Diagnostic of chemical abundances and ages from the line strength indices Hb, <Fe>, and Mg2: what do they really imply ?

The line strength indices Hb, Mg2, and <Fe>, together with their gradients and dependence on the galaxy luminosity (mass), observed in elliptical galaxies are customarily considered as reliable indicators of systematic differences in age and abundances of Mg and Fe. In this paper, we address the question whether or not the indices Mg2 and <Fe> (and their gradients) are real indicators of chemical abundances and enhancement of these or other effects must be taken into account. We show that this is not the case because the above indices are severely affected by the unknown relative percentage of stars as function of the metallicity. In order to cast the problem, first we provide basic calibrations for the variations dHb, dMg2, and d<Fe> as a function of the age Dlog(t) (in Gyr), metallicity Dlog(Z/Z_o), and D[Mg/Fe]. Second, we analyze the implications of the gradients in Mg2 and <Fe> observed across these systems. Finally, the above calibration is used to explore the variations from galaxy to galaxy of the nuclear values of Hb, Mg2, and <Fe>. The differences dHb, dMg2, and d<Fe> are converted to differences Dlog(t), Dlog(Z/Z_o), and D[Mg/Fe]. We thoroughly examine the relationship Dlog(t)-Mv, Dlog(Z/Z_o)-Mv, and D[Mg/Fe]-Mv, and advance the suggestion that the duration of the star forming period gets longer or the age of the last episode of stellar activity gets closer to the present at decreasing galaxy mass. This result is discussed in the context of current theories of galaxy formation and evolution. i.e. merger and isolation. In brief, we conclude that none of these can explain the results of our analysis, and suggest that the kind of time and space dependent IMF proposed by Padoan et al. (1997) and the associated models of elliptical galaxies elaborated by Chiosi et al. (1997) should be at work.