Magnetohydrodynamic solar/stellar wind models

Abstract

This paper reviews a method to calculate steady, axisymmetric wind models with frozen-in magnetic fields, as a straightforward extension of the one-dimensional model developed by Weber and Davis. The wind solution along the magnetic field is given by an algebraic equation (the Bernoulli equation) for the density. There appear two critical points, the slow mode and the fast mode critical points. The shape of the magnetic field should be determined in such a way that the force-balance across the field is satisfied. This requirement leads to a second-order partial differential equation for the magnetic stream function. This equation is singular at the Alfvén point, and an additional constraint is introduced there to obtain a regular solution. A numerical scheme is developed following this basic formulation, and examples of solutions are presented. The basic feature of the solution is the poleward deflection of the flow due to the build-up of toroidal magnetic field in the wind. The magnetic winds from rotating objects are therefore collimated along the rotation axis.