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The observed central densities of Milky Way dwarf spheroidal galaxies (dSphs)are significantly lower than the densities of the largest (Vmax about 35 km/s)subhalos found in dissipationless simulations of Galaxy-size dark matter hosts.One possible explanation is that gas removal from feedback can lower coredensities enough to match observations. We model the dynamical effects ofsupernova feedback through the use of a time-varying central potential in highresolution, idealized numerical simulations and explore the resulting impact onthe mass distributions of dwarf dark matter halos. We find that in order tomatch the observed central masses of M_star about 10^6 M_sun dSphs, the energyequivalent of more than 40,000 supernovae must be delivered with 100%efficiency directly to the dark matter. This energy requirement exceeds thenumber of supernovae that have ever exploded in most dSphs for typical initialmass functions. We also find that, per unit energy delivered and per cumulativemass removed from the galaxy, single blow-out events are more effective thanrepeated small bursts in reducing central dark matter densities. We concludethat it is unlikely that supernova feedback alone can solve the "Too Big toFail" problem for Milky Way subhalos.

Can Feedback Solve the Too Big to Fail Problem?