Self-interacting dipolar boson stars and their dynamics

We construct and dynamically evolve dipolar, self-interacting scalar boson stars in a model with sextic (+ quartic) self-interactions. The domain of existence of such dipolar $Q$-stars has a similar structure to that of the fundamental monopolar stars of the same model. For the latter it is structured in a Newtonian plus a relativistic branch, wherein perturbatively stable solutions exist, connected by a middle unstable branch. Our evolutions support similar dynamical properties of the dipolar $Q$-stars that: 1) in the Newtonian and relativistic branches are dynamically robust over time scales longer than those for which dipolar stars without self-interactions are seen to decay; 2) in the middle branch migrate to either the Newtonian or the relativistic branch; 3) beyond the relativistic branch decay to black holes. Overall, these results strengthen the observation, seen in other contexts, that self-interactions can mitigate dynamical instabilities of scalar boson star models.