ANALYTICAL STUDIES OF COLLIMATED WINDS .2. TOPOLOGIES OF 2-D HELICOIDAL MHD SOLUTIONS

An analytic class of solutions of the full MHD equations for steady, rotating, nonspherically symmeric and helically collimated magnetized outflows from a gravitating central object is presented. By assuming a streamline geometry appropriate for helicoidally collimated outflows, the required heating/cooling and temperature distribution to drive the outflow is calculated. The novel approach is followed of relaxing the restrictive assumption of a polytropic equation of state, which has been used in almost all available studies of rotating magnetized winds. It is found that our solutions correspond to a polytropic relationship between pressure and density but with a variable index-gamma. The topology of the solutions is governed by a pair of hydromagnetic critical points that select a unique wind-type outflow solution. The parameter space of the solutions is fully explored by varying the strength of the magnetic field, rotation and collimation. Special emphasis is given on the role of the magnetic field that (a) specifies the latitudinal extent of the polar conical flow, (b) introduces new critical points and (c) subsequently changes drastically the topologies of pure hydrodynamic rotating outflows that were studied in the previous article of this series. By comparing the magnetically dominated solutions with the hydrodynamically dominated ones, it is found that (i) the more magnetically dominated is the outflow, the more bipolar is its character, i.e., the more confined is the cone of the flow around the rotation and magnetic axis, (ii) the heating is more isothermal-like extending over larger distances, (iii) the asymptotic radial speed of magnetized outflows is larger than that of unmagnetized outflows and increases logarithmically, as in the isothermal Parker wind, and (iv) the initial acceleration is considerably reduced relative to the initial acceleration of unmagnetized outflows. As in pure hydrodynamic flows, the higher is the degree of collimation and ratation amplitude, the larger is the terminal wind speed and the total heating. Some general properties are briefly discussed in connection to astrophysical systems, such as coronal hole/helmet structures and helicoidal bipolar flows/surrounding denser disks.