7.4.3 ${ <{\rm Fe}>}$ versus ${ {\rm Mg}_2}$

The strong ${ {\rm Mg}_2}$-$\sigma$ relation and the weak ${ <{\rm Fe}>}$-$\sigma$ relation indicate that there is no strong correlation between $\log { <{\rm Fe}>}$ and ${ {\rm Mg}_2}$. This can be seen in Fig. . Overplotted as dashed lines are the model predictions from the single-age single metallicity stellar population models from Vazdekis et al. (1996). It is seen that no variation of age or metallicity can reproduce the shallow slope of the $\log { <{\rm Fe}>}$- ${ {\rm Mg}_2}$ relation in the interval in ${ {\rm Mg}_2}$ spanned by the data. The Vazdekis et al. models have solar abundance ratios, including [Mg/Fe] = 0. Also overplotted on the figure are predictions from the Weiss et al. (1995) models. These have [Mg/Fe] = 0.45, and they are able to reproduce the shallow slope of the $\log { <{\rm Fe}>}$- ${ {\rm Mg}_2}$ relation (by varying only the age). Based on these arguments, several authors (e.g. Worthey et al. 1992, J97) have concluded that at least some E and S0 galaxies must have [Mg/Fe] > 0. Already O'Connell (1976) concluded, that Mg I exhibited a distinct enhancement in giant E nuclei with respect to the Fe-peak elements. J97 further noted, that since $\log { <{\rm Fe}>}$ and ${ {\rm Mg}_2}$ depend in the same way on the mean age of the stellar population (at least in the Vazdekis et al. models), the different slope of the ${ {\rm Mg}_2}$-$\sigma$ and the ${ <{\rm Fe}>}$-$\sigma$ relations imply that [Mg/Fe] is correlated with $\sigma$. We determine [Mg/Fe] in a more direct way in the next section (Sect. ).