Two-dimensional MHD models for stellar winds

We present a new class of exact solutions of the steady axisymmetric MHD equations relevant for stellar winds. The geometry of the streamlines and fieldlines is helicoidal. All quantities depend both on distance to the central object and on latitude. A technique based on a nonlinear separation of variables yields the most general solution which depends on latitude via three anisotropy parameters. These are related to typical values of the different quantities at the base of the outflow. We are thus able to model a wide range of winds from almost spherically symmetric to highly anisotropic ones. Topologically, there are two critical points present in the solution for the radial dependence of the outflow speed. One appears at the familiar star-point Alfvenic singularity while the other is at the X-type singularity where the radial flow speed equals the fast MHD wave speed in the radial direction. A unique solution corresponding to zero pressure at infinity must pass through both these two points. For the wind to be able to accelerate to large distances, the density at the equator must exceed the density at the pole. In these circumstances, the polar speed is always greater than the equatorial one. This trend is confirmed by the Ulysses data on the heliolatitudinal dependence of the solar wind as well by interplanetary scintillation data.