Can Feedback Solve the Too Big to Fail Problem?

The observed central densities of Milky Way dwarf spheroidals (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 proposed solution is that gas removal from feedback can lower core densities enough to match observations and that repeated bursts can aid in this process. We use high-resolution, idealized simulations to explore the effects of time-varying central potentials on the density distributions of dwarf dark matter halos, mimicking repeated bursts of baryonic feedback. We find that for the same mass of gas removed, cyclic blow-outs are less effective at lowering dark matter densities than a single large burst. In order to match the observed densities of M about 10^6 M_sun dSphs, the energy equivalent of more than 40,000 supernovae must be delivered with 100% efficiency directly to the dark matter. This exceeds the number of supernovae that have ever exploded for typical initial mass functions. The mass-loading required is also significant. More than 500 times the total mass in stars today must be ejected from these galaxies, a mass that exceeds the baryonic allotment for the halos of concern. Based on these results, we conclude that it is unlikely that episodic supernova feedback can solve the 'Too Big to Fail' problem for Milky Way subhalos.