Modeling the Response of Dark Matter Halos to Gas Ejection

We propose an analytic CuspCore model for the response of dark matter (DM) halos to central gas ejection, as a mechanism for generating DM-deficient cores in dwarfs and high-z massive galaxies. We test this model and its other three variants using idealized N-body simulations. The model assumes an instantaneous change of potential, followed by a relaxation to a new Jeans equilibrium. The process turns out to be violent relaxation during the first few orbital periods, followed by phase mixing. By tracing the energy diffusion iteratively, the model reproduces the simulated DM profiles with ~10% accuracy or better. A variant based on adiabatic invariants shows similar precision for moderate mass change but underestimates the DM expansion for strong gas ejection. A variant based on a simple empirical relation between DM and total mass ratios makes slightly inferior predictions. The energy of a shell encompassing fixed DM mass is not conserved under shell crossing, making the earlier version of the CuspCore model (Freundlich+20) underestimate the DM response, which can be partially remedied by introducing an alternative “energy” definition. Our model enables the study of the differential response of a multi-component system of stars and DM in the formation of DM-deficient galaxies.