We derive the star formation histories of eight dwarf spheroidal ( dSph ) Milky Way satellite galaxies from their alpha element abundance patterns .
Nearly 3000 stars from our previously published catalog ( Paper II ) comprise our data set .
The average [ \alpha /Fe ] ratios for all dSphs follow roughly the same path with increasing [ Fe/H ] .
We do not observe the predicted knees in the [ \alpha /Fe ] vs. [ Fe/H ] diagram , corresponding to the metallicity at which Type Ia supernovae begin to explode .
Instead , we find that Type Ia supernova ejecta contribute to the abundances of all but the most metal-poor ( { [ Fe / H ] } < -2.5 ) stars .
We have also developed a chemical evolution model that tracks the star formation rate , Types II and Ia supernova explosions , and supernova feedback .
Without metal enhancement in the supernova blowout , massive amounts of gas loss define the history of all dSphs except Fornax , the most luminous in our sample .
All six of the best-fit model parameters correlate with dSph luminosity but not with velocity dispersion , half-light radius , or Galactocentric distance .