At lowest order the large scale magnetic field of the Sun can be represented as a dipole tilted relative to the rotation axis, ignoring for the moment the contributions due to active regions and other localized regions. Consider the effects of outflow of the solar wind plasma and of rotation. Physically, both effects tend to distend the field lines near the equator, where the flow is approximately perpendicular to the magnetic field lines, due to the flow tending to drag the frozen-in magnetic field with it. These effects are shown quantitatively in Figure 11.1, which displays the results of MHD simulations of a dipolar magnetic field imposed at the photosphere and solar wind outflow [e.g., Pneuman and Kopp, 1971]. Note that the polar magnetic field lines have been pulled ``open'' while the closed field lines near the equator have been pulled out into a current sheet. Inspection of Ampere's Law (3.13) show that this current flows perpendicular to the page. This current sheet is known as the ``heliospheric current sheet''. The axis of the current sheet, where the normal magnetic field strength is very small, is known as the ``magnetic neutral line''. A similar process occurs at the top of more localized coronal loops and helmet streamers.
Figure 11.1: A dipole source of magnetic field is imposed at the photosphere and the MHD equations are used to construct the magnetic field lines in the cases with (solid lines) and without (dashed lines) a self-consistent solar wind outflow [Pneuman and Kopp, 1971].
Digressing for a moment, note that current sheet/neutral line configurations like Figure 11.1 involve field lines that are almost anti-parallel near the neutral line. If plasma flows or stresses cause these field lines to come together then the magnetic energy can be released in a process called ``magnetic reconnection''. The favoured models for solar flares and terrestrial substorms involve magnetic reconnection, as discussed in Lectures 8, 14 and 15.
The heliospheric current sheet persists into the outer heliosphere and is responsible for both local and global phenomena in the solar wind. Moreover, for a uniform plasma density at the base of the corona, easier escape of the plasma particles will cause the plasma density on open field lines to be smaller (and the outflow speed larger) than on closed field lines at the same distance from the Sun. This concentration of plasma in the solar equatorial band is expected to produce higher levels of thermal X-rays and other emission (Figure 11.2), as indeed observed.
Figure 11.2: An artist's sketch of the plasma structure and magnetic configuration expected near the solar equator [Hundhausen, 1972].
Neither the solar rotation axis nor the effective dipole axis are perpendicular to the ecliptic plane. Accordingly, the Sun's rotation causes the heliospheric current sheet to move up and down at a fixed observer's position, with associated changes in the plasma density and the direction (towards/away) of the magnetic field (Figure 11.3). This wavy pattern of the current sheet is sometimes referred to as the ``ballerina skirt'' effect. Localized coronal magnetic configurations can also be expected to modify the position and properties of the heliospheric current sheet.
Figure 11.3: The ``ballerina skirt'' ripples predicted on the heliospheric current sheet [Dryer, 1998].