On the dependence of spectroscopic indices of early-type galaxies on age, metallicity and velocity dispersion

We investigate the Mg-sigma and (Fe)-sigma relations in a sample of 72 early-type galaxies drawn mostly from cluster and group environments using a homogeneous data set which is well calibrated on to the Lick/IDS system. The small intrinsic scatter in Mg at a given sigma gives upper limits on the spread in age and metallicity of 49 and 32 per cent respectively, if the spread is attributed to one quantity only and if the Variations in age and metallicity are uncorrelated, The age/metallicity distribution as inferred from the H beta versus < Fe > diagnostic diagram reinforces this conclusion, as we find mostly galaxies with large luminosity-weighted ages spanning a range in metallicity. Using Monte Carlo simulations, we show that the galaxy distribution in the H beta Versus < Fe > plane cannot be reproduced by a model in which galaxy age is the only parameter driving the index-sigma relation. In our sample we do not find significant evidence for an anticonelation of ages and metallicities which would keep the index-sigma relations tight while hiding a large spread in age and metallicity. As a result of correlated errors in the age-metallicity plane, a mild age-metallicity anticorrelation cannot be completely ruled out by the current data. Correcting the line-strength indices for non-solar abundance ratios, following the recent paper by Trager et al., leads to higher mean metallicity and slightly younger age estimates while preserving the metallicity sequence. The [Mg/Fe] ratio is mildly correlated with the central velocity dispersion, and ranges from [Mg/Fe] = 0.05 to 0.3 for galaxies with sigma > 100 kms(-1). Under the assumption that there is no age gradient along the index-sigma relations, the abundance-ratio-corrected Mg-sigma, Fe-sigma and H beta-sigma relations give consistent estimates of Delta [M/H]/Delta log sigma similar or equal to 0.9 +/- 0.1. The slope of the H beta-sigma relation limits a potential age trend as a function of sigma to 2-3 Gyr along the sequence.