  Recently the problem of singular galactic cores and over-abundant formation
of dwarf galaxies, inherent to the standard cold dark matter model, had
attracted a great deal of attention. One scenario which may be free of these
problems invokes a self-interacting Bose-field. We find the limiting core
density in this model due to the self-annihilation of the scalar field into its
own relativistic quanta. The limiting density may correspond to the observable
one if there is only one dark matter component. Alternatively, there may be
more than one dark matter species and the annihilation of one species may be
very efficient with subsequent expansion of the other, thus avoiding the
problem of singular cores.
