Concept

Solar cycle — where it appears

The roughly eleven-year rise and fall in the number of sunspots, whose latitudes migrate towards the equator through each cycle. The magnetic polarities reverse between cycles, so the underlying period is twenty-two years and the familiar number is a property of the count rather than the field.

Named by 5 essays across 2 fields — each of them below, with the objects they name alongside it.

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.

stars · Solar cycle

Down by 280 km, and faster by 164 m/s. A circular orbit at 400 km with a ballistic coefficient of 100 kg/m², integrated down to 120 km through a tabulated atmosphere at solar minimum and solar maximum. At solar min it takes 1.2 years; at solar max it takes 147 days — a factor of 2.9 for the same satellite in the same orbit, decided by an eleven-year cycle nobody controls. The rising curves are the orbital speed on the right-hand scale, and they are the point: the drag force is opposite the motion and takes energy out, and the body goes faster, from 7673 to 7836 m/s. There is no contradiction in it. The specific energy is −μ/2a, so removing energy shrinks a, and the circular speed √(μ/a) rises when a falls; the kinetic energy gained is exactly half the potential energy lost, and the other half is what the air took. Every point on every curve was integrated from da/dt = −(ρ/β)√(μa), and the speed at each point is √(μ/a) at that point rather than a separate model.

An orbit that speeds up as it is slowed down

Drag takes energy out of a satellite and the satellite goes faster. There is no paradox in it, only a sign — and the same sign makes a re-entry date a space-weather forecast rather than an orbital computation, which is why Skylab was predicted for 1983 and came down in 1979.

spaceflight · Atmospheric drag $The Sun's internal rotation: differential above 0.693 R, rigid below, and the 15 nHz between two modes. Angular velocity against fractional radius, in nanohertz, from the inversion of hundreds of thousands of measured rotational splittings. Two features had to be discovered rather than deduced. The convection zone rotates differentially in latitude — 473 nanohertz at the equator, 330 at sixty degrees — and that latitude dependence persists all the way down through it, in surfaces that are very nearly radial rather than the cylinders a rotating convective fluid was expected to produce. And below about 0.693 of the radius the latitude dependence stops: the radiative interior turns as a single rigid body at 430 nanohertz, which is a remarkable thing for a fluid with no strength to do, and requires something — most likely a weak internal magnetic field — to be enforcing it. The two regimes are joined by a shear layer a few per cent of the radius thick, the tachocline, and it is where the solar magnetic cycle is generally thought to be generated, because it is the only place in the Sun with the shear a dynamo of that strength needs. The horizontal marks are what individual modes would report: the rotation averaged over the cavity each one occupies, weighted by the time the wave spends at each radius. A mode of degree 100 is trapped near the surface and reports 473 nanohertz; one of degree 1 passes through the deep interior and reports 458. The 15-nanohertz difference between them is the measurement, and splittings are measured to about a nanohertz — which is why the profile can be resolved at all. The kernels used here have the right support and the right sense; a real inversion uses computed eigenfunctions, and its resolution below 0.2 R is poor for the reason the previous figure gives.$

A fluid that turns as one piece

The Sun's surface turns faster at its equator than at its poles, and everyone expected the inside to do something similar. Below seven-tenths of the way down it does not — the radiative interior rotates as rigidly as a bell, and nothing in hydrodynamics makes a fluid do that.

stars · Internal rotation

The darkness a field pays for

A sunspot is not cool because something is missing. It is cool because a three-thousand-gauss field supplies part of the pressure that holds the column up, the gas therefore supplies less, and the level at which that gas becomes opaque sits some hundreds of kilometres deeper than the surface around it.

stars · Plasma beta

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.

stars · Solar cycle

Named alongside it

The objects these essays reach for when they reach for this one.

Tachocline Convection Differential rotation Maunder minimum Polar field Sunspot Active region Angular momentum transport Asteroseismology Atmospheric drag Babcock leighton dynamo Ballistic coefficient

All concepts