Astronomy & Celestial Mechanics
the sky, computed
Concept

Pitch angle — where it appears

The angle a spiral makes with a circle about its centre, or the angle between a charged particle's velocity and the magnetic field. For a trapped particle it sets how far along the field line it travels before being reflected, and so which particles the atmosphere removes.

Named by 4 essays across 2 fields — each of them below, with the objects they name alongside it.

The winding problem, drawn. A straight spoke of stars in the Milky Way from 2 to 15 kpc, and the same stars after 0.15, 0.3, 0.6 Gyr. Nothing has been done to them except let them orbit: the star at radius R has turned through Ω(R)t, and Ω falls as 1/R wherever the rotation curve is flat, so the inner end laps the outer one. By 0.6 Gyr the arm has a pitch angle of 3.4° at 8 kpc, which is tighter than any spiral galaxy that has ever been photographed, and the disc is thirteen gigayears old rather than 0.6.

An arm that cannot be made of stars

A galaxy's disc turns differentially, so any feature made of a fixed set of stars is wound to invisibility within a couple of rotations. Spiral arms are ten billion years old and still open, which means an arm is a place rather than a thing.

galaxies · Spiral structure The weak spot in the field. Contours of the strength of the Earth's magnetic field at the surface, in microtesla, over longitude and latitude, from an eccentric dipole: a dipole tilted to pass through the geomagnetic poles and displaced about 570 km from the Earth's centre towards the western Pacific. The field is strongest near the poles and weakest near the equator, as any dipole's is, but the displacement makes the side of the Earth furthest from the dipole's centre weaker still: the minimum, 22.9 µT, lies at 8° S, 40° W, over the South Atlantic. The measured anomaly sits further south and west, near 26° S and 55° W, and is slightly deeper, because the real field has higher harmonics that no dipole carries; the eccentric dipole gets the side of the planet and the size right and the exact place approximately. Trapped particles mirror where the field reaches a fixed strength, so wherever the field is weak they mirror closer to the ground — and over this region the inner belt reaches down into the upper atmosphere.

A belt emptied over one ocean

The Earth's magnetic field is not centred on the Earth. Its dipole sits five or six hundred kilometres towards the western Pacific, so the opposite side of the planet — the South Atlantic — has the weakest field at any altitude, and a trapped particle that mirrors safely above the atmosphere everywhere else dips into it there. The inner edge of the inner radiation belt is drawn by that one region, and it is moving.

spaceflight · Radiation belts Two clocks for a radiation-belt electron, at Kp 2. Two times against drift shell L, on a logarithmic scale, for electrons of about 1 MeV. The first is how long radial diffusion takes to move an electron by one Earth radius, the inverse of an empirical diffusion coefficient that grows as the tenth power of L — at Kp 2, 550 years at L = 2, 10 years at L = 3, 21 days at L = 5. The second is how long the electron survives before it is scattered into the loss cone. Inside the plasmapause, here at L = 4.7, that is set by plasmaspheric hiss: years at L = 1.3, 14 days at L = 2.5, 5.2 days at L = 3; outside it a single lifetime of 30 days stands for every other loss. Inside L = 4.8 the electron is lost before diffusion can carry it further in, which is the shaded region; outside, diffusion wins and the belt is fed. The two curves cross at a single place, and that crossing is the inner edge of the outer belt.

The gap between the belts is a race between two clocks

Electrons reach the inner magnetosphere by diffusing inward from the outer edge, and they are lost there to waves that scatter them into the atmosphere. The diffusion slows as the tenth power of distance and the loss does not, so the two clocks cross at one sharp place. Inside it lies the slot, and at megaelectronvolt energies the inner electron belt is not a steady population at all but what the last great storm left behind.

spaceflight · Radiation belts Arms drawn into a disc that has none. Left: 1400 gas clouds spread uniformly over a disc between 3 and 13 kpc from the Galactic centre (cross), seen from above with the Sun (ring) 8.2 kpc out; the two thin curves mark where a two-armed spiral density wave of pitch 12° has its arms. The clouds have no arms in their positions, only in their motions: each streams by 10 km/s in a pattern locked to the arms. Right: the same clouds placed at their kinematic distances, read from their velocities with a circular rotation curve and on the correct side of every tangent point. The streaming has moved them by up to a few kiloparsecs, along lines of sight, and into bands. Lines of sight within 12° of the Galactic centre and 18° of the anticentre, where the velocities carry no distance, are left out. Counted in square kiloparsecs between 4 and 12 kpc, the densest fifth of the map holds 30 per cent of the clouds in reality and 45 per cent in the kinematic map.

A spiral drawn by velocities alone

A map of the Milky Way's gas is built by turning each cloud's velocity into a distance with a circular rotation curve. Gas in a spiral arm does not move on circles: it streams by ten or fifteen kilometres a second in a pattern locked to the arms, so the distance errors are locked to the arms too. Read that way, a disc with no arms in it at all comes out of the calculation with arms.

galaxies · Galactic structure

Named alongside it

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

Density waveLoss coneRadiation beltsAdiabatic invariantCorotationDifferential rotationDrift loss coneEccentric dipoleGalactic planeGeomagnetic fieldGeomagnetic stormKinematic distance

All concepts