ON THE RELATION OF LIMITING CHARACTERISTICS TO CRITICAL SURFACES IN MAGNETOHYDRODYNAMIC FLOWS

We investigate the relation between critical surfaces and limiting cha racteristics or separatrices in the set of magnetohydrodynamic (MHD) d ifferential equations that govern astrophysical flows such as winds, j ets, accretion-type inflows, siphon flows in coronal loops, etc. For t he particular case of axisymmetric self-similar solutions, we show tha t, at these critical/separatrix surfaces, the component of the flow ve locity that is perpendicular to the directions of axisymmetry and self -similarity equals the slow/fast MHD wave speed in that direction. Our general analysis and claims are fully supported by analytical example s of three broad classes of axisymmetric self-similar solutions for fl ows in a uniform or spherical gravitational field. For these examples of exact solutions, we plot the various families of characteristics of the MHD partial differential equations. We then find that one member of each family of characteristics is asymptotically tangent to the cor responding separatrix which coincides with a critical surface there. B esides the well-known polytropic cases with constant polytropic index, more general flows with a variable polytropic index are also analysed .