H-K Project

The Sunspot Cycle

1. Introduction

Since the invention of the astronomical telescope in the early seventeenth century, the Sun has been one of the most-studied objects in the universe. After almost four centuries, however, many of the puzzles of the Sun remain unsolved - from a detailed understanding of the nature of the 11-year sunspot cycle to a simple answer to the simple question, ``Is the Sun a normal star?''

Compared to some stars, the Sun seems to be very ordinary; in fact, its relative quiescence is beneficial to our existence on the planet. However, that doesn't mean that the Sun is completely static either. The Sun is changing minutely as it evolves from burning hydrogen in its core, and in several billion years, will swell to the size of a red giant star.

Photograph of the sun, 1906
Figure 1: Photograph of the Sun taken by Palmer on 30 July 1906.

2. The Earliest Observations
Observing Sunsports in 1630
Figure 2: An illustration from Scheiner's Rosa Ursina, published in 1630, showing how observations of sunspots were made.
However, on shorter time scales, the Sun is also changing. Images of the Sun have been made since the 17th century; first from traces done by earlier astronomers such as Scheiner, Galileo, and Hevelius, to the modern day where we monitor layers of the Sun using tools like spectroscopy, photometry, and helioseismology.

The observations of Scheiner and Hevelius were taken on several consecutive days by projecting an image of the Sun onto a sheet of white paper and tracing out the positions and appearence of sunspots.

Those observations show the motion of sunspots across the disk of the Sun due to the solar rotation, and the changes in the size and shape of individual sunspots from day to day. This was a very important discovery - it shows that the spots were not due to imperfections in the telescopes used to make the observations, and that they were physically related to the Sun itself. This revelation was also controversial because heavenly spheres like the Sun were thought to be perfect and unblemished.

These are not the first observations of sunspots; Chinese astrononers had recorded occurrences of sunspots for centuries - the first edition of the great Chinese Encyclopaedia, published in 1322 contained accounts of observations of 45 sunspots between AD 301 and AD 1275.

Sunspot Diagram
Figure 3: This drawing was made by Hevelius in May of 1643.

Galileo and his contemporaries noticed that the individual sunspots were not static; the sunspots grew and decayed. Furthermore, the number of sunspots on the surface at any one time also varied. But the ``sunspot cycle'' was not recognized for another 200 years.


3. Discovery of the 11-year Sunspot Cycle

Although regular observations of the Sun began in the 17th century, the recognition of the sunspot cycle didn't occur for almost 200 years. Although noted astronomers such as LaLande and Wm. Herschel observed the Sun and recorded the presence of sunspots, it wasn't until 1843 that Heinrich Schwabe noted that the number of sunspots varied with a period near 10 years. Even so, his idea was not immediately accepted, until the 1850's. In 1847, Wolf in Zurich has begun compiling the available sunspot observations in an effort to calibrate the observations of each astronomer to a unified ``official'' sunspot number. From this improved record, Wolf was able to measure the mean sunspot cycle length of 11.1 years.

 
Wolf's record of sunspots
Figure 4: Figure 4 shows the Wolf's record of sunspots form 1749-1862 and the number of aurorae (Northern Lights) observed each year back to 1710.
 

In 1858, Wolf published his formula for determining the daily sunspot number, R = k(10g + f), where g is the number of spot groups, and f is the number of spots seen on the surface (including those in groups). The quantity k is a calibration factor that is different for each observer. From using this formula, observations from a large number of different observers could be compiled, thereby making sure that measurements of the sunspot number would be unbroken, regardless of inclement weather at some of the observatories on any particular day. This method of determining the sunspot number is still used today.


4. Surface Differential Rotation and the Butterfly Diagram

Coincident to Wolf's and Schwabe's observations, were those by Carrington, an amateur astronomer in England. He noticed in his measurements a latitude drift of sunspots towards the equator with time, and discovered that at the beginning of a solar cycle, that new sunspots developed at mid-latitudes. This ``law of latitudes'' was confirmed by Wolf and by Spörer in Anklam and later on at Potsdam (it is sometimes called ``Spörer's Law'') who traced the phenomenon back to records dating from 1621.

Maunder's ``Butterfly'' diagram
Figure 5: Maunder's ``Butterfly'' diagram, published in 1904 (M.N.R.A.S., 64, 747).
Maunder, another Englishman published a paper showing the drift of the mean latitude of sunspots in 1904, in what is now called ``Maunder's butterfly digaram'', so named because the distribution of sunspots in each hemisphere over the sunspot cycle resembles a series of butterfly wings.

Figure 5 shows the distribution of sunspot latitudes from 1876 to 1902. What is immediately noticable is that at the beginning of a sunspot cycle, new spots appear at higher latitudes. Throughout the course of the cycle, spots appear closer to the equator.


5. From Astronomy to Astrophysics: the Magnetic Sunspot Cycle
Mount Wilson Observatory's founder, George Ellery Hale, discovered the magnetic nature of sunspots from spectra of sunspots obtained at the 60-ft solar tower in 1908. He then began monitoring the polarity of sunspots, especially bipolar sunspot pairs, where two spots traveled together with different polarities. He also noticed that the polarity of the leading spot was switched from the Northern and Southern hemispheres of the Sun. During the decline of the sunspot cycle to its minimum in 1913, Northern Hemisphere leading spots had ``south-seeking poles'' (negative polarity), while following spots had north (positive) polarity. This was reversed in the Southern Hemisphere, preceeding spots were of north, following spots of south, polarity.
Photograph of a bipolar sunspot
Figure 6: A photograph of a bipolar sunspot. The two spots have different polarities.
However as the next cycle began, and new spots began forming at higher latitides, their polarities were found to be reversed. Using the newly-completely 150-ft tower telescope, Hale and others (particularly Ellerman, Nicholson, Joy and Pettit) monitored the polarity of over 2,000 sunspot groups throughout the next cycle. When the very first spot appeared for the following cycle in June of 1922 (even before the current cycle had ended) and was observed by Ellerman to have the same pattern of polarity that was observed 19 years earlier. Thus the 11-year sunspot cycle of Wolf, Schove, Maunder and Spörer was really a 22-year magnetic cycle.

6. The Present-Day Sunspot Cycle
reconstructed sunspot number
Figure 7: The reconstructed sunspot number from AD 1609 to the present.

In Figure 7, the yearly mean sunspot number is plotted from 1609 to 1995. It is obvious that the length and the strength of each individual cycle varies; the time between successive sunspot maxima is between 8 and 15 years. For the most part, the rise time of a sunspot cycle is shorter than the decay time, and sometimes, for example circa AD 1790 the decay is prolonged.

The period of time between AD 1630 and 1710 is known as the ``Maunder Minimum''. The apparent lack of sunspots during this time is not simply due to lack of observations, or observational error. In fact, such notable scientists as Sir William Herschel, Cassini, and other made careful observations of the Sun during this time, but few if any sunspots were seen. Another lull in the sunspot number occurred between AD 1795 and 1820, known as the ``Dalton Minimum''. It is now believed that the Sun varies on timescales longer than the 11-year sunspot cycle or the 22-year magnetic cycle.

The shape of the sunspot cycle seems to be linked to the height; cycles which rise rapidly generally have higher maxima (for example compare the cycles from the 1960's and 1970's). In Figure 8, individual cycles are overlayed (the gridmarks are one year in the x direction and 20 in sunspot number on the y axis). More active cycles reach their peaks as much as two years earlier than weaker cycles, although they all nearly converge during the decay phase.

 

1996 marked the beginning of a new sunspot cycle.

Relationship between cycle rise time and peak height
Figure 8: A plot by Waldmeier (Figure 8) showing the relationship between cycle rise time and peak height.