Figure 1
The number of sunspots as a function of time
since the invention of the telescope.
The period of almost no sunspots in the 17th century
is named the Maunder Minimum.
Each cycle has received a number;
cycle 20, for instance, starts in 1964 and ends in 1976.
[After Zirin (1988).]
In 1843 Schwabe discovered that the number of sunspots exhibits a cyclic behaviour with a period of about 11 yr: the sunspot cycle. Sunspots live a few days or weeks and then disappear again. Early in a cycle the sunspots appear at mid-latitude, and then at progressively lower latitudes (Spörer's law, 1894). The result of this migration process is the familiar butterfly diagram which shows the latitudes of sunspots on the surface as a function of time; it was first drawn by Maunder in 1922. Figure 2 presents an example of such a diagram.
Figure 2
The observed migration of sunspots from mid-latitudes to the equator.
Each "butterfly" represents one 11-yr sunspot cycle.
[After Kiepenheuer (1959).]
Hale proved in 1908 that sunspots are associated with strong magnetic fields. Modern magnetograms of the Sun show that sunspots are components of magnetic bipolar regions. Hale observed that on one hemisphere the leading parts of these active regions (with respect to the direction of the solar rotation) all have the same polarity, while on the other hemisphere the polarities are oppositely oriented. In subsequent 11-yr sunspot cycles the polarities in the active regions are reversed. This are Hale's polarity laws (Hale, 1924); there are only few exceptions to these rules. The Sun therefore exhibits in fact a 22-year magnetic cycle.
The nature of the "dark spots" on the solar surface has long been a mystery. Early observers thought they were planets in front of the Sun, others that they are the slag of the burning Sun or clouds of smoke. Nowadays it is known that sunspots are darker than the surrounding surface because they are cooler: the normal solar surface (photosphere) has a temperature of about 5800 K, whereas sunspots are about 4000 K. The lower temperature is presumably caused by the magnetic fields in sunspots suppressing the convective heat transfer. Sunspot magnetic fields have a strength of a few thousand gauss*), whereas the average photospheric field strength is much less: less than a few gauss (G). For comparison: the strength of the Earth's magnetic field is about 0.6 G at the poles.
The time in which an existing magnetic field in the Sun decays due to resistivity alone is of the order of 10 milliard years, which is comparable to the Sun's lifetime. The origin of the solar cycle is therefore sought in some kind of dynamo process in (the convection zone of) the Sun which continuously regenerates the magnetic field and thus sustains the cyclic behaviour. This dynamo process, described qualitatively in Sect. 3, must then explain the observed magnetic features. Surface effects of emerging magnetic flux are not discussed here in detail; for a description see, for instance, Babcock and Babcock (1955), Howard (1974), Spruit et al. (1987) and Zwaan (1985, 1992).
Observations indicate that active regions are the surface manifestation of a toroidal magnetic field (i.e. a field parallel to the equator) which erupts from the interior of the Sun in the form of loops (cf. Fig. 6). These bipolar active regions live a few days to weeks, sometimes a few months, and then disintegrate in progressively smaller magnetic regions and thus gradually dissolve. What actually happens during this decay process is unknown, but it seems that the field disappears underneath the surface. In the course of the 11-yr cycle this process of development and decay of active regions takes place at progressively lower latitudes, which shows up as the apparent migration of sunspots towards the equator in the butterfly diagram (Fig. 2). It thus seems that it is the toroidal field which moves towards the equator and which reverses direction every 11 yr.
During the decay of active regions the leading parts are mainly spread (by surface diffusion) towards the equator and the trailing parts mainly towards the poles. Most of these regions gradually disappear. A number of following parts, however, does not disappear but forms so-called unipolar magnetic regions which migrate poleward. These unipolar regions have a polarity which is opposite to the polarity of the existing polar field (cf. Fig. 6). This causes a reversal of the polar field, which takes place some years after the reversal of the toroidal field and not at both poles simultaneously (see also Yoshimura, 1976; Wang et al., 1989b; Wilson et al., 1990; Wang and Sheeley, 1991).
The mean polar field of the Sun is relatively week (only a few gauss) and it is not organized in active regions; see e.g. Babcock (1961), Stenflo (1970, 1971), Howard (1974), and Howard and LaBonte (1981). Only about 1% of the total magnetic flux is at the poles, whereas about 70% is concentrated in the area between ca. 30 degrees latitude. Information on the polar field is rather difficult to obtain since we are looking almost along the surface of the Sun there. The Ulysses probe which flies above the solar south pole in 1994 and north pole in 1995 will provide us with a "look from above".
*) To keep in pace with the rest of the astronomers' world
the c.g.s. system of units is used in this thesis.
In the International System of MSKA units
the magnetic field strength is measured in tesla (T);
1 gauss (G) in the c.g.s. system equals 0.0001 T.
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