On the Nature of Solar Activity and Sunspots

Solar physics provides a basis for our comprehension of solar phenomena, and we use this knowledge to explain previous solar events or to forecast future activity. The relationship between sun and earth is of profound importance for a variety of reasons. An unequivocal linkage between certain solar phenomena and the ionospheric state was established decades ago, largely the result of ionospheric measurements using HF sounders, incoherent scatter radars and rocket probes. More recently, advanced satellite observation platforms has made the case even stronger. Herbert Friedman's Sun and Earth [1985] is recommended for additional reading.

To study the origin of sunspots, it is necessary to examine the magnetic field structure on the sun, because, in the absence of the solar magnetic field, current theory does not explain the generation of sunspots or their cyclic behavior. To first order, the sun's field is oriented N-S in its quiescent configuration (sunspot minimum), and its intensity is little more than that of the earth's magnetic field, being approximately I gauss. However, the sun differs from the earth, where the primary source of the field is within the metallic core, because the solar field is confined near the surface. The field is frozen-in to the surface plasma that can move, transporting the field lines with it. In short, the magnetic field is generally too weak to extricate itself from the control of the highly ionized solar plasma. Since the sun and its surface plasma rotate about its NS axis, co-rotation of the surface magnetic field also occurs. However, since the sun is a fluid, this rotation is not uniform as a function of solar (or heliographic) latitude. Indeed, the solar surface rotates differentially, with the equatorial region moving more rapidly than higher heliographic latitudes. This causes the solar magnetic field to become wrapped around the sun over a period of time. It also increases the equatorward magnetic field. Eventually the neighboring stretched field lines become intertwined because of turbulent motion originating in the underlying convection zone. Figure 2-4 shows how this happens. The twisted field lines are hidden below the visible surface and the most intense regions are associated with local magnetic fields of about 4000 gauss. Such fields exert enormous magnetic pressure on the surrounding plasma. As the magnetic pressure begins to exceed the plasma pressure, the fields penetrate the surface and appear as bipolar loops. This phenomenon arises first at a solar latitude of ~ 40 degrees where the field line stretching and convergence is most intense. At the points where the field lines protrude from the surface, the magnetic field intensity is so large that energy is prevented from reaching the surface. These points of opposite polarity are several thousand degrees cooler than their surroundings and appear as dark spots on the photosphere.

Sunspot pairs usually occur in large groups and are contained within rather long-lived (calcium plage) regions. The preceding sunspots of the sunspot pairs have the same polarity as the pole of their hemisphere, whereas the following sunspots have the opposite polarity. Because of differential rotation, the following sunspots lag the overall group motion and form distended unipolar regions that gravitate toward the pole. As a result the latitude of maximum stress moves equatorward and the polar fields become eroded. At sunspot maximum, the polar fields have become completely neutralized. Beyond this point in time, the pole reversal process begins, and the amount of sunspots, now being formed near the low latitude region of limited differential rotation, begins to wane.

Magnetic Flux

Magnetic Flux

T1 T2 T3

(a) Differential Rotation

(b) Bipolar Sunspots

Figure 2-4: Effects of differential rotation on the sun: (A) Development of east-west component of the surface field as the field lines become stretched out between the times T]5 T2, and T3. This brings the lines of magnetic flux closer together. (B) Formation of kinks in the plasma field configuration, leading to the development of bipolar sunspots. An eventual reversal of the field at the poles results from the effective poleward migration of the following spots, which have an algebraic sign opposite to that of the pole in their hemisphere. Adapted from Gibson [1973],

By the time the polarity of the magnetic field has completely reversed, no sunspots are evident. Near solar minimum, the field lines that had been intertwined return to a mostly longitudinal (i.e., N-S) configuration. It takes about 11 years for this process to be completed, and it takes about 22 years for the original magnetic configuration to recur. The process is shown in Figure 2-5. From the figure, we see that the spots first start to appear below 40 degrees latitude, both north and south. The maximum solar activity, as represented by the sunspot area index, occurs several years after sunspots first emerge and several years before the last sunspots appear near the equator.

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Figure 2-5: The top curve is a so-called Butterfly diagram, which shows the migration of sunspots from high latitudes to low as the solar cycle progresses. Also shown is the area of sunspots (middle plot) and a measure of magnetic activity (bottom). Adapted from Chapman [1968].
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