Core collapse in resonant self-interacting dark matter across two decades in halo mass

Core collapse, a process associated with self-interacting dark matter (SIDM) models, can increase the central density of halos by orders of magnitude with observable consequences for dwarf galaxy properties and gravitational lensing. Resonances in the self-interaction cross section, features of hidden-sector models with light mediators and attractive potentials, can boost the strength of self-interactions near specific relative velocities, accelerating collapse in halos with central velocity dispersions near the resonance. To explore this phenomenon, we present a suite of idealized $N$-body simulations of isolated halos with masses ${10}^{7}--{10}^{9}{M}_{\ensuremath{\bigodot}}$ evolved under two resonant cross section (RCS) models with localized enhancements to the cross section on scales $v\ensuremath{\sim}5--50\text{ }\text{ }\mathrm{km}\text{ }{\mathrm{s}}^{\ensuremath{-}1}$. We show that the change in halo internal structure depends on how the velocity distribution of bound particles moves across resonances in the cross section during core formation and collapse. The interplay between the velocity distribution of bound particles and localized features of the cross section causes deviations from self-similar evolution, a characteristic of velocity-independent cross sections, at the level of up to 20%. Depending on the alignment with resonant features, halos of different masses reach different evolutionary stages after a fixed physical time and develop diverse density profiles and rotation curves.