Self-interactions can stabilize excited boson stars

We study the time evolution of spherical, excited ($i.e.$ nodeful) boson star models. We consider a model including quartic self-interactions, controlled by a coupling $\Lambda$. Performing non-linear simulations of the Einstein-(complex)-Klein-Gordon system, using as initial data equilibrium boson stars solutions of that system, we assess the impact of $\Lambda$ in the stability properties of the boson stars. In the absence of self-interactions ($\Lambda=0$), we observe the known behaviour that the excited stars in the (candidate) stable branch decay to a non-excited star without a node; however, we show that for large enough values of the self-interactions coupling, these excited stars do not decay (up to timescales of about $t\sim 10^4$). The stabilization of the excited states for large enough self-interactions is further supported by evidence that the nodeful states dynamically form through the gravitational cooling mechanism, starting from dilute initial data. Our results support the healing power (against dynamical instabilities) of self-interactions, recently unveiled in the context of the non-axisymmetric instabilities of spinning boson stars.