The acceleration of the nonsymmetric and nonpolytropic MHD solar wind

Abstract

Abstract A method for obtaining analytically several classes of solutions of the full MHD equations for steady, rotating, nonspherically symmetric and nonpolytropic collimated magnetized outflows from a gravitating central object is outlined. These solutions correspond to a polytropic relationship between pressure and density but with a variable polytropic index, while their topology is governed by several hydromagnetic critical points that select a unique wind-type outflow solution. The deviation of the solutions from the original Parker model is parameterized with the introduction of appropriate parameters, such as the deviation of the density from the spherically symmetric case, ω, the deviation of the pressure from a spherically symmetric pressure distribution, κ, the deviation of the streamlines from the spherically symmetric case, s , the effects of rotation, λ and the effects of the magnetic field, β. If ω = κ = λ = β = s = 0, a dipolar, spherically symmetric in density and pressure, nonrotating and nonmagnetized radial Parker-type wind outflow is obtained. We find that the higher is the deviation of the density distribution from the spherically symmetric case, the larger is the initial acceleration. On the other hand, the more magnetically dominated is the outflow and the larger is the pressure inhomogeneity, the rotation amplitude and the flaring, the smaller is the initial acceleration. These results are at variance with attempts to generalize to nonpolytropic outflows the well established result of polytropic outflows wherein, for example, large flaring is usually associated with higher initial acceleration; in nonpolytropic flows exactly the opposite holds. Such properties should be considered in modelling the initial acceleration of the hydromagnetic solar wind.