8 - The two-dimensional representation of the extended activity cycle

Summary

For you'll look sweet upon the seat of a bi-cycle built for two.

iMusic-hall song

Introduction

Chapter 5 described the one-dimensional characteristics of the solar activity cycle in terms of variations of the scalar function N(t), where N is a number representing the number of sunspots (or sunspot groups or faculae or any other indicator) and t is the time. The butterfly diagram, shown again in Figure 8.1, provides a two-dimensional characterization of the cycle in terms of a function N(λ, t), where λ is the latitude, a representation which yields additional information of obvious importance to the heuristic models discussed in Chapter 6. (Strictly speaking, the existence of active longitudes emphasizes that N is a function of three variables, N(λ, φ, t), where φ is the Carrington longitude.)

It has been known for ∼ 130 years that the wings of the butterfly diagram overlap to some extent. The overlap is marginal between some cycles, e.g. 18 and 19, but in other cases, e.g. 19 and 20, it extends over ∼ 2 years. Sunspot minimum, therefore, is a point on the one-dimensional plot determined partly by the decay of the old cycle and partly by the rise of the new.

In the one-dimensional approach, all activity lying between successive minima is associated with that particular cycle but, in the two-dimensional approach of the butterfly diagram, active regions of each cycle are distinguished by two properties: latitude and orientation of the magnetic axis (see§ 2.10). Spots of the new cycle should appear at higher latitudes (20° – 40°) and exhibit a reversed magnetic orientation compared with those of the old cycle for a given hemisphere.