Multi-state Boson Stars
  Motivated by the increasing interest in models which consider scalar fields
as viable dark matter candidates, we have constructed a generalization of
relativistic Boson Stars (BS) composed of two coexisting states of the scalar
field, the ground state and the first excited state. We have studied the
dynamical evolution of these Multi-state Boson Stars (MSBS) under radial
perturbations, using numerical techniques. We show that stable MSBS can be
constructed, when the number of particles in the first excited state, N2, is
smaller than the number of particles in the ground state, N1. On the other
hand, when N2 > N1, the configurations are initially unstable. However, they
evolve and settle down into stable configurations. In the stabilization
process, the initially ground state is excited and ends in a first excited
state, whereas the initially first excited state ends in a ground state. During
this process, both states emit scalar field radiation, decreasing their number
of particles. This behavior shows that even though BS in the first excited
state are intrinsically unstable under finite perturbations, the configuration
resulting from the combination of this state with the ground state produces
stable objects. Finally we show in a qualitative way, that stable MSBS could be
realistic models of dark matter galactic halos, as they produce rotation curves
that are flatter at large radii than the rotation curves produced by BS with
only one state.
