Astronomy & Celestial Mechanics
the sky, computed
Concept

Disc heating — where it appears

The slow growth of the random velocities of stars in a galactic disc as they age. Encounters with giant gas clouds, spiral arms and satellites each pump energy into stellar orbits, which is why older disc stars move faster out of the plane.

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

An arm that moves angular momentum outwards, and is spent doing it. Where a 2-armed spiral pattern of 25 km/s per kiloparsec takes angular momentum from the disc and where it gives it back, against galactocentric radius, for the Milky Way's rotation curve. The resonances are found on that curve rather than placed: the inner Lindblad resonance at 1.91 kiloparsecs, corotation at 8.67, the outer Lindblad resonance at 13.80. The lower curve is the angular momentum removed per unit radius and the upper one what the wave delivers; between them runs the flux the wave carries, which is flat across the whole region where nothing is resonant, because a wave that is not interacting with anything simply travels. The two deposits are required to cancel to a part in a million — the pattern is a conveyor and keeps nothing — so the disc's total angular momentum is unchanged while its distribution is not. That is the sense in which a spiral is a machine: it moves mass inwards by moving angular momentum outwards, which is the same operation an accretion disc performs and the same one a protostellar disc must perform to make a star. The cost is paid in random motion. Every exchange heats the stellar disc, a hotter disc supports a weaker wave, and the pattern that did the work is the thing the work destroys. What the figure cannot show is the pattern's own lifetime, which is the unsettled part of the subject.

An arm that is undone by the work it does

A spiral pattern takes angular momentum from the inner disc and delivers it to the outer, which lets mass move inwards without violating anything. It is paid for in random motion, and a disc with too much random motion cannot carry a wave — so the pattern destroys the conditions it needs to exist.

galaxies · Spiral structure How fast a disc forgets, by the mass of the lumps it is made of. The two-body relaxation time of a star moving at 30 km/s among perturbers of mass m, against m, for a fixed mass density of 0.015 solar masses per cubic parsec — about the density of molecular gas in the plane near the Sun — with a Coulomb logarithm of 5. The time falls as one over the perturber's mass: the same mass in heavier lumps relaxes a population proportionally faster. The orange point is the stars themselves, 0.04 solar masses per cubic parsec in half-solar-mass pieces: 4.9·10⁹ million years, 3.5·10⁵ times the age of the universe (dashed). Molecular clouds of 5·10⁵ solar masses give 13 billion years as point masses — comparable to the age of the disc. Fewer than a hundred-thousandth of the bodies, carrying less than half the mass, relax the disc 3.8·10⁵ times faster than all the stars together.

A few thousand clouds outrun a hundred billion stars

Encounters between stars relax the Galactic disc in a time hundreds of thousands of times the age of the universe, so in practice they do nothing. Put a fraction of the same mass into a few thousand molecular clouds and the time falls to the age of the disc — because relaxation counts the mass of each perturber, not their number. The disc's present thickness is the record of that, and of a bound on anything heavier hiding in the halo.

gravitation · Two-body relaxation

Named alongside it

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

Velocity dispersionAge velocity relationAngular momentumAngular momentum transportCorotation resonanceCoulomb logarithmDark matterDensity waveEpicyclic frequencyLindblad resonanceMassive compact halo objectMolecular cloud

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