The hot coronal plasma making up the solar wind possesses an extremely high electrical conductivity. In such a plasma, we expect the concept of ``frozen-in'' magnetic field-lines, discussed in Section 7.3, to be applicable. The continuous flow of coronal material into interplanetary space must, therefore, result in the transport of the solar magnetic field into the interplanetary region. If the Sun did not rotate then the resulting magnetic configuration would be very simple. The radial coronal expansion considered previously (with the neglect of any magnetic forces) would produce magnetic field-lines extending radially outward from the Sun.
Of course, the Sun does rotate, with a (latitude dependent) period of about 25 days.7.1 Because the solar photosphere is an excellent electrical conductor, the magnetic field at the base of the corona is frozen into the rotating frame of reference of the Sun. A magnetic field-line starting from a given location on the surface of the Sun is drawn out along the path followed by the element of the solar wind emanating from that location. As before, let us suppose that the coronal expansion is purely radial in a stationary frame of reference. Consider a spherical coordinate system that co-rotates with the Sun. Of course, the symmetry axis of the coordinate system is assumed to coincide with the axis of the Sun's rotation. In the rotating coordinate system, the velocity components of the solar wind are written
Figure 7.4 illustrates the interplanetary magnetic field close to the ecliptic plane (i.e., ). The magnetic field-lines of the Sun are drawn into Archimedean spirals by the solar rotation. Transformation to a stationary frame of reference gives the same magnetic field configuration, with the addition of an electric field
The interplanetary magnetic field at 1 AU is observed to lie in the ecliptic plane, and is directed at an angle of approximately from the radial direction to the Sun (Priest 1984). This is in basic agreement with the spiral configuration predicted previously.
The previous analysis is premised on the assumption that the interplanetary magnetic field is too weak to affect the coronal outflow, and is, therefore, passively convected by the solar wind. In fact, this is only the case if the interplanetary magnetic energy density, , is much less that the kinetic energy density, , of the solar wind. Rearrangement yields the condition
Well inside the Alfvén radius (i.e., in the region ), the solar wind is too weak to modify the structure of the solar magnetic field. In fact, in this region, we expect the solar magnetic field to force the solar wind to co-rotate with the Sun. Observe that flux-freezing is a two-way-street: if the energy density of the flow greatly exceeds that of the magnetic field then the magnetic field is passively convected by the flow, but if the energy density of the magnetic field greatly exceeds that of the flow then the flow is forced to conform to the magnetic field.
The previous discussion leads us to the following, rather crude, picture of the interaction of the solar wind and the interplanetary magnetic field. We expect the interplanetary magnetic field to be the undistorted continuation of the Sun's magnetic field for . On the other hand, we expect the interplanetary field to be dragged out into a spiral pattern for . Furthermore, we expect the Sun's magnetic field to impart a non-zero azimuthal velocity to the solar wind. In the ecliptic plane ( ), we infer that