Radial spectra and dynamical signatures of excited boson stars

Abstract

We compute the lowest radial mode of spherically symmetric boson stars along equilibrium branches with a fixed number of radial nodes, considering both mini boson stars and quartically self-interacting models. By reformulating the pulsation equations in additive variables that remain regular at the zeros of the background scalar field, the eigenvalue problem can be integrated directly through the nodes of excited configurations. For all branches examined, the first zero of the constrained fundamental radial eigenvalue coincides, within numerical resolution, with the first simultaneous critical point of the Arnowitt--Deser--Misner (ADM) mass, Noether charge, and binding energy. We further evaluate the radial eigenvalue for the threshold models identified in nonlinear spherical evolutions of excited boson stars and find a simple empirical correlation with the node number and self-interaction strength. Our results provide a regular perturbative framework for excited boson stars and clarify the relation between constrained radial modes, equilibrium critical points, and nonlinear stability diagnostics.