Magnetized galactic halos and velocity lags
  We present an analytic model of a magnetized galactic halo surrounding a
Mestel gravitating disc. The magnetic field is taken to be in energy
equipartition with the pressure dominant rotating halo gas ({\it not} with the
cosmic rays), and the whole system is in a steady state. A more flexible
`anisotropic equipartition' model is also explored. A definite pressure law is
required to maintain the equilibrium, but the halo density is constant. The
velocity/magnetic system is scale-free. The objective is to find the rotational
velocity lag in such a halo. The magnetic field is not force-free so that
angular momentum may be transported from the halo to the intergalactic medium.
We find that the `X'-shaped structure observed for halo magnetic fields can be
obtained together with a simple analytic formula for the rate of decline of the
velocity with height $z$. The formula also predicts the change in lag with
radius, $r$.
