Astronomy & Celestial Mechanics
the sky, computed
Concept

Depletion time — where it appears

The time a galaxy's star formation would take to consume its present gas: the gas mass divided by the star-formation rate. It is a few billion years in nearby discs and sets how quickly a galaxy's chemistry can respond to a change in its supply.

Named by 4 essays across one field — each of them below, with the objects they name alongside it.

The star-formation law, and the clock inside it. 46 model discs on the Kennicutt–Schmidt plane, built from Σ_SFR = 2.5e-4 Σ_gas^1.4 with 0.28 dex of scatter, with the exponent then fitted back off the drawn points at 1.42. The diagonal dashed lines are constant depletion times: gas divided by the rate consuming it. Every disc on this plane consumes its gas within a few gigayears, and a galaxy that has been forming stars for ten of them therefore cannot have been working from the gas it started with. The slope steeper than one is what makes the depletion time shorter where the gas is richer, which is the opposite of the intuition that a full tank lasts longer.

The gas runs out before the galaxy does

Divide a disc's gas by the rate it is turning that gas into stars and the answer is about two billion years — a seventh of the age of the disc. Every spiral still forming stars is therefore being fed from outside, and the star-formation law says the richer the disc, the sooner it starves.

galaxies · Star formation A slope of 0.57 at the low-mass end, against the 0.59 and 0.24 two winds give there. Gas-phase oxygen abundance against stellar mass for star-forming galaxies. The solid measured curve is the relation found from electron-temperature abundances in stacked spectra, which rises as a power of mass below a turnover near 10^8.9 solar masses and saturates above it at 12 + log(O/H) = 8.798. The two model curves are a galaxy in equilibrium with its gas supply, whose metallicity is the yield divided by one plus the mass it ejects per unit mass of stars and one plus the dilution by the gas it must keep accreting. Only the ejection changes with mass. A wind driven by the energy of supernovae must lift gas out of a potential whose depth goes as v², so its loading goes as v⁻² and, with v ∝ M^(1/3), as M^(−2/3); a wind driven by momentum goes as v⁻¹ and M^(−1/3). Those set the limiting slopes far below the turnover, 0.67 and 0.33; at log M = 7.5, where dilution still matters, the drawn curves have slopes of 0.59 and 0.24. The measured slope there is 0.57. The dashed measured curve uses a strong-line calibration of the same galaxies' spectra; it sits higher, flattens sooner and has a slope of only 0.40 at log M = 9 — so which wind the data prefer is decided as much by the choice of abundance calibration as by the galaxies. Above the turnover every curve saturates, because a galaxy that ejects almost nothing keeps what it makes and its abundance is the yield, diluted.

The metals a galaxy keeps measure what it threw away

Small star-forming galaxies are metal-poor and large ones are not, in a relation tight enough to be a law. Read as an equilibrium between inflow, star formation and wind, its slope says how the wind is driven, its turnover says where galaxies stop losing what they make — and its redshift evolution says galaxies were poorer because they were still being filled.

galaxies · Chemical evolution A disc built from the inside out, with a gradient of −0.066 dex per kiloparsec at 12 Gyr. The metallicity of the gas, in solar units on a logarithmic scale, against galactocentric radius, at ages of 2, 6, 12 Gyr, for a disc in which every ring is its own box with infall: pristine gas arrives on a timescale that grows with radius, from 1 Gyr in the centre to 7 Gyr at 8 kpc, turns into stars on the depletion time of a Kennicutt law, which is shorter where the gas is denser and much longer below a threshold of 7 M☉ pc⁻², and keeps everything it makes. The slopes fitted between 4 and 14 kpc: −0.259 dex/kpc at 2 Gyr, −0.124 dex/kpc at 6 Gyr, −0.066 dex/kpc at 12 Gyr. The inner disc has had its gas early and turned it over many times, so it is near the yield; the outer disc is still accreting and forming stars slowly, so its gas is diluted and young in the chemical sense. At 8 kpc the model's present abundance is 1.16 of the yield. Every ring is independent here: no gas flows between them and no star moves, which are the two processes that real discs add and which both act to flatten what is drawn.

A gradient the old stars have walked away from

The gas in a disc galaxy is richer in metals near the centre than at the edge, by about six-hundredths of a dex per kiloparsec in the Milky Way. Two ingredients of disc growth make that slope, a disc that grows from the inside out makes it flatten with time — and the old stars that should carry the steeper history have moved several kiloparsecs from where they were born.

galaxies · Chemical evolution 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

Named alongside it

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

Chemical evolutionFree-fall timeGalactic outflowGas infallThe Kennicutt–Schmidt lawAbundance gradientAge metallicity relationCircumgalactic mediumCold neutral mediumCorotationEffective yieldGas accretion

All concepts