Perturbations of Solitonic Boson Stars: Nonlinear Radial Stability and Binding Energy

We study the nonlinear radial stability of boson stars with a solitonic potential across the entire parameter space, focusing especially on families of solutions that support ultracompact models on the perturbatively stable branch. Using a dimensional reduction of the CCZ4 formulation of numerical relativity, we dynamically evolve these models with both internal and external perturbations. We find in particular that there are perturbatively stable models with positive binding energy that do not effectively disperse even under explicit perturbations, challenging the conventional wisdom that negative binding energy is a necessary condition for the dynamical stability of boson stars and other compact objects.