Not all cores are equal: Phase-space origins of dynamical friction, stalling and buoyancy

Dynamical friction governs the orbital decay of massive perturbers within galaxies and dark matter halos, yet its standard Chandrasekhar formulation fails in systems with cores of (roughly) constant density, where inspiral can halt or even reverse, phenomena known respectively as core stalling and dynamical buoyancy. Although these effects have been observed in simulations, the conditions under which they arise remain unclear. Using high-resolution N-body simulations and analytic insights from kinetic theory, we systematically explore the physical origin of these effects. We demonstrate that the overall distribution function (DF) of the host, not just its central density gradient, determines the efficiency and direction of dynamical friction. Core stalling arises when the perturber encounters a plateau in the DF, either pre-existing or dynamically created through its own inspiral, while buoyancy emerges in systems whose DFs possess an inflection that drives an unstable dipole mode. We show that double power-law density profiles with rapid outer-to-inner slope transitions naturally produce such DF features, which is why structurally similar cores can yield radically different dynamical outcomes. Our results provide a unified framework linking the phase-space structure of galaxies to the fate of embedded massive objects, with direct implications for off-center AGN, the dynamics of nuclear star clusters, and the stalled coalescence of black holes in dwarf galaxies and massive ellipticals.