2014ApJ...782L..39A

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 Type II supernovae (SNe II) is sufficient to create a substantial DM core. Assuming the efficiency of energy injection of the SNe II into DM particles is ε_gc= 0.05, we find that a single early episode, z ≳ z_infall, that combines the energy of all SNe II 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 SNe II. 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 halos.