  We investigate the gravitational evolution of dark matter halos made up of a
massless bosonic field. The coupled Einstein-Klein-Gordon equations are solved
numerically, showing that such a boson halo is stable and can be formed under a
large class of initial conditions. We also present an analytical proof that
such objects are stable in the Newtonian limit. In the context of boson stars
made of massive scalar fields, we introduce new solutions with an oscillatory
scalar field, similar to boson halos. We find that these solutions are
unstable.
