  We study boson star configurations with generic, but not non-topological,
self-interaction terms, i.e. we do not restrict ourselves just to consider the
standard $\lambda |\psi|^4$ interaction but more general
U(1)-symmetry-preserving profiles. We find that when compared with the usual
potential, similar results for masses and number of particles appear. However,
changes are of order of few percent of the star masses. We explore the
stability properties of the configurations, that we analyze using catastrophe
theory. We also study possible observational outputs: gravitational redshifts,
rotation curves of accreted particles, and lensing phenomena, and compare with
the usual case.
