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Published online by Cambridge University Press: 25 May 2016
We analyzed 10 dwarf spheroidal galaxies (dSphs) in the Local Group, and found two distinct sequences on the Mvir/L - Mvir plane: Mvir/L ∝ Mvir1.6 for Mvir < 108M⊙ whereas Mvir/L ≃ const. for Mvir > 108M⊙ (Mvir and L are the virial mass and the total luminosity of a dSph, respectively). We interpret the discontinuity as the threshold for the gas in dSphs to be blown away by successive supernovae. We succeeded in giving a quantitative explanation of the discontinuity mass of 108M⊙ as the blow-away condition. We further derived the above relation for the low-mass dSphs, assuming that the initial star formation rate of the dSphs is proportional to the inverse of the cooling time. The relation of high-mass dSphs is also explained along with the same consideration, with the condition that the gas cannot be blown away.