It is widely accepted that starbursts can dramatically affect their host galaxies via feedback-driven outflows, especially for gas-rich dwarfs with shallow potential wells. The removal of gas from a galaxy's center is predicted to change the gravitational potential, causing "cuspy" cold dark matter (CDM) density profiles to transform into constant-density "cores." Recent hydrodynamical simulations have identified this mechanism as a potential solution to the long-standing core-cusp problem in CDM cosmology, and further predict that cusps can reform within a few 100 Myr post-burst as gas cools and collects in the galaxy center, creating the conditions for another starburst.

We propose a novel, direct test of how feedback from starbursts impacts dwarf galaxy dynamics. We have assembled a sample of nearby dwarf galaxies spanning a range of central density profiles from cuspy to cored, determined from high-quality HI rotation curves, that have archival HST imaging of resolved stars suitable for deriving recent star formation histories (SFHs). We will identify current and recent starbursts and measure their timing, duration, energetics, and spatial extent across our sample, which is large enough to include diverse recent SFHs. With galaxies at a range of times post-burst, we will statistically sample the time evolution of central density profiles following a starburst and test the hypotheses that (1) cored galaxies are post-starburst, and (2) cusps reform on timescales comparable to the dynamical time. This study will probe the fundamental connection between starbursts, gas, and dark matter and provide an observational test of the favored solution to the core-cusp problem.