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

We combine the detailed Star Formation Histories of the Fornax and Sculptor dwarf Spheroidals with the Mass Assembly History of their dark matter (DM) halo progenitors to estimate if the energy deposited by Supernova type II (SNeII) is sufficient to create a substantial DM core. Assuming the efficiency of energy injection of the SNeII into DM particles is $ε_{\rm gc}=0.05$, we find that a single early episode, $z \gtrsim z_{\rm infall}$, that combines the energy of all SNeII due to explode over 0.5 Gyr, is sufficient to create a core of several hundred parsecs in both Sculptor and Fornax. Therefore, our results suggest 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 that the probability of a subsequent complete regeneration of the cusp is small for a substantial fraction of dwarf-size haloes.