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 earl y-type galaxies drawn mostly from cluster and group environments using a ho mogeneous 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 sp read in age and metallicity of 49 and 32 per cent respectively, if the spre ad is attributed to one quantity only and if the Variations in age and meta llicity 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 ran ge in metallicity. Using Monte Carlo simulations, we show that the galaxy d istribution in the H beta Versus < Fe > plane cannot be reproduced by a mod el in which galaxy age is the only parameter driving the index-sigma relati on. 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 correla ted errors in the age-metallicity plane, a mild age-metallicity anticorrela tion cannot be completely ruled out by the current data. Correcting the lin e-strength indices for non-solar abundance ratios, following the recent pap er 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 assu mption that there is no age gradient along the index-sigma relations, the a bundance-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 tr end as a function of sigma to 2-3 Gyr along the sequence.