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, $r$.