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We combine the detailed Star Formation Histories of the Fornax and Sculptordwarf Spheroidals with the Mass Assembly History of their dark matter (DM) haloprogenitors to estimate if the energy deposited by Supernova type II (SNeII) issufficient to create a substantial DM core. Assuming the efficiency of energyinjection of the SNeII into DM particles is $\epsilon_{\rm gc}=0.05$, we findthat a single early episode, $z \gtrsim z_{\rm infall}$, that combines theenergy of all SNeII due to explode over 0.5 Gyr, is sufficient to create a coreof several hundred parsecs in both Sculptor and Fornax. Therefore, our resultssuggest that it is energetically plausible to form cores in Cold Dark Matter(CDM) halos via early episodic gas outflows triggered by SNeII. Furthermore,based on CDM merger rates and phase-space density considerations, we argue thatthe probability of a subsequent complete regeneration of the cusp is small fora substantial fraction of dwarf-size haloes.

Dark matter cores in the Fornax and Sculptor dwarf galaxies: joining halo assembly and detailed star formation histories