Self-Similar Magnetohydrodynamics
Abstract
For the solution of the full set of magnetohydrodynamics (MHD) equations in the presence of gravity due to a central point-mass, a self-similar theory for a general polytrope has already suggested a set of exact time-dependent solutions by analytical methods for a, (gamma = 43) polytrope, since (gamma = 4/3) is the simplest to treat. In the present paper while going for a complete set of self-similar solutions, we find that (gamma = 4/3) is the only physically-possible polytrope and that then, pressure is independent of the scalar function A, and depends on angle and time only. We also obtain a specific form of time-dependence for the self-similar variable.
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