Astronomy & Celestial Mechanics
the sky, computed
Concept

Helium flash — where it appears

The runaway ignition of helium in a degenerate stellar core, whose energy lifts the degeneracy rather than reaching the surface. It reaches ten thousand million solar luminosities for a few seconds and none of it is seen, because every erg goes into lifting the degeneracy rather than out through the envelope.

Named by 4 essays across 2 fields — each of them below, with the objects they name alongside it.

A furnace with the thermostat taken out. Left, the two pressures in a red giant's helium core at 10⁶ g/cm³. The ideal-gas pressure rises with temperature, as the whole regulation of a star depends on it doing; the degenerate electron pressure is a horizontal line, because the exclusion principle does not know the temperature. At the ignition point near 10⁸ K the degenerate term is 5.1 times the gas term, so a temperature rise there raises the total pressure by almost nothing and the core does not expand. Right, what that costs. Both curves start at the same temperature with the same triple-alpha rate, whose logarithmic slope is 41 — the famous T⁴⁰, differentiated here rather than quoted. The regulated core settles; the degenerate one, with nowhere to put the extra energy, goes vertical. The flash reaches 10¹⁰ solar luminosities for a few seconds and not one photon of it is seen: every erg goes into lifting the degeneracy, and the star's visible response is to become fainter and settle on the horizontal branch.

The resonance that had to exist

Three alpha particles cannot meet at once, and the two-body intermediate falls apart in 8×10⁻¹⁷ seconds. That is a hundred thousand times longer than a crossing time, which is just enough — provided a nuclear level sits at 7.65 MeV. Hoyle argued from the existence of carbon to the existence of the level, and it was found where he said.

stars · Fusion The mirror: an envelope 62 times larger around a core 1.48 times smaller. Envelope radius and core radius against helium-core mass for a 1 solar-mass star, both in solar radii on one logarithmic axis. Two curves with opposite slopes at every point: the envelope grows from 2.0 to 122 solar radii — 0.57 astronomical units — while the degenerate core contracts from 13,848 to 9,368 kilometres, and the two are separated by a factor of 364 in the middle of the range. The figure is drawn from two stated relations rather than from a stellar model: a core-mass–luminosity law of the sixth power, calibrated to 2,500 solar luminosities at 0.48 solar masses of core, and a Hayashi temperature falling from 5000 to 3700 kelvin across the range. Everything else follows exactly — the radius by the Stefan–Boltzmann law, the core radius by the cold degenerate relation R ∝ M⁻¹ᐟ³. Note what the tip radius is and is not: it is the red-giant branch, and the later asymptotic-giant tip is a different and larger number.

The star that swells because its centre shrank

A helium core contracts, and the envelope around it expands by a factor of sixty. The central density rises at the same time as the radius, which is the opposite of what a self-gravitating body is expected to do, and a burning shell between the two is the whole reason it happens.

stars · Stellar evolution A furnace with the thermostat taken out. Left, the two pressures in a red giant's helium core at 10⁶ g/cm³. The ideal-gas pressure rises with temperature, as the whole regulation of a star depends on it doing; the degenerate electron pressure is a horizontal line, because the exclusion principle does not know the temperature. At the ignition point near 10⁸ K the degenerate term is 5.1 times the gas term, so a temperature rise there raises the total pressure by almost nothing and the core does not expand. Right, what that costs. Both curves start at the same temperature with the same triple-alpha rate, whose logarithmic slope is 41 — the famous T⁴⁰, differentiated here rather than quoted. The regulated core settles; the degenerate one, with nowhere to put the extra energy, goes vertical. The flash reaches 10¹⁰ solar luminosities for a few seconds and not one photon of it is seen: every erg goes into lifting the degeneracy, and the star's visible response is to become fainter and settle on the horizontal branch.

The explosion that never reaches the surface

When helium ignites in a degenerate core the thermostat every other burning stage runs on is disconnected. The runaway reaches ten billion solar luminosities for a few seconds, and the star's visible response is to get fainter.

stars · Stellar evolution The end of the red giant branch, found as an edge. The luminosity function of a synthetic galaxy halo — the number of red giants against apparent magnitude in the I band, smoothed — and its derivative, which is what the edge detector computes, searched over the magnitudes brighter than the branch's crowded lower part, as every application of the method does. 1582 stars are drawn: red giants rising in number towards fainter magnitudes as ten to the 0.3 times the magnitude, ending at the tip at magnitude 24, with a sixth as many asymptotic giants thinning out above it, all measured with errors of 0.08 magnitudes. The derivative peaks sharply where the counts jump, here at 24.09 — 0.09 from the true tip. The red giant branch ends where helium ignites in a degenerate core of almost fixed mass, so the tip's absolute magnitude is close to −4.05 for old, metal-poor stars, and the edge's apparent magnitude is a distance.

An edge that needs no pulsation

The local measurement of the expansion rate rests on a calibration step, and for decades that step was the Cepheid variables. The tip of the red giant branch replaces it with an edge — the brightness at which old stars ignite helium, nearly the same in every galaxy — found by counting stars rather than modelling them. It gives a slightly lower expansion rate, and whether the difference is a flaw in one calibration or in both is the local half of the Hubble tension.

cosmology · Hubble constant

Named alongside it

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

Degeneracy pressureStellar evolutionTip of the red giant branchTriple alphaBinding energyCepheid variableColour magnitude diagramConvectionCore massDegeneracyEffective temperatureElectron degeneracy

All concepts