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 onto 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 % 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 { \mathrm { H } } \beta vs < 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 { \mathrm { H } } \beta vs < Fe > plane can not 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 anti-correlation 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 anti-correlation can not be completely ruled out given the current data .
Correcting the line-strengths 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 km s ^ { -1 } .
Under the assumption that there is no age gradient along the index– \sigma relations , the abundance-ratio corrected Mg– \sigma , Fe– \sigma and { \mathrm { H } } \beta – \sigma relations give consistent estimates of \Delta { \mathrm { [ } M / H ] } / \Delta \log \sigma \simeq 0.9 \pm 0.1 .
The slope of the { \mathrm { H } } \beta – \sigma relation limits a potential age trend as a function of \sigma to 2-3 Gyrs along the sequence .