An analytical MHD wind model with latitudinal dependences obtained using separation of the variables

A new class of analytical 2-D solutions of the full set of the steady magnetohydrodynamic (MHD) equations, describing an axisymmetric helicoidal magnetized outflow originating from a rotating central object, is presented. The solutions are systematically obtained via a nonlinear separation of the variables in the momentum equation. The analysis yields three parameters which measure the anisotropy in the latitudinal distribution of various flow quantities. Topologically, the wind speed is controlled by an X-type critical point that acts to filter out a single wind-type branch and the Alfven singularity. The solutions can be regarded as an extension outside the equatorial plane of the Weber & Davis (1967) model of magnetized winds but with a variable polytropic index.