Astronomy & Celestial Mechanics
the sky, computed
Concept

Star formation — where it appears

The conversion of interstellar gas into stars, measured through the ultraviolet and infrared light of the most massive members rather than by counting. Its rate scales as a power of the gas surface density steeper than one, so removing gas removes more than its share of it.

Named by 10 essays across 2 fields — each of them below, with the objects they name alongside it.

The winding problem, drawn. A straight spoke of stars in the Milky Way from 2 to 15 kpc, and the same stars after 0.15, 0.3, 0.6 Gyr. Nothing has been done to them except let them orbit: the star at radius R has turned through Ω(R)t, and Ω falls as 1/R wherever the rotation curve is flat, so the inner end laps the outer one. By 0.6 Gyr the arm has a pitch angle of 3.4° at 8 kpc, which is tighter than any spiral galaxy that has ever been photographed, and the disc is thirteen gigayears old rather than 0.6.

An arm that cannot be made of stars

A galaxy's disc turns differentially, so any feature made of a fixed set of stars is wound to invisibility within a couple of rotations. Spiral arms are ten billion years old and still open, which means an arm is a place rather than a thing.

galaxies · Spiral structure Gas kept inside 3.6 to 6.8 kiloparsecs, depending only on the speed of the fall. The pressure holding a disc galaxy's gas down, against radius, with the ram pressure of the cluster gas it is falling through drawn as three levels. The restoring pressure is two pi times the gravitational constant times the product of the stellar and gaseous surface densities, both exponential with scale lengths of 3 and 5 kiloparsecs, so it falls steeply outward; the ram pressure is the intracluster density times the square of the infall speed and does not depend on radius at all. Where the level crosses the curve, the gas goes. A galaxy entering at 700 kilometres a second keeps everything inside 6.8 kiloparsecs; at 1600 it keeps only 3.6. Nothing in this touches the stars, which are not a fluid and feel no pressure at all, so the galaxy emerges with its stellar disc and its rotation curve intact and its star formation stopped from the outside in. That is the mechanism behind the most conspicuous fact about clusters: their spirals are red, gas-poor and still spiral-shaped, which no process acting on the stars could produce.

Red, gas-poor, and still spiral-shaped

A galaxy falling into a cluster meets a headwind of hot gas at two thousand kilometres a second. Where that ram pressure exceeds the disc's own grip on its gas, the gas goes; the stars, which are not a fluid and feel no pressure, do not. The result is a spiral with no fuel, and it is the commonest kind of galaxy in a cluster.

galaxies · Clusters The field a collapse would arrive with, and the one it has. Field strength against hydrogen density, both logarithmic, over the eight decades between diffuse gas and a protostellar core. The steeper line is what perfect flux freezing demands: a sphere collapsing conserves both mass and flux, so B goes as R⁻² while ρ goes as R⁻³, and therefore B goes as the two-thirds power of the density exactly — an exponent with no free parameter in it. The shallower locus is what Zeeman measurements find: a flat branch at about 10 µG up to 300 per cubic centimetre, where the density is rising and the field is not, and a rise as the 0.65 power of the density above it. By the density of a core the two differ by a factor of 1, and a star built at the frozen-flux value would carry a field four orders of magnitude beyond anything measured on one. The flat branch is the important half: it says the gas is moving along field lines without dragging them, which is what gravity does to a cloud that is still magnetically supported, and it locates where the freezing has to break.

A field that would have arrived ten thousand times too strong

A collapsing cloud carries its magnetic field with it, and the arithmetic of that is not negotiable — the field grows as the two-thirds power of the density. Run it from a diffuse cloud to a protostellar core and the answer is four orders of magnitude above anything measured on a young star.

stars · Flux freezing A layer several times thicker than its heat can explain. The vertical density profile of the neutral gas layer, drawn twice. The narrow curve is what thermal pressure alone supports: an 8-kilometre-a-second sound speed against the vertical gravity of the stellar disc gives a scale height of 47 parsecs. The broad curve adds the three pressures that are not heat — turbulent motion, the magnetic field and the cosmic rays — which together roughly triple the total and, because the scale height goes as the square of the effective dispersion, thicken the layer by a factor of 3.1 to 145 parsecs. The observed half-thickness of the H I layer is about 150. The narrow curve is a real prediction and it is wrong, and what is missing from it is precisely the two terms that emit nothing: a field measured by Zeeman splitting and Faraday rotation, and a particle population measured by what it does to a detector on a mountain. A galaxy's gas disc is inflated by things that cannot be photographed, and the thickness is how the inflation is measured.

A disc held open by what cannot be photographed

Solve hydrostatic equilibrium for the galaxy's gas layer using its temperature and the disc's gravity, and the answer is a layer several times thinner than the one that is there. What is missing from the calculation is turbulence, a magnetic field and a population of cosmic rays — three pressures of comparable size, two of which emit nothing.

galaxies · Interstellar medium One dimensionless number decides whether a cloud may collapse. Field strength against hydrogen column density, with three loci of constant mass-to-flux ratio. The ratio of mass to magnetic flux is conserved under flux freezing, so it cannot be changed by anything that happens during a collapse — which is what makes it a criterion rather than a description. Its critical value is the pure constant 1/(2π√G), and dividing by that gives the dimensionless λ drawn here: below λ = 1 the field can hold the cloud up for ever, however cold it gets, because gravity and the magnetic force scale the same way with radius; above it no field strength suffices. Each locus is a straight line of slope exactly one, because at fixed λ the required field is exactly proportional to the column. Zeeman measurements of dense cores put them a little above the line and their envelopes a little below it, which is the arrangement a slow leak of flux out of the centre would produce and is the observational case for ambipolar diffusion.

A threshold with no free parameter in it

Divide a cloud's mass by the magnetic flux threading it. Gravity and the magnetic force both fall as the inverse square of the radius, so the ratio cannot change during a collapse — and the critical value that separates a cloud which must collapse from one that never can is one over two pi root G, a pure constant.

stars · Star formation The orbit that turns across the bar. The radial displacement with which a nearly circular orbit answers a weak rotating bar, against radius in kiloparsecs, in linear theory, scaled to its largest value: positive means the orbit's long axis lies along the bar, negative across it. The disc's rotation curve rises within 0.35 kpc to 220 km/s, the bar ends at 3 kpc and turns with corotation at 3.6 kpc, and the disc then has two inner Lindblad resonances, at 0.37 and 0.78 kpc (vertical lines). Without dissipation (dashed) the response diverges at each resonance and changes sign across it: orbits between corotation and the outer resonance are elongated along the bar — the x1 family that builds the bar itself — and orbits between the two resonances are elongated across it — the x2 family. Gas, which dissipates (solid, damping 8 km/s/kpc), cannot follow the flip abruptly; its orbits turn through ninety degrees over a band round the resonance, where streams of gas on neighbouring orbits cross, collide and shock. That band is where a nuclear ring forms. Near corotation the linear theory itself fails, and the curves stop short of it.

The bar leaves its gas where the orbits turn

A rotating bar in a disc galaxy drives gas inwards from kiloparsecs out, and the gas does not fall to the centre. It stops in a ring a few hundred parsecs across and forms stars there at rates the rest of the galaxy cannot match. The ring sits at the bar's inner Lindblad resonance, where the orbits that support the bar give way to orbits turned across it — so its existence says there is mass concentrated at the centre, and its size says how fast the bar turns.

galaxies · Spiral structure Atomic gas that stops growing: a cloud holds at most 10, 35, 104 M☉ pc⁻² of HI. The surface density of atomic hydrogen in a slab lit on both faces, against the slab's total gas surface density, both logarithmic, for metallicities of solar, 0.3 solar, 0.1 solar. A thin slab is atomic throughout and sits on the one-to-one line (grey). A thick one shields its interior and turns it molecular, so every gram added beyond the transition is a gram of H₂ and the atomic column stops at 10.1 M☉ pc⁻² for solar, 34.7 M☉ pc⁻² for 0.3 solar, 103.7 M☉ pc⁻² for 0.1 solar. The saturation is the same thing the 21-centimetre maps of nearby galaxies show: atomic gas surface densities that rarely exceed about ten solar masses per square parsec in metal-rich discs, however much gas there is, and that climb in metal-poor dwarfs.

An atomic ceiling set by the dust

Pile more gas into a galaxy's disc and the atomic hydrogen stops growing at about ten solar masses per square parsec; everything beyond that is molecular. The ceiling is the column a cloud needs to shield its interior from ultraviolet light, and because dust both makes the molecules and does the final shielding, it scales as the inverse of the metallicity — and hardly at all with the starlight, since the cold gas thickens in step with the field that would break it apart.

galaxies · Interstellar medium Molecules take longer to form than a cloud takes to fall. Three timescales for a shielded cloud of 100 hydrogen atoms per cubic centimetre, against its metallicity relative to the Sun's on a logarithmic scale, all in years on a logarithmic scale. Molecular hydrogen forms on dust grains, and the time to turn the cloud's atoms into molecules is inversely proportional to the dust, so to the metallicity: 5.3 million years at solar, 53 million years at a tenth, 530 million years at a hundredth. The cloud's free-fall time, 4.3 million years, does not depend on its metals. The two cross near solar metallicity: above it the molecules form as fast as the cloud can collapse, below it the cloud collapses before most of its hydrogen has become molecular. The dashed line is a galaxy's molecular depletion time, two billion years — the timescale that equilibrium arguments implicitly assume is short compared with everything else.

A molecule that forms too slowly to wait for

The atomic hydrogen in a galaxy's disc turns molecular wherever a cloud is thick enough to shield itself from starlight, and stars form where it does. That is an equilibrium statement, and equilibrium takes time. Molecular hydrogen forms on dust grains, so in gas with a tenth of the Sun's metals it forms ten times more slowly — slowly enough that a cloud can finish collapsing before most of its hydrogen has become molecular, and form its stars from atoms.

galaxies · Interstellar medium Two ways of pointing an aperture, and the fork between them. The gas-to-young-star flux ratio inside apertures of size l, relative to the whole galaxy's, for apertures centred on peaks of molecular gas (upper branch) and on peaks of Hα from young stars (lower branch), if clouds live 20 Myr, the young stars shine in Hα for 4.3 Myr, the two overlap for 2 Myr and independent regions are 150 pc apart. On large scales every aperture averages many regions at all stages and both branches return to one. On small scales an aperture holds one region at one stage, and the branches split: ×2.1 on the gas peaks and ×0.10 on the stars at 10 pc. With the young stars' phase known from stellar evolution, the upper branch gives the overlap, the lower branch the clouds' lifetime, and the scale where the fork closes the regions' separation.

A lifetime read from how gas and stars sit apart

No molecular cloud has been watched for long enough to see it age, and every cloud looks the same whether it lives for one free-fall time or for ten. But a galaxy holds thousands of clouds at every stage at once, and how often molecular gas and young stars appear in the same place — measured in apertures of shrinking size, centred first on one and then on the other — turns a single snapshot into a clock, calibrated by how long the young stars shine.

galaxies · Molecular clouds A lifetime that stops getting shorter. Main-sequence lifetime against stellar mass, both logarithmic, from a simple model in which luminosity rises as the 3.8th power of mass until radiation pressure caps it at 40% of the Eddington limit (solid), and without the cap (dashed). The Sun lives 10 billion years, a 10 M☉ star 36 million, a 40 M☉ star 3.2 million, and above about 60 M☉ the lifetime stops falling: 2.7 million at 100 M☉, 3.0 million at 300. Without the cap the steep law would give the heaviest stars lifetimes of tens of thousands of years; with it, every very massive star lives a few million years whatever its mass.

A lifetime that stops getting shorter

A star twice the Sun's mass lives a fifth as long, ten times the mass a few hundredths. Extrapolate the steep law that says so to the most massive stars known, a hundred and fifty or two hundred suns, and they should burn out in a few tens of thousands of years. They do not: every star above about sixty solar masses lives between two and a half and three million years, whatever its mass. Radiation pressure caps how bright a star can be per unit of its mass, and once luminosity and fuel both grow in proportion to mass, the mass cancels out of the lifetime.

stars · Stellar lifetimes

Named alongside it

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

Interstellar mediumMolecular cloudsAmbipolar diffusionCorotationCosmic raysDensity waveFlux freezingFree-fall timeInterstellar dustJeans massMass to flux ratioMetallicity

All concepts