Scaling behaviour of a scalar field model of dark matter haloes

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(Φ) leads to dark halo models which have the form of quasi-isothermal spheres. We argue that these fit the observed rotation curves of galaxies better than the centrally cusped haloes of standard cold dark matter. The scalar field model predicts a proportionality between the central densities of the dark haloes 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.