In this paper we compute new multi-zone photo-chemical evolution models for elliptical galaxies, taking into account detailed nucleosynthetic yields, feedback from supernovae and an initial infall episode. By comparing model predictions with observations, we derive a picture of galaxy formation in which the higher is the mass of the galaxy, the shorter are the infall and the star formation timescales. Therefore, in this scenario, the most massive objects are older than the less massive ones, in the sense that larger galaxies stop forming stars at earlier times. Each galaxy is created outside-in, i.e. the outermost regions accrete gas, form stars and develop a galactic wind very quickly, compared to the central core in which the star formation can last up to ~1.3 Gyr. In particular, we suggest that both the duration of the star formation and the infall timescale decrease with galactic radius. (abridged) By means of our model, we are able to match the observed mass-metallicity and color-magnitude relations for the center of the galaxies as well as to reproduce the overabundance of Mg relative to Fe, observed in the nuclei of bright ellipticals, and its increase with galactic mass. Furthermore, we find that the observed Ca underabundance relative to Mg can be real, due to the non-neglibile contribution of type Ia SN to the production of this element. We predict metallicity and color gradients inside the galaxies which are in good agreement with the mean value of the observed ones. (abridged)
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