ANALYTICAL STUDIES OF COLLIMATED WINDS .4. ROTATING AND COLLIMATED MHD OUTFLOWS

This paper continues the study of the initial acceleration and final c ollimation of magnetized and rotating astrophysical winds, via analyti cal and exact steady MHD solutions, selfsimilar in the meridional dire ction. By prescribing the shape of the streamlines on the poloidal pla ne for a nonspherically symmetric gas pressure, related a posteriori t o the density via a nonconstant polytropic index gamma relationship (P proportional to rho(gamma)), the main physical features of the outflo wing plasma are deduced. Simple analytical relations show that cylindr ical collimation and superAlfvenic terminal velocities can be attained asymptotically which depend on the rotation rate, the collimation dis tance from the base and the pressure gradient. If the plasma is overpr essured at the flow axis, the pinching magnetic field can confine the jet, while if the gas is underpressured at its axis, the centrifugal f orce cannot always counterbalance the pinching magnetic stress and inw ards pressure gradient. Physically acceptable solutions are obtained b y a numerical integration of the radial dependence of the MHD system f rom the subAlfvenic to the asymptotically collimated regions and by a smooth crossing of the Alfven critical surface. Two classes of solutio ns are found where either the flow speed increases monotonically to an asymptotic value, or it reaches a maximum value at an intermediate re gion. In the last case it is the toroidal magnetic field that collimat es asymptotically the wind, while in the former the outflow of a slow rotator (respectively fast rotator) is collimated by the gas pressure (respectively by the magnetic field). The possible implications of the se results on the modelling of astrophysical winds from slow and fast magnetic rotators are shortly discussed.