Astronomy & Celestial Mechanics
the sky, computed
Concept

Magnetosphere — where it appears

The cavity a planet's magnetic field carves out of the stellar wind, bounded where magnetic pressure balances the wind's ram pressure. Because a dipole falls as the cube of distance, the boundary moves only as the sixth root of the pressure, which makes it a remarkably stable structure.

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

A line nothing spun up by accretion can lie above, and the millisecond pulsars beneath it. The period–period-derivative diagram with the spin-up line drawn on it. An accreting neutron star is torqued by the disc until its magnetosphere turns at the same rate as the material arriving there, which fixes an equilibrium period as a function of the magnetic field and the accretion rate. Eliminating the field between that relation and the dipole formula that every point in this diagram is already read through leaves a straight line of slope 1.33, drawn here for accretion at the Eddington rate — the fastest a star can be pushed. The 7 recycled pulsars all sit below it, which is what the figure is for: none of them was spun up faster than the limit allows, and their positions are a record of how much mass each one received rather than of how old it is. The young pulsars are in the opposite corner, above the line and to the right, spinning down from birth. The two populations are not two stages of one life. A star that reaches the bottom left has been fed by a companion for a hundred million years, which is why almost every millisecond pulsar has one and almost no young pulsar does.

A corner of the diagram that has to be earned

A pulsar spinning a thousand times a second cannot have been born that way and stayed that way, because its own radiation would have slowed it in a few million years. It got there by being fed, and the line it cannot lie above is where the accretion torque balances the magnetic one.

stars · Pulsars A boundary that a sixty-fourfold gust moves by a factor of two. The standoff distance of a dipole magnetosphere against a wind, in planetary radii, against the wind's proton density, for three wind speeds. The boundary sits where magnetic pressure equals ram pressure — the only balance available, since the field exerts no force on neutral gas and the wind touches nothing. Because a dipole falls as the cube of distance its pressure falls as the sixth power, so the standoff goes as the ram pressure to the −1/6: at 450 km/s a density of 6 per cubic centimetre puts the nose at 9.3 radii — against a measured average of ten to eleven — and a sixty-fourfold compression moves it only to 4.7. That exponent is the reason a magnetosphere is a stable thing to have. It is also the reason the boundary's position is a poor measurement of the field: a factor of two in the distance is a factor of sixty-four in what caused it, so the standoff measures the wind badly and the planet's moment hardly at all.

A boundary that hardly moves

The magnetopause sits where the planet's magnetic pressure equals the solar wind's ram pressure. Because a dipole falls as the cube of distance, its pressure falls as the sixth power — so a sixty-fourfold gust in the wind moves the boundary by a factor of two, and a boundary that will not move is what makes a magnetosphere a stable thing to have.

sky · Magnetosphere Three motions, three decades apart, and that is the point. The three periods of a trapped 1-MeV electron's motion against the shell it is trapped on, on a logarithmic time axis. It gyrates about a field line in 0.22 milliseconds, bounces between its mirror points in 0.33 seconds, and drifts right round the planet in 16 minutes — ratios of 1498 and 3015 at L = 4. Each motion carries a conserved quantity: the magnetic moment, the longitudinal invariant, and the magnetic flux the drift shell encloses. The separation is what makes them conserved. An invariant survives anything that changes slowly compared with its own period, so a disturbance lasting minutes destroys the third and leaves the first two untouched — and a particle that keeps its magnetic moment while being moved inward to a stronger field must gain energy. That is not a loophole; it is how the belts are filled.

Three clocks and nothing to fall onto

A charged particle in a dipole field gyrates, bounces and drifts, on timescales a millisecond, a second and a quarter of an hour. The three periods are three decades apart, and that separation is not a curiosity — it is the reason each motion has a conserved quantity, and the reason a magnetic storm can accelerate particles rather than merely stir them.

spaceflight · Radiation belts The shield that does not shield. Above: measured ion escape rates for three planets against their surface magnetic field. Venus and Mars have no dynamo at all and Earth has one, and the three rates lie within a factor of 9 — with the magnetised planet losing the most. The intuition that a magnetosphere protects an atmosphere is not a small correction away from being right; the measurement does not support it. Below: why. A dipole's field lines are not all closed. Those emerging within a polar cap reconnect with the wind's own field and lead straight to space, and the cap's area is set by how far the magnetosphere reaches — a boundary at ten planetary radii still leaves 5.1 per cent of the surface open. So a magnetosphere is both a shield and a funnel: it deflects the wind from most of the planet and collects ions from the whole ionosphere into the polar wind, which is exactly what an instrument above the poles measures leaving. Whether the net is protection depends on quantities nobody can compute from the field strength alone, and the three points above are the state of the evidence.

The shield that is also a funnel

A magnetic field is supposed to protect an atmosphere from the stellar wind. Venus and Mars have no dynamo and Earth has one, and their measured ion escape rates lie within a factor of a few — with the magnetised planet losing the most, because a dipole's polar field lines are open and lead straight to space.

exoplanets · Atmospheric escape A resonance with the planet's rotation, and it sorts by size. Above: the radii at which a charged grain's orbital frequency is commensurate with the planet's spin, in planetary radii, with the measured edges of Jupiter's halo ring drawn over them. The synchronous radius is 2.24; the 3:2 resonance falls at 1.71 and the 2:1 at 1.41. The halo's outer boundary is at 1.71 and its inner extent near 1.4 — the ring ends where the resonances are, and both numbers were measured by a spacecraft camera with no reference to this arithmetic. Below: which grains care. The charge on a grain is proportional to its radius and the mass to the cube, so the force per unit mass goes exactly as the inverse square of the size, and the resonance grips sub-micron dust while leaving anything larger on a Keplerian orbit. That is why the halo is a cloud of fine dust puffed a thousand kilometres out of the ring plane while the coarse material stays flat: the same field acting on the same orbit sorts the material by size, which no gravitational resonance can do.

A resonance with the planet itself

Every other resonance in celestial mechanics is a commensurability between two orbits. A charged dust grain has a third clock available — the planet's rotation, which sweeps its magnetic field past the grain — and the commensurability with that selects by charge-to-mass ratio, which means by grain size.

orbits · Planetary rings

Named alongside it

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

Geomagnetic stormAccretionAdiabatic invariantAngular momentumAtmospheric escapeAuroraBinary pulsarBow shockBremsstrahlungCharge to mass ratioDipole fieldDrift shell

All concepts