We present a new chemical evolution model for dwarf spheroidal galaxies (dSphs) in the local universe. Our main aim is to explain both their observed star formation histories and metallicity distribution functions simultaneously. Applying our new model for the four local dSphs, that is, Fornax, Sculptor, Leo II, and Sextans, we find that our new model reproduces the observed chemical properties of the dSphs consistently. Our results show that the dSphs have evolved with both a low star formation efficiency and a large gas outflow efficiency compared with the Milky Way, as suggested by previous works. Comparing the observed [α/Fe]-[Fe/H] relation of the dSphs with the model predictions, we find that our model favors a longer onset time of Type Ia supernovae (i.e., 0.5 Gyr) than that suggested in previous studies (i.e., 0.1 Gyr). We discuss the origin of this discrepancy in detail.
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