How Many Bursts Does It Take to Form a Core at the Center of a Galaxy?

We present a novel method for systematically assessing the impact of the central potential fluctuations associated with bursty outflows on the structures of dark matter halos for classical and ultrafaint dwarf (UFD) galaxies. Specifically, we use dark-matter-only simulations augmented with a manually added massive particle that modifies the central potential and approximately accounts for a centrally concentrated baryonic component. This approach enables precise control over the magnitude, frequency, and timing of rapid outflow events. We demonstrate that this method can reproduce the established result of core formation for systems that undergo multiple episodes of bursty outflows. In contrast, we also find that equivalent models involving only single (or a small number of) burst episodes do not form cores with the same efficacy. This is important because many UFDs in the local Universe are observed to have tightly constrained star formation histories that are best described by a single early burst of star formation. Using a suite of cosmological zoom-in simulations, we identify the regimes in which single bursts can and cannot form a cored density profile. Our results suggest that it may be difficult to form cores in UFD-mass systems with a single early burst, regardless of its magnitude.