A Correlation between Various Indices of Solar Activity and Solar Cycles

Abstract

A variation with time of various parameters of relationship between relative numbers and total areas of sunspots is considered on the basis of Zürich and Greenwich data for 1879–1964. A significant difference of these indices on the descending and ascending branch of the 11-year cycle is found. Their variation is essentially different in the even and odd 11-year cycles. Secular variations in parameters of relationship W-S were found for the ascending branch of 11-year cycles. An interpretation is given of the revealed time variations in the relationship between W and S.

It is generally thought that there is a stable correlation between annual relative numbers and total areas of sunspots as Waldmeier (1955) stated. This permits to singly determine the total sunspot area S using the Wolf number W in the formula

$$S = 16.7 W.$$

(1)

However, Xanthakis (1960) showed that the annual ratio S/W is greater during the epoch of maximum of the 11-year solar cycle than during its minimum.. Moreover, the value of the ratio varies in a different way than the Wolf numbers W during the cycle (Kopecký and Rúžičková-Topolová, 1978) and from cycle to cycle (Mergentaler, 1959). All these made us doubt the stable correlation S-W.

The present paper reports on the investigation of the variation in parameters of relationship between monthly Wolf numbers and total sunspot areas (correlation coefficient r, the ratio S/W, and their standard deviation ratio σ_S,/σ_W,) with the 11-year and 22-year and secular solar cycle. The resultslof observations made in Zürich and at the Greenwich Observatory in the years 1879–1964, i.e. 8 eleven-year solar cycles (cycles No. 12–19 according to Zürich) were used as the basic data.