent and rho approximate to -0.5), with younger galaxies being more metal-rich.