Astronomy & Celestial Mechanics
the sky, computed
Concept

Violent relaxation — where it appears

The rapid settling of a collapsing collisionless system towards equilibrium, driven by a gravitational potential that changes on the same timescale as the orbits. It redistributes energy among stars without any encounters, in a few free-fall times.

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

Prograde and retrograde, the same encounter. The same encounter twice: a companion of 1 times the primary's mass passing at 1.5 disc radii, with the disc spinning the same way the companion orbits and then the other way. Nothing else differs. The prograde disc grows a bridge towards the companion and a tail away from it; the retrograde one is barely disturbed. The reason is a resonance rather than a force: in the prograde case the outer particles keep pace with the companion for a substantial part of the encounter and are pulled the whole time, and in the retrograde case they sweep past it and the impulses cancel.

Whether it merges is a ratio of two times

Two galaxies passing each other either merge or do not, and what decides it is not how close they come. It is whether the encounter lasts long enough for the internal motions to respond — a slow, prograde passage transfers orbital energy into stellar orbits and the pair is bound; a fast one leaves both galaxies heated and still moving.

galaxies · Galaxy interactions A cold sphere collapsing onto the virial theorem. The virial ratio 2K/|W| — twice the kinetic energy over the magnitude of the potential energy — counted over the bound shells, of 400 concentric shells released almost at rest (2K/|W| = 0.1) from a sphere whose density falls as one over the radius, against time in units of the sphere's free-fall time. It starts near zero; overshoots to 1.7 as the collapse reaches the centre, the inner shells first; rebounds and oscillates; and settles to 1.03, the virial value, staying within ten per cent of it from about 4.9 free-fall times on. The shells never collide with anything; each feels only the mass inside it. What damps the oscillation is phase mixing — shells of different energy oscillate with different periods and drift out of step — and what redistributes the energy is the potential changing while they move through it. A system of stars reaches equilibrium this way in a few dynamical times, where encounters between the stars would take far longer than the age of the universe.

An equilibrium reached without a single encounter

Every dynamical mass of a galaxy assumes its stars obey the virial theorem, and no two of those stars have ever exchanged energy. A collapse computed shell by shell shows how a system gets there anyway — in a few free-fall times, at half the size it fell from, by a potential that changes while its orbits are still moving through it.

gravitation · Virial theorem

Named alongside it

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

Adiabatic invariantCross-sectionDark matter haloDynamical frictionFree-fall timeGalaxy mergerGravitational focusingImpulse approximationKinetic energyOrbital energyPhase mixingPotential energy

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