Astronomy & Celestial Mechanics
the sky, computed
Concept

Gravitational instability — where it appears

The collapse of a region of gas or stars under its own gravity when self-gravity outweighs the pressure and rotation that resist it. In a disc the threshold is Toomre's Q falling below about one, and the outcome is clumps, spirals or star formation.

Named by 3 essays across 2 fields — each of them below, with the objects they name alongside it.

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

A star fed in bursts by a disc that cannot pass its supply on. The accretion rate onto a 0.5 M☉ protostar over 100 thousand years, for a steady supply of 10⁻⁶ M☉ a year into a disc whose active layer can carry only 10⁻⁸ M☉ a year at 1 AU. The excess fills the dead zone until the column inside 1 AU reaches 4.4·10⁴ grams per square centimetre — 0.016 M☉, the column at which it becomes gravitationally unstable and its spiral arms heat it to ignition — and then drains on the hot disc's viscous time of 189 years, at 8.3·10⁻⁵ M☉ a year. The cycle repeats every 16,083 years, 6 times in the span drawn. The star spends 1.2 per cent of its time in outburst and gains 99 per cent of its mass there: a census at a random moment finds almost every protostar faint, while almost all of the mass arrives during events nobody happens to be watching.

A disc that stores its inflow and spends it in a century

Where only a thin ionised skin of a young disc can transport angular momentum, the gas arriving from the cloud cannot be passed on, and it piles up in the dead midplane until gravity stirs it and the whole column ignites. The star then gains most of its mass in bursts of a century every ten thousand years — which is why almost every protostar ever observed is fainter than its growth requires.

gravitation · Magnetorotational instability Turbulence against star formation, driven two ways. Gas velocity dispersion against star-formation rate per unit area, both on logarithmic scales, for model discs of increasing gas surface density: a nearby spiral (circular speed 200 km/s at 8 kpc, gas a fifth of the disc's mass) and a disc at redshift two (the same speed at 4 kpc, gas half). Dashed: turbulence driven by supernovae alone, a tenth of their energy staying in the gas — it settles between 11 and 13 km/s however fast the disc forms stars, because more gas means both more stars and faster dissipation. Solid: the same discs when gravity can also stir them, holding the gas at marginal stability once supernovae fall short — which in the redshift-two disc happens above a gas surface density of 72 M☉ pc⁻², after which the dispersion climbs with the star-formation rate to 76 km/s. The shaded boxes are the approximate ranges in which nearby spirals and redshift-two discs are observed. Feedback alone reaches the first and not the second; with gravity the model reaches the second at its lower edge in star formation, a sign that its simple star-formation law, one per cent of the gas per free-fall time of the whole layer, is slow for the clumpy gas of those discs.

A stirring supernovae cannot pay for

The gas in a disc forming stars at redshift two moves at fifty kilometres a second in random directions, five times faster than in a spiral today, and turbulence that fast decays in a few tens of millions of years. Supernovae are the obvious source of the energy, and they run out at about thirteen kilometres a second however fast the disc forms stars. What holds the discs up is gravity — gas stirring itself by falling inward — and a disc stirred that way is also a disc pouring its gas into its own centre.

galaxies · Tully–Fisher One patch of ring, many optical depths. The normal optical depth an observer infers from the starlight transmitted through one patch of the A ring, treating it as a uniform sheet, against the direction of the sight line projected onto the ring plane — measured round from the radial direction — for sight lines 12°, 30°, 60° above the plane. The ring is the slab-and-gap model of the wakes: slabs 33 m wide and 8 m tall every 60 m, tilted 22° from the orbital direction, gaps of optical depth 0.12. The minima are where the sight line runs along the slabs, twice per circle; the maxima where it runs across them, where at low elevation the slabs' shadows close the gaps altogether (curves cut off at 3). At 12° the inferred value runs from 0.29 to opaque; at 60° from 0.81 to 0.97. The dashed line is the same particles spread into a uniform layer, 1.43: every observer along the slabs sees less ring than is there.

A ring that is thinner from one side

Saturn's A ring is not a sheet of particles but a field of tilted slabs, each a few dozen metres across, pulled together by the ring's own gravity and sheared apart again within an orbit. Starlight passing through it threads the gaps or meets the slabs depending on its direction, so one patch of ring has a different optical depth for every observer — and a uniform model of it hides most of the particles it contains.

gravitation · Planetary rings

Named alongside it

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

Toomre qAccretion discAccretion rateDead zoneHill sphereMagnetorotational instabilityOptical depthPlanetary ringsPressure supportProtoplanetary discProtostarRadial inflow

All concepts