Abstract
Abstract We describe asymptotic solutions for stationary, axisymmetric, perfect MHD, polytropic winds, both classical and relativistic. They are expressed as field-region solutions and current-carrying boundary layer solutions smoothly joined by asymptotic matching. The vicinity of the polar axis is one of these boundary layers. In general, the boundary layers are null surfaces. It is argued that the boundary layer regions, in particular the axial one, should stand out observationally because of their larger density and activity. We associate the axial boundary layer with a jet. Current closure is self-consistently achieved in these solutions, which we obtain both in the case of vanishing or non-vanishing circumpolar asymptotic current. It is shown that the total current about the polar axis is simply related to the set of the five first integrals which characterize the flow and that non-vanishing values of this quantity are not available to all winds, but only to a restricted class which we present here....
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