Astronomy & Celestial Mechanics
the sky, computed
Concept

Polar cap — where it appears

The region around each magnetic pole where field lines are open to the solar wind, bounded by the auroral oval. It grows while dayside reconnection opens flux and shrinks when nightside reconnection closes it, so its area traces the balance between the two.

Named by 3 essays across one field — each of them below, with the objects they name alongside it.

A factor of 100 in the wind, 8 degrees in the aurora. The latitude of the last closed field line against the solar wind's dynamic pressure, for a dipole of 0.31 gauss at the equator. The chain is short and every link is exact. Pressure balance puts the magnetopause at a distance going as the sixth root of the field pressure over the ram pressure; a dipole line reaching equatorial distance L returns to the surface at colatitude arcsin(1/√L); so the polar cap's edge is that, and the aurora sits just equatorward of it on the outermost closed lines. Across the 100-fold range of pressure drawn — which covers everything from a quiet wind to a severe storm — the magnetopause moves from 13.1 to 6.1 planetary radii and the oval from 74.0 to 66.1 degrees. The shaded band is where the oval is actually observed. The open magnetic flux is exactly the reciprocal of the standoff distance, so it rises by a factor of 2.15 over the same range — which is the quantity that actually matters for a storm, and it is the only one of the three that changes by much.

An aurora that is a sixth root inside an arcsine

The magnetopause distance fixes which field lines are open, the open ones map to a cap around each pole, and the cap's edge is where the aurora is. A hundredfold change in the solar wind moves that edge by eight degrees — and across planets whose fields differ by four orders of magnitude it moves by ten.

sky · Magnetosphere The rate at which the solar wind opens the Earth's field. The rate at which reconnection at the dayside magnetopause turns closed field lines into open ones, as a voltage in kilovolts — webers of flux per second — against the clock angle of the interplanetary field in the plane perpendicular to the Sun–Earth line, 0° pointing north and 180° south, for a wind at 450 km/s carrying transverse fields of 5, 10, 20 nT. The law is empirical: the rate rises as the speed to the four-thirds, in proportion to the field, and as the sine of half the clock angle to the power 4.5. Due south, a 5 nT field opens flux at 57 kV; turned to within 20° of north, at 22 volts. The steepness in angle is the whole of the solar wind's leverage on the magnetosphere: the wind's pressure decides how large the cavity is, and one component of its field decides whether anything gets in.

A substorm timed by webers and volts

The solar wind opens the Earth's magnetic field at a rate that can be quoted as a voltage — tens of kilovolts, which is webers of flux per second — and the tail closes it again. Half a gigaweber loaded at fifty kilovolts takes three hours, and three hours is how often substorms recur. The aurora's position is the open flux, its surges are the unloading, and above a certain driving the ionosphere starts to limit the circuit that drives it.

sky · Magnetosphere Whether a field helped, depending on what limits the escape. The ratio of the atmospheric loss of a magnetised Earth to that of the same Earth without a field, against the Sun's age, both on logarithmic scales, set at 2 today — the magnetised planet losing more — for two ways an unmagnetised planet's loss can scale. If both planets lose atmosphere in proportion to the solar-wind power they intercept (blue), the magnetosphere's cross-section shrinks as the young Sun's denser wind compresses it while the bare planet's does not, and the ratio falls to 0.46 at 0.7 billion years: the field protected the young Earth, on balance from before 1.9 billion years. If instead the bare planet's loss is set by the ions the Sun's ultraviolet makes above it (orange), the ultraviolet rises more slowly into the past than the wind's pressure does, and the ratio grows to 3.7: the field cost the young Earth more than it saves today. The answer to whether a magnetic field protects an atmosphere is not a property of fields; it is a statement about which process limits the escape, and the young Sun amplifies the difference.

A shield that depends on what limits the leak

Today the Earth, with its magnetic field, loses ions to space about as fast as Venus and Mars without one — a little faster, by most measures. Whether that was also true under the young Sun, whose wind pressed eighty times harder, depends on something no measurement of the present can settle. If escape is limited by the wind's power, the field protected the young Earth; if it is limited by the ions the Sun's ultraviolet makes, the field cost it more than it does now. The young Sun does not decide the question. It amplifies whichever answer is right.

sky · Magnetosphere

Named alongside it

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

Auroral ovalDungey cycleMagnetic reconnectionMagnetopauseMagnetosphereSolar windAtmospheric escapeClock angleDipole fieldExtreme-ultravioletGeomagnetic stormIon outflow

All concepts