Collapse versus Disruption: The Fate of Compact Self-Gravitating Systems in Ultralight Dark Matter Halos

Time-varying gravitational fluctuations induced by ultralight dark matter (ULDM) are expected to stochastically heat self-gravitating systems and drive them toward more diffuse configurations. Here we show that this intuition breaks down for sufficiently compact systems. We uncover a counterintuitive dynamical mechanism in which external heating can _accelerate_, rather than suppress, relaxation-driven core collapse. Using numerical simulations of compact stellar systems embedded in fluctuating backgrounds induced by ULDM, we find that their long-term evolution is governed by a nontrivial competition between two-body relaxation and stochastic heating, leading to distinct evolutionary outcomes, including core collapse, disruption, and quasi-stationary configurations. We further introduce a dimensionless parameter that quantifies the relative importance of relaxation and heating, which helps organize these regimes into a predictive phase diagram. Near the disruption boundary, we identify remnants with properties resembling those of ultra-faint dwarf galaxies. Our results reveal a previously unrecognized dynamical phase structure of self-gravitating systems in fluctuating gravitational backgrounds, with important implications for small-scale probes of ULDM.