Dynamical Evolution of Boson Stars II: Excited States and Self-Interacting Fields

The dynamical evolution of self-gravitating scalar field configurations in numerical relativity is studied. The previous analysis on ground state boson stars of non-interacting fields is extended to excited states and to fields with self couplings. Self couplings can significantly change the physical dimensions of boson stars, making them much more astrophysically interesting (e.g., having mass of order 0.1 solar mass). The stable ($S$) and unstable ($U$) branches of equilibrium configurations of boson stars of self-interacting fields are studied; their behavior under perturbations and their quasi-normal oscillation frequencies are determined and compared to the non-interacting case. Excited states of boson stars with and without self-couplings are studied and compared. Excited states also have equilibrium configurations with $S$ and $U$ branch structures; both branches are intrinsically unstable under a generic perturbation but have very different instability time scales. We carried out a detailed study of the instability time scales of these configurations. It is found that highly excited states spontaneously decay through a cascade of intermediate states similar to atomic transitions.