We propose a cosmological scenario for the formation and evolution of dwarf spheroidal galaxies (dSphs), satellites of the Milky Way (MW). An improved version of the semi-analytical code GAMETE (GAlaxy Merger Tree & Evolution) is used to follow the dSphs evolution simultaneously with the MW formation, matching the observed properties of both. In this scenario dSph galaxies represent fossil objects virializing at z = 7.2 +/- 0.7 (i.e. in the pre-reionization era z > z_rei = 6) in the MW environment, which at that epoch has already been pre-enriched up to [Fe/H] ~ -3; their dynamical masses are in the narrow range M = (1.6 +/- 0.7) x 10^8 M_sun, although a larger spread might be introduced by a more refined treatment of reionization. Mechanical feedback effects are dramatic in such low-mass objects, causing the complete blow-away of the gas ~100 Myr after the formation epoch: 99% of the present-day stellar mass, M_* = (3 +/- 0.7) x 10^6 M_sun, forms during this evolutionary phase, i.e. their age is >13 Gyr. Later on, star formation is re-ignited by returned gas from evolved stars and a second blow-away occurs. The cycle continues for about 1 Gyr during which star formation is intermittent. At z = 0 the dSph gas content is M_g = (2.68 +/- 0.97) x 10^4 M_sun. Our results match several observed properties of Sculptor, used as a template of dSphs: (i) the Metallicity Distribution Function; (ii) the Color Magnitude Diagram; (iii) the decrement of the stellar [O/Fe] abundance ratio for [Fe/H] > -1.5; (iv) the dark matter content and the light-to-mass ratio; (v) the HI gas mass content.

12 pages, 6 figures, MNRAS accepted