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

We investigate the Mg–σ and –σ 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 σ 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 Hβ vs 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 Hβ vs plane cannot be reproduced by a model in which galaxy age is the only parameter driving the index-σ relation. In our sample we do not find significant evidence for an anti-correlation of ages and metallicities which would keep the index–σ 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 cannot 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 σ > 100 km s. Under the assumption that there is no age gradient along the index–σ relations, the abundance-ratio corrected Mg–σ, Fe–σ and Hβ–σ relations give consistent estimates of ∆[M/H]/∆log σ ≃ 0.9± 0.1. The slope of the Hβ–σ relation limits a potential age trend as a function of σ to 2-3 Gyrs along the sequence.