The Solar Wind and its Angular Momentum

Citation

Weber, Edmund John (1967) The Solar Wind and its Angular Momentum. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/MZKH-1K10. https://resolver.caltech.edu/CaltechETD:etd-09232002-112104

Abstract

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A steady-state model is developed for the solar wind in the equatorial plane. Included in the equation of motion are forces due to gravity, viscosity, pressure gradients and magnetic fields. The electrical conductivity of this plasma is taken to be infinite. Since it is impossible to determine the qualitative features of the solar wind motion from a study of the complete set of equations, a simplified model is treated at first. This model has an isotropic pressure, no viscosity and an energy supply characterized by a polytrope law. It is found that the solution of the radial motion must pass through three critical points, whose significance is explained in terms of the characteristic velocities with which small amplitude disturbances propagate. Similarly, the solution of the azimuthal motion has to pass through the radial Alfv?c critical point where the radial Alfv?c Mach number equals unity. The conditions at this point together with the solution of the radial motion then determines uniquely the values of the azimuthal velocity and of the magnetic field everywhere, in particular at the surface of the sun. A numerical solution is obtained for typical parameters. The solution indicates that the magnetic field produces only a modest tendency toward corotation of the solar wind, azimuthal velocities of the order of 1 km sec[^-1] at 1 a.u. being typical, but that the magnetic stresses apply a torque to the sun equal to that required to produce effective corotation out to the radial Alfv?c critical point. For typical solar wind values this will occur between 15 and 50 solar radii out, which implies a substantial loss in the angular momentum of the sun.

The polytrope model does not represent a very real model of the energy supply to the solar wind. To obtain information on the energy transport in the inner part of the solar system a solar wind model is developed in which the density distribution between the photosphere and 10 r[?] is determined from observations and where between 10 r[?] and 1 a.u. heat is supplied by thermal conduction only. With this model the amount of heating due to waves in the solar corona can be determined.

Since the azimuthal motion does not influence the radial motion appreciably, the stability of the azimuthal motion is investigated on the assumption that the radial solution is a given function of distance. It is shown that under these conditions disturbances travel along the characteristics and that for such disturbances the model is stable. Using the same assumption about the radial velocity, the effect of viscosity and anisotropy in the pressure on the azimuthal motion is investigated. The results indicate that the total torque on the sun is slightly less than that obtained from the non?viscous model, but that the torque on the solar wind due to these additional forces results in an azimuthal velocity at 1 a.u. which is approximately 5 km sec[^-1].

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