Astronomy & Celestial Mechanics
the sky, computed
Concept

Disc scale length — where it appears

The radius over which a disc galaxy's surface brightness falls by a factor of e, the standard measure of a disc's size. It follows from the angular momentum the disc's gas brought in, and so from its halo's spin.

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

A halo is born with a spin of a few hundredths. The distribution of the dimensionless spin parameter λ = J|E|^½ ÷ (G M⁵ᐟ²) across dark matter haloes, drawn as a lognormal of median 0.035 and logarithmic width 0.5, with the disc scale length each λ implies printed along the lower axis. The distribution is required to integrate to one and to peak at 0.0272, which is the median times e raised to minus sigma squared, and is the signature of a lognormal rather than of a bell curve drawn to look like one. λ is small because a halo is supported by random motion rather than by rotation: a value of 0.035 means the halo turns at about three and a half per cent of the rate it would need to hold itself up centrifugally. It is also nearly independent of halo mass, which is what points at a common origin. Mapping it to a disc through R_d = λ R₂₀₀/√2 with all of the specific angular momentum retained, a 10¹²-solar-mass halo of radius 206 kiloparsecs gives 5.1 kiloparsecs at the median, against the 2.6 kiloparsecs the Milky Way's disc actually has. The gap is not a failure of the estimate; it is the measurement that the baryons arrived with less spin per unit mass than the halo they arrived in.

A disc the size its halo was born with

A galaxy's mass says how much light it makes. It does not say how big it is. What sets a disc's size is a single dimensionless number describing how fast the dark halo around it happens to be turning — a number the disc had no part in choosing, distributed the same way for every halo mass in the universe.

galaxies · Galaxy spin The share of discs that should bar. The fraction of haloes whose spin is too low to keep a disc stable, against the disc's share of the halo's mass, for spin distributions of width 0.4, 0.5, 0.6. At a share of 1 per cent it is 1 per cent; at 3 per cent, 50; at 5 per cent, 85. Observed bar fractions among nearby discs, a third to two-thirds (shaded), fall where discs hold 2.5 to 4 per cent of their haloes' mass.

A spin too low to keep a disc from barring

A disc galaxy's size is set by how fast its dark halo happened to be turning. A slowly turning halo makes a small, dense disc, and a disc dense enough to supply much of its own rotation is unstable: it rearranges itself into a bar. With halo spins scattered as simulations find them, the fraction of discs that should bar depends almost entirely on one number — how much of the halo's mass ended up in the disc — and the bar fractions astronomers count say it is about three per cent.

galaxies · Galaxy spin

Named alongside it

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

Dark matter haloExponential discSpecific angular momentumSpin parameterAdiabatic contractionAngular momentumDynamical frictionGalaxy formationGalaxy spinLognormal distributionPseudo bulgeSurface brightness

All concepts