Astronomy & Celestial Mechanics
the sky, computed
Concept

Buoyancy frequency — where it appears

The natural frequency at which a parcel of fluid displaced vertically in a stratified ocean or atmosphere oscillates about its level. It measures how strongly the stratification resists vertical motion, and sets both the internal waves the fluid can carry and the work mixing must do against it.

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

Two stars at the same point of every other diagram, 4.1 times apart in one. Above: the gravity-mode period spacing against the large frequency separation, for 90 shell-burning giants and 55 core-burning ones. These are the same stars in every other measurement. They have the same luminosity, the same temperature, the same colour, the same surface gravity and — inside the band drawn — the same Δν, which means the same mean density; the global scaling relations return the same mass and the same radius for both. What separates them is a quantity that comes from nowhere near the surface: ΔΠ₁ is set by the buoyancy frequency integrated across the core, and a core that has ignited helium is expanded and convective, so its integral is smaller and its period spacing larger. The two sequences do not touch — 61 seconds against 248 — and the gap sorts a catalogue of tens of thousands of giants into stars burning hydrogen in a shell and stars burning helium in a core, by a Fourier transform of a light curve. Below: what that looks like in the spectrum itself, drawn over two radial orders. The number of mixed ℓ = 1 modes between consecutive radial modes is Δν/(ΔΠ₁ν²), so the shell burner has about 12 of them and the core burner about 3: the star with the larger period spacing has the sparser spectrum. The picture cannot show what the same modes are also used for and cannot settle — the splitting of each mixed mode gives the rotation rate of the core separately from the envelope, and the cores come out spinning some ten times faster than the surface and a hundred times slower than any model of angular-momentum transport predicts.

Two stars only a Fourier transform can tell apart

A giant burning hydrogen in a shell and one burning helium in its core sit at the same luminosity, the same temperature and the same mean density. Every scaling relation returns the same mass and radius for both. The gravity-mode period spacing is fifty seconds for one and three hundred for the other.

stars · Asteroseismology Where the tide's energy goes, and what the deep ocean needs. Power in terawatts. The Moon and Sun do work on the oceans at about 3.7 TW, measured from the slowing of the Earth's spin and the Moon's recession and, since the 1990s, located by satellite altimetry: about 2.6 TW is lost in shallow seas, about 1 TW in the deep ocean where the tide flows over ridges and seamounts and makes internal waves, and about 0.1 TW in the solid Earth. The open bar is what Munk and Wunsch estimated the deep ocean needs to keep its stratification against the upwelling of cold water, about 2 TW; the winds supply part of it, the tides — on these estimates — about half.

The tide that holds up the deep ocean

Cold water sinks near the poles and fills the deep ocean, and something has to stir heat back down into it or the whole ocean below the surface would become one cold pool. The stirring costs about two terawatts. The winds supply some of it. The rest comes from the Moon: about a terawatt of the tide's energy is lost not on continental shelves but in the deep ocean, where the tide flowing over ridges and seamounts makes waves on the ocean's internal layers that break far below the surface.

gravitation · Tides

Named alongside it

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

Angular momentum transportAsteroseismologyCore helium burningCritical latitudeEarth moon systemEvanescent zoneGravity modeInternal wavesMixed modeOcean mixingPeriod spacingPressure mode

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