Interaction between the solar wind and the sun's general magnetic field.

An analytical study of the interaction between the solar wind, assumed to start uniformly from the sun's surface, and the sun's general magnetic field, assumed to be a dipole, is presented. Coupled hydrodynamic and hydromagnetic equations are used to obtain solutions with the property of axial symmetry about the dipole axis. The sun's rotation is not considered. A perturbation analysis is carried out to show how the dipole magnetic field is drawn out by the flow, and how the flow is distorted by the magnetic field. A solution for the interplanetary magnetic field is presented and compared with Parker's curl-free solution. This solution shows the radial component of the magnetic field to be proportional to r~ 2 for large values of r, where r is the radial distance from the sun's center measured in terms of the solar radius. The perturbation of the solar wind by the magnetic field is found to be generally small but different in the subsonic and supersonic regions of the velocity field of the solar wind. In the subsonic region, the solar wind velocity in the polar regions is increased and that near the equator is reduced. In the supersonic region, there is a tendency to reverse this perturbation. I. Introduction I N 1958, Parker1 presented his solar wind theorjr and pointed out that the sun's general magnetic field could be drawn out by the solar wind. Thus the interplanetary magnetic field at the orbit of the earth could be of the order of a few 7?s (17 is equal to 10~5 gauss). Moreover, based on the idea that the magnetic lines are fixed in the sun and rotate with the corona, Parker suggested that the magnetic lines will be in the form of simple Archrinedean Spirals. Recent space measurements2'3 have confirmed both Parker's solar wind theory and his model of the interplanetary magnetic field. So far, the physical process by which the sun's general magnetic field is drawn out has not been studied in any detail. The curl-free magnetic solution obtained by Parker 4 shows that the field strength is of the order of r~2 for large values of r measured in solar radii. However, in Parker's analysis, the solar wind is assumed to concentrate near the sun's equatorial plane as a thin sheet and its only action is to cut off the magnetic lines along the equatorial plane. In the present paper, an analytical study of the interaction between the solar wind and the sun's general magnetic field is made by a perturbation technique. In Fig. 1, the solar wind is shown schematically as starting uniformly from the sun's surface. Since the solar wind is composed of hightemperature plasma, it will interact with the sun's general magnetic field, which is assumed to be dipole-like at the sun's surface. Only the interaction outside of the sun is considered. The magnetic field is not assumed to be curl-free. The purpose is to find not only how the sun's general magnetic field is drawn out by the solar wind, but also how the solar wind is distorted by the action of the magnetic field. The sun's rotation is not considered. Thus, the spiral structure of the interplanetary magnetic field is not obtained. In earlier studies5-6 by the present author, the simpler case of an incompressible "solar wind" was considered. In this paper, these studies are extended to include the compressibility effects of the solar wind.