Astronomy & Celestial Mechanics
the sky, computed
Concept

Sunspot — where it appears

A dark region of the solar photosphere where a field of some three kilogauss suppresses convection, cooling the gas to around four thousand kelvin. The field supplies part of the pressure holding the column up, so the gas is evacuated and the visible surface sits several hundred kilometres deeper than its surroundings.

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

A spot is dark because it is squeezed. Pressure against depth below the quiet photosphere's optical surface, drawn as a ratio to the pressure there. The rising curve is the surrounding gas, which grows exponentially with a 140-kilometre scale height because that is what hydrostatic equilibrium in an ideal gas produces. The flat pair of bands is the spot's own budget: a magnetic pressure of 3.58·10⁵ dyn/cm² from a 3000-gauss field, which is 25 per cent of the total, plus the gas pressure left over. Horizontal balance requires the two columns to reach the same total at the same geometric level, and the level at which they do is 348 kilometres below the quiet surface — so the spot's own optical surface sits in a hollow. Measured Wilson depressions, obtained from the foreshortening of a spot near the limb, are four to six hundred kilometres. Nothing about the darkness was assumed: a field strength read off a Zeeman splitting fixes the magnetic share, the share fixes the depression, and the depression fixes the temperature the deeper layer must have to carry the reduced flux.

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.

Solar cycleBabcock leighton dynamoConvectionDynamoFlux transportFlux tubeHydrostatic equilibriumJoys lawMagnetic pressureMaunder minimumMeridional circulationOpacity

All concepts