Concept

Spin parameter — where it appears

The dimensionless measure of how fast a dark matter halo turns, comparing its angular momentum against what rotational support would require. Its median is about 0.035 across four decades of mass, which is why it points at a scale-free origin.

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

Also named here as tidal torque theory — the same set of essays touches all of them, so they are one junction rather than several.

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 torque that stops when the patch lets go. Left, the mechanism: a protogalactic patch drawn as an ellipsoid of axis ratios 1:0.72:0.5, with the principal axes of the surrounding tidal field drawn across it at 30 degrees to its own. The torque is proportional to the difference of the patch's principal moments times the sine of twice that angle, so it is exactly zero when the two sets of axes agree — checked at both alignments — and largest at forty-five degrees. A spherical patch takes no torque whatever the field around it does, which is why the spin of every galaxy begins as a statement about its shape. Right, the angular momentum against time in units of the turnaround time: in linear theory the torque acts on a patch still expanding with the universe and the angular momentum grows as the first power of time, measured off the drawn curve as t^1.000. At turnaround the patch detaches from the expansion, its quadrupole shrinks, and the torque switches off — so a galaxy's spin is fixed before it has collapsed at all, by neighbours it will never interact with again. What the figure cannot show is the sign: the same mechanism gives no preferred direction, and the observed near-absence of alignment between neighbouring galaxies' spins is the check on that.

Spin acquired before there was anything to spin

Every galaxy turns, and nothing in a smooth expanding universe turns. The rotation was applied while the material was still a mildly overdense patch spread across megaparsecs — torqued by the tidal field of its neighbours, growing steadily with time, and switching off the moment the patch stopped expanding.

cosmology · Tidal torque theory

Named alongside it

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

Angular momentum Tidal torque theory Adiabatic contraction Correlation function Dark matter halo Density perturbation Disc scale length Dynamical friction Exponential disc Galaxy formation Gaussian random field Inertia tensor

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