The predicted metallicity distribution of stars in dwarf spheroidal galaxies

We predict the metallicity distribution of stars and the ageÐmetallicity relation for six dwarfspheroidal (dSph) galaxies of the Local Group by means of a chemical evolution model thatis able to reproduce several observed abundance ratios, and the present-day total mass andgas content of these galaxies. The model adopts up-to-date nucleosynthesis and takes into account the role played by supernovae of different types (II, Ia) allowing us to follow indetail the evolution of several chemical elements (H, D, He, C, N, O, Mg, Si, S, Ca and Fe). Each galaxy model is specified by the prescriptions of the star formation rate and by the galactic wind effciency chosen to reproduce the main features of these galaxies. These quantities are constrained by the star formation histories of the galaxies as inferred by the observed colourÐmagnitude diagrams (CMD). The main conclusions are: (i) Þve of the six dSph galaxies are characterized by very low star formation efÞciencies ( 0.005Ð0.5 Gyr1) with only Sagittarius having a higher one ( 1.0 Ð5.0 Gyr1); (ii) the wind rate is proportional to the star formation rate and the wind efÞciency is high for all galaxies, in the range i 6Ð15; (iii) a high wind efÞciency is required in order to reproduce the abundance ratios and the present-day gas mass of the galaxies; (iv) the predicted ageÐmetallicity relation implies that the stars of the dSphs reach solar metallicities in a time-scale of the order of 2Ð6 Gyr, depending on the particular galaxy; (v) the metallicity distributions of stars in dSphs exhibit a peak around [Fe/H] 1.8 to 1.5 dex, with the exception of Sagittarius, which shows a peak around [Fe/H] 0.8 dex; (iv) the predicted metallicity distributions of stars suggest that the majority of stars in dSphs are formed in a range of metallicity in agreement with the one of the observed stars.