Astronomy & Celestial Mechanics
the sky, computed
Concept

Red giant branch — where it appears

The sequence of evolved stars with helium cores and swollen convective envelopes, rising steeply in luminosity at nearly constant temperature. Its colour at fixed brightness depends on metallicity, which makes it a composition indicator in old clusters.

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 Hayashi lines: a luminosity that moves and a temperature that does not. The effective temperature a fully convective star must have, against its luminosity, for 0.5, 1, 2 solar masses, drawn as a Hertzsprung–Russell diagram with temperature falling to the right. The temperature follows from matching the star's convective adiabat to a photosphere whose opacity, from the negative hydrogen ion, rises as the ninth power of temperature. Over a factor of thirty thousand in luminosity each line moves by only 363 K, 398 K, 436 K respectively: the lines are nearly vertical, at 3650 K, 4000 K, 4383 K for one solar luminosity. A contracting young star, or a swelling giant, moves up or down its line almost without changing colour. To the right of the lines no star in hydrostatic equilibrium can sit.

A wall built by a steep opacity

A star that is convective all the way to its surface cannot choose its surface temperature. The interior fixes a relation between pressure and temperature, the photosphere fixes another through its opacity, and the negative hydrogen ion's opacity rises so steeply with temperature that the two meet at nearly the same temperature whatever the star's size. Young stars contracting and old stars swelling slide up and down a line in the diagram almost without changing colour — and nothing in equilibrium can sit to its right.

starlight · Opacity

Named alongside it

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

Angular momentum transportAsteroseismologyBuoyancy frequencyConvectionCore helium burningEvanescent zoneGravity modeHayashi trackMetallicityMixed modeNegative hydrogen ionOpacity

All concepts