Astronomy & Celestial Mechanics
the sky, computed
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Solar cycle — the series

2 essays on one idea, from the one that introduces it to the one that assumes the rest.
  1. 4 cycles of wings, and the polarity reverses at every boundary. Sunspot latitude against date, one mark per spot group, over 4 cycles of 11 years. The pattern is the reason the plot is called a butterfly diagram, and both of its features are laws with names. Spörer's law is the downward slope: spots emerge near ±28° at the start of a cycle and near ±7° at the end, so each wing narrows towards the equator and never crosses it. Hale's law is what the two mark shapes say: the leading spot of a pair has one magnetic polarity in the north and the other in the south, and both reverse when a new cycle starts — so a diagram that repeats every 11 years in appearance repeats only every 22 in magnetism. The wings overlap: the first high-latitude spots of a cycle appear about 1.6 years before the last low-latitude spots of the one before, which is why counting spots gives a cycle length slightly different from measuring one between polarity reversals. The dot density in time is the sunspot number itself, drawn from the standard skewed fitting function — the rise to maximum takes about four years and the decline about seven, in every cycle ever recorded.

    A magnetic clock read off a butterfly

    Plot sunspot latitude against date and the marks form wings that open at thirty degrees and march to the equator. The polarities reverse between wings, so the magnetic period is twenty-two years and the famous eleven is an artefact of counting spots rather than fields.

    part 1 · stars
  2. One step of memory, and it is kept at the poles. Two predictors of a solar cycle's amplitude, each tested against the seven cycles for which both quantities exist, with amplitudes scaled so that cycle 21 is one. Left: the polar field measured at the minimum before the cycle begins, which correlates with what follows at r = 1.00. Right: the amplitude of the previous maximum, which correlates at r = 0.34 — that is, not at all. The cycle is therefore not a pendulum with momentum; it is a process with exactly one state variable, and the variable is the poloidal field that the decay of the previous cycle's spots leaves behind at high latitude. That is the observational core of the flux-transport picture: spots emerge tilted, their trailing polarity drifts poleward, and what accumulates there is the seed the next cycle's shear will wind up. It is also the only prediction in solar physics with a lead time of years, and it was what said, correctly and unpopularly, that cycle 24 would be the weakest in a century.

    One step of memory kept at the poles

    The amplitude of a solar maximum tells almost nothing about the next one. The polar field measured at the minimum in between tells a great deal — so the cycle is not a pendulum with momentum but a process with exactly one state variable, and the variable is a field of a few gauss at latitudes nobody can see well.

    part 2 · stars

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