5 - The one-dimensional configuration of the cycle

Summary

A point once said to a line

‘It is a belief of mine

that it's merely pretension

to claim a dimension’

Punch

Introduction

The standard concept of the sunspot cycle is of an 11-year variation in the number of sunspots present on the Sun, N(t), at time t. The data from which N(t) must be determined are the daily values of the Zurich sunspot number R_z (defined in §2.5), but, because only half the Sun is visible at any one time, R_z is a measure of the number of spots on the visible hemisphere, and it is not possible, even in principle, to determine N(t) at any instant t. For this reason N(t) must be derived from a time average of R_z over a longer period, such as a Carrington rotation or a calendar year. The variable t is therefore discrete rather than continuous, and the function N(t) is strictly a sequence, N_i, which represents twice the mean value of R_z during the i^th time interval.

The sunspot number R_z is not the only scalar quantity that exhibits cyclic variations with an 11-year period. Other such quantities include total sunspot area, active region counts, flare counts, the strength of Call emission, the 10 cm radio flux, the incidence of aurorae, the flux of cosmic rays as measured through certain indicators, and even the widths of terrestrial tree rings. Each of these quantities exhibits a slightly different pattern of variation, and the investigation of the various time series can provide different insights into the nature of the cycle. Such a variety of indicators must, however, raise the question as to what is the fundamental physical variable which generates these variations in secondary phenomena which we call the solar cycle.