SIMBAD references

We investigate distributions of the stellar metallicity Z which can solve the local (within the effective radius) and/or the global G-dwarf problem in elliptical galaxies. We represent an elliptical galaxy with the spherical and isotropic model by Hernquist (1990ApJ...356..359H) and relate the Z dispersion to the stellar binding energy E. Such a Z-E relation may be a single-valued function Z(E), or an E-dependent Z spectrum for each value of E in its proper range. In this preliminary paper we only consider a stellar component of one age, thus disregarding a superposition of several independent Z-E relations. Moreover, we adopt an exploratory approach with the aid of a few simple Z-E relations, and take into account the observed colours and metallicity radial gradients together with the (U-V)-(V-K) and (1550-V)-Mg₂ correlations. We find that some of the adopted Z-E relations fit reasonably well the observed correlations and, at the same time, can solve the local and/or the global G-dwarf problem. In particular, the `Simple Model' can remove the local G-dwarf problem but not the global one, whereas the `Best Accretion Model' by Lynden-Bell (1975VA.....19..299L) can avoid both problems. Furthermore, our results suggest a viable approach to the formulation of a flexible Z-E relation, either as a single-valued Z(E) or an E-dependent Z spectrum, that can solve the G-dwarf problem and agree with all the major observational evidences. We confirm that the mean metallicities, as inferred from the Single Stellar Populations and observed colours or spectral indices (e.g. Mg₂), may be underestimated by up to a factor of two, owing to the stellar metallicity spread in real ellipticals.