Linear stability of nonrelativistic self-interacting boson stars

In this paper, we study the linear stability of self -interacting boson stars in the nonrelativistic limit of the Einstein -Klein -Gordon theory. For this purpose, based on a combination of analytic and numerical methods, we determine the behavior of general linear perturbations around the stationary and spherically symmetric solutions of the Gross-Pitaevskii-Poisson system. In particular, we conclude that ground state configurations are linearly stable if the self -interaction is repulsive, whereas there exists a state of maximum mass that divides the stable and the unstable branches in case the self -interaction is attractive. Regarding the excited states, they are in general unstable under generic perturbations, although we identify a stability band in the first excited states of the repulsive theory. This result is independent of the mass of the scalar field and the details of the self -interaction potential, and it is in contrast to the situation of vanishing self -interaction, in which excited states are always unstable.