Using current models of spectrophotometric properties of single age , single metallicity stellar populations I have computed the Mg _ { 2 } , H \beta , Fe52 and Fe53 line strengths for stellar populations with a metallicity spread .
The comparison of these models with the nuclear indices of early type galaxies yield the following major conclusions .
The metallicity distribution of the closed box , simple model for the chemical evolution of galaxies is not able to account for Mg _ { 2 } and Fe52 , Fe53 values in excess of \sim 0.27,3 and 2.7 , respectively , which are observed in the nuclei of a large fraction of Ellipticals .
To reproduce the line strengths in these galaxies high average metallicities , small metallicity dispersion and old ages are required .
In particular , Mg _ { 2 } values of \sim 0.3 are reproduced only with a metallicity distribution ranging from \sim 0.5Z _ { \odot } to \sim 3Z _ { \odot } , and \sim 15 Gyr old stellar populations .
I interpret the data as indicating that the gas out of which the nuclei of ellipticals formed was pre-enriched , to larger metallicities for increasing Mg _ { 2 } .
The presence of a metallicity dispersion does not alter the relation between Mg _ { 2 } and Iron indices with respect to the SSP models .
Thus , the need for a Mg/Fe overabundance in the strongest lined galaxies is confirmed , and I present a simple way to estimate the [ Mg/Fe ] ratio on the basis of existing models with solar abundance ratios .