Non-parametric star formation histories for four dwarf spheroidal galaxiesof the Local Group

We use recent Hubble Space Telescope colour-magnitude diagrams of the resol ved stellar populations of a sample of local dSph galaxies (Carina, Leo I, Leo II and Ursa Minor) to infer the star formation histories of these syste ms, SFR(t). Applying a new variational calculus maximum likelihood method, which includes a full Bayesian analysis and allows a non-parametric estimat e of the function one is solving for, we infer the star formation histories of the systems studied. This method has the advantage of yielding an objec tive answer, as one need not assume a priori the form of the function one i s trying to recover. The results are checked independently using Saha's W s tatistic. The total luminosities of the systems are used to normalize the r esults into physical units and derive SN type II rates. We derive the lumin osity-weighted mean star formation history of this sample of galaxies.