Astronomy & Celestial Mechanics
the sky, computed
Concept

Asymmetric drift — where it appears

The amount by which a population of stars rotates more slowly than the circular speed, because random motion supplies part of its support. It grows with the population's velocity dispersion. The Jeans equation gives the correction needed to recover a rotation curve from stars.

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

How the scatter depends on how much dispersion is added to rotation. The scatter of the baryonic Tully–Fisher relation, in dex of mass, when the same 80 turbulent model discs are measured with S = √(K Vᵣₒₜ² + σ²), against the weight K given to the rotation, for rotation measured at 1 and 2.2 disc scale lengths. Measured at 1 scale length the scatter is smallest, 0.076 dex, at K = 0.55, and is 0.076 dex at K = 0.5; measured at 2.2 scale lengths the scatter is smallest, 0.077 dex, at K = 0.23, and is 0.134 dex at K = 0.5. For an exponential disc with constant dispersion the pressure correction is exactly K = one over twice the radius in scale lengths, so the best weight depends on where the rotation is measured. The widely used K = 0.5 is the value that makes a pure rotator and a pure isothermal sphere of the same mass agree; it is also the pressure correction for rotation measured at one scale length, and not at any other.

A disc that turns slower than its mass requires

The star-forming discs of ten billion years ago were not the thin, cold, orderly discs of today. Their gas moved randomly at tens of kilometres a second, and that motion is a pressure that holds up part of each disc, so it turns more slowly than its mass alone would require. Read those rotation speeds as if rotation did all the work and the Tully–Fisher relation tilts and scatters as if galaxies had evolved, when what differs is how much of their weight is carried by disorder.

galaxies · Tully–Fisher One set of mean velocities, three rotation curves. The circular speed recovered from one set of measured mean rotation velocities through the Jeans equation, for tracer densities with scale lengths of 2, 3, 5 kpc. The velocities are built so that a scale length of 3 kpc reproduces a published declining curve, 217 km/s at 10 kpc and 178 km/s at 25 kpc. At 25 kpc the three give 188, 178, 169 km/s, and the measured mean rotation there is 151 km/s.

A falling curve seen from one side of the Galaxy

The rotation curve that first demanded dark matter stays flat, and in 2023 the Milky Way's own, measured from the space astrometry catalogue, appeared to fall as though the mass had simply run out at twenty kiloparsecs. The velocities are excellent. What turns them into a circular speed is a correction carrying the slope of a tracer's density, a dispersion and an assumption of steady rotation, each least known exactly where the fall is seen.

galaxies · Rotation curves

Named alongside it

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

Rotation curveThe baryonic Tully–Fisher relationDark matterDark matter haloJeans equationLarge magellanic cloudTully fisher relationVelocity dispersionVirial theorem

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