The Wolf Number

Until the middle of century XIX there wasn’t a standard method to quantify the solar activity. In those years (1843 and 1851) the double announcement of Schwabe showing the solar cycle took place and, in 1848, Wolf introduced the number that is named after him. With it, he could confirm the existence of the cycle and reconstruct previous cycles. Although Wolf thought that the area of the sunspots was the best indicator of the activity, he finally decided to make a simple count, easier to calculate during a solar observation.

Although the method has some problems, its simplicity has allowed to maintain it up to the present; in fact, there probably isn’t a group of data in Astronomy covering such a long time with the homogeneity of the Wolf number.

It is calculated by means of the following formula:

 

R = k ( 10 g + f )

 

where R is the Wolf number (also called "relative number of sunspots"), k is a factor for standardization, g is the number of groups and f is the number of umbras.

K is only used for statistical purposes, to combine data from several observers. For one observer can consider k = 1.

G is the most imprecise factor when it comes to determining the Wolf number. The reason is the ambiguity that exist in the concept of "group", specially when the groups are very small or there are several of them in the same active region. A good understanding of the nature and behavior of the sunspots is helpful. Frequently,  two or more groups appear nearby one another and, sometimes, the only way to distinguish them is by observing their evolution. For that reason, a continuity in the observations is advisable.

The number of spots, f, includes the pores (sunspots without penumbra) and the umbras. Although there isn’t a standard criterion, in general, the smallest pores are not included in the count. When there are several cores in a same penumbra, each one is counted as a sunspot. An isolated sunspot is considered as a group.

Examples:

- One sunspot: R = 10*1+1 = 11
- One group with 8 spots: R = 10*1+8 = 18
- One group with 3 spots, one group with 19 spots and one spot with 2 umbras: R = 10*3+24 = 54