Astronomy & Celestial Mechanics
the sky, computed
Concept

Adiabatic contraction — where it appears

The inward pull of a dark-matter halo's inner orbits as ordinary gas cools and settles at its centre. Orbits that change slowly keep their adiabatic invariants, so each shell of dark matter shrinks to conserve r·M(r), and the halo ends denser in the middle than it was born.

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 A cusp pulled deeper by the disc inside it. The dark-matter density of a halo of 10¹² solar masses and concentration 10 before and after an exponential disc of 5·10¹⁰ solar masses and scale length 3 kpc settles slowly into its centre, computed shell by shell from the adiabatic invariant r·M(r). Far outside the disc the two profiles coincide — 4.8% apart at 83 kpc — because contraction moves mass inward without changing how much there is. Inside, the dark matter is pulled in after the baryons: at half a disc scale length the density is 2.9 times higher, and at 1 kpc the logarithmic slope goes from −1.09 to −1.25. The cusp that dark-matter-only simulations predict is therefore the shallowest the inner halo of a disc galaxy can be before feedback acts, not the profile feedback starts from. The calculation assumes circular orbits and slow settling, and simulations that include gas find the true response weaker than this.

The halo a galaxy drags inward

The cusp that dark-matter simulations predict is a halo with no galaxy in it. When gas cools and settles into a disc at the centre, the dark matter is pulled in after it, and a quantity conserved on slowly changing orbits says by how much. In a large disc galaxy the pull triples the dark matter at the centre and multiplies tenfold the energy needed to dig a core; in a dwarf it barely registers.

galaxies · Halo profiles

Named alongside it

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

Dark matter haloAdiabatic invariantAngular momentumBaryon fractionCusp core problemDisc halo decompositionDisc scale lengthDynamical frictionExponential discGalaxy formationInner slopeLognormal distribution

All concepts