The Eleven-Year Sunspot Cycle

Peter O. Taylor

The science of astronomy is filled with serendipity: those times when an individual seeks one answer, only to be surprised by finding another. One of the best known instances concerns the discovery of the sunspot-cycle by the German amateur astronomer, Heinrich Schwabe, in the mid-nineteenth century.

Schwabe began to observe the Sun in 1826 after studying science at the University of Berlin and returning to Dessau to enter business. His interest was not in the Sun itself, but rather in the search for an additional inferior planet; one orbiting inside the path of Mercury. Schwabe believed that eventually this elusive planet must cross (transit) the solar disk and thus reveal its presence to him.

In order to distinguish the proposed planet from a sunspot, he patiently recorded the daily position and movement of each spot. Of course Schwabe never found his "missing" planet. However, in 1843 after seventeen years of almost daily spot observations, he announced a corollary to his fruitless search: the possibility of a ten-year periodicity in the numbers of sunspots.

Rudolf Wolf, then director of the Bern Observatory, became interested in Schwabe's discovery and searched through as much of the available telescopic data as he could locate. Armed with data which extended back to the time of Galileo (1610), Wolf determined the more likely value of eleven years between successive sunspot cycle minima. At the same time, Wolf devised the concept of the "Relative" sunspot number, and began his own series of sunspot observations.

Wolf continued his observational program and computation of the daily Relative Sunspot Number during his long directorship of the Swiss Federal Observatory in Zurich, and these values came to be called, "Zurich Relative Sunspot Numbers." The program was maintained at Zurich until 1980, when the work was assumed by the Royal Observatory of Belgium, and the numbers were re-named, "International Relative Sunspot Numbers."

At about the time that Wolf became intrigued by Schwabe's work, the interest of a young English astronomer, Richard Carrington, was also aroused. Carrington's systematic observations of the positions of sunspots reached its fulfillment in 1858 with his discovery of the relationship of sunspot latitude and sunspot cycle-phase. That is, the average latitude of spot emergence is greatest during the beginning of each cycle (around +/- 28o), and then progresses smoothly towards the equator to average only around 7o at cycle's end. This process has come to be known as "Spoerer's Law," after Gustav Spoerer who investigated the phenomenon at length. The effect is graphically represented by the well-known, "butterfly-diagram."

The overwhelming majority of sunspots occur in two latitude belts stretching from the Sun's equator to about latitudes +/- 35. (Sunspots seldom span the equator.) They are only occasionally seen at 50 or 60 degrees latitude, although sunspot pores have been sighted at latitudes as high as 70o. However, they are generally very short-lived at these extremely high latitudes.

Sunspots are usually not evenly distributed by hemisphere. In fact, the maximum of a given cycle may occur much earlier in one hemisphere than it does in the other; sometimes by a time difference which excedes a year or more.

The intensity (the number of spots at maximum) of the sunspot-cycle maximum varies considerably from one cycle to another. There is some tendency for high and low-intensity cycles to alternate, although this phenomenon is better seen when the maxima of adjacent odd-numbered cycles are averaged and then compared with the (lower maximum) even-numbered cycle which they bracket. Considerable variations in the monthly-mean sunspot number occur during each cycle.

The shape of an individual cycle is mainly dependent upon its intensity at maximum. This factor can be of great significance since it allows for a prediction of the future course of a particular cycle from the observation of only a portion of its lifetime. However, in practice reliable predictions are still very difficult to make.

The table below, from Bray and Loughhead (1965, Sunspots, John Wiley & Sons, Inc., NY.) provides an interesting statistical look at the eleven-year cycle. It is mostly based upon data published by Waldmeier (1961, "The Sunspots in the Years 1610-1960," Zurich) which cover the interval from 1750 to 1958, although some information from recent cycles has been included. The data which refer to cycle intensity have been smoothed after the manner of Waldmeier.

Average Range
Period between maxima: 10.9 years 7.3-17.1 years
Period between minima: 11.1 years 9.0-13.6 years
Time of rise to maximum: 4.5 years 2.9-6.9 years
Time of fall to minimum: 6.5 years 4.0-10.2 years
Maximum sunspot number: 108.2 48.7-201.3
Minimum sunspot number: 5.1 0.0-12.1

In this brief discussion we have been primarily concerned with the performance of the sunspot cycle since the mid-eighteenth century. It is far from certain that sunspot activity has varied with even this predictability prior to that time. For example, very few sunspots were recorded during the years 1645 to 1715, a period which is known as "Maunder's Minimum." At least two other similar instances of prolonged periods of very low sunspot numbers may have occurred before that time.

Still, there are good reasons (dealing with auroral, carbon 14, and naked-eye sunspot indices, and studies of ancient varves, etc.) to presume that the numbers of sunspots has increased and decreased in a fairly regular manner for a very long time, perhaps for hundreds of millions of years.

Peter O. Taylor
AAVSO Solar Division Chairman