To what Extent are Mg2 and <Fe> indicators of Mg and Fe Abundances?

The gradients in line strength indices such as Mg2 and <Fe> (Carollo & Danziger 1994a,b; Carollo et al. 1993), and their increase toward massive system (Worthey et al. 1992, Faber et al. 1992, Davies et al. 1993, Weiss et al. 1995) observed in elliptical galaxies are customarily considered as indicators of gradients in the chemical abundances of Mg and Fe and arguments are given for an enhancement of Mg ($\alpha$-elements in general) with respect to Fe toward the center of these galaxies or going from dwarf to massive ellipticals. In this paper, we present a detailed analysis of the whole problem aimed at understanding how the indices Mg2 and <Fe> depend on the the chemical abundances and age of the stellar mix of a galaxy. We find that Mg2 and <Fe> do not simply correlate with the abundances of Mg and Fe and the ratio Mg/Fe, but depend also on the underlaying distribution of stars in different metallicity bins N(Z), or equivalently on the past history of star formation. In practice, inferring the abundance of Mg and Fe and their ratio is hampered by the need of some information about N(Z). Finally, the observational gradients in Mg2 and <Fe> do not automatically imply gradients in chemical abundances.