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 the order of 0.1 solar mass). The stable $\mathrm{}\left(S\right)\mathrm{}$ and unstable $\mathrm{}\left(U\right)\mathrm{}$ 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 carry 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.