  Galactic dark matter is modelled by a scalar field. In particular, it is
shown that an analytically solvable toy model with a non-linear
self-interaction potential U(Phi) leads to dark halo models which have the form
of quasi-isothermal spheres. We argue that these fit better the observed
rotation curves of galaxies than the centrally cusped halos of standard cold
dark matter. The scalar field model predicts a proportionality between the
central densities of the dark halos and the inverse of their core radii. We
test this prediction successfully against a set of rotation curves of low
surface brightness galaxies and nearby bright galaxies.
