We calculate the energy that baryons must inject into cold dark matter (CDM) halos in order to remove centrally divergent DM cusps on scales relevant to observations of dwarf spheroidal galaxies (dSphs). We estimate that the CDM halos often associated with the Milky Way's dSphs (Mvir/M☉ ∼ 109–10) require ΔE ∼ 1053–55 erg in order to form cores on scales comparable to the luminous size of these galaxies. While supernova Type II (SNeII) explosions can in principle generate this energy, the actual contribution is limited by the low star formation efficiency implied by the abundance of luminous satellites. Considering that CDM's well-known "core/cusp" and "missing satellite" problems place opposing demands on star formation efficiencies, existing observational evidences for large cores in the most luminous dSphs require that CDM models invoke some combination of the following: (1) efficient (of the order of unity) coupling of SNeII energy into dark matter particles, (2) star formation histories peaking at unexpectedly high redshifts (z ≳ 6), (3) a top-heavy stellar initial mass function, and/or (4) substantial satellite disruption or other stochastic effects to ease the substructure abundance constraints. Our models show that the tension between CDM problems on small scales would increase if cored DM profiles were to be found in fainter dwarfs.

THE COUPLING BETWEEN THE CORE/CUSP AND MISSING SATELLITE PROBLEMS