Astronomy & Celestial Mechanics
the sky, computed
Concept

Nucleosynthesis — where it appears

The building of heavier nuclei from lighter ones, in the first minutes of the universe and thereafter in the brief late stages of stars. The first three minutes made hydrogen, helium and lithium and stopped; everything heavier was made in stars, and the division is sharp enough to be a test.

Named by 3 essays across one field — each of them below, with the objects they name alongside it.

How long a star lasts, against its mass. Main-sequence lifetime against mass, on logarithmic axes. Fuel grows in proportion to mass and consumption grows as its three-and-a-half power, so the lifetime falls steeply — a star of thirty solar masses lives for a few million years.

Why the biggest stars die first, and take the galaxy with them

A star thirty times the Sun's mass has thirty times the fuel and burns it forty thousand times faster. It lasts a few million years, and everything heavier than iron exists because of it.

stars · Stellar lifetimes 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 abundances the slow neutron-capture process leaves behind. The abundance of each mass number produced by the s-process model at a mean neutron exposure of 0.3 per millibarn, relative to the iron seed, on a logarithmic axis. Dividing σN by the cross section turns the steps into peaks: nuclei at the closed shells capture so reluctantly that material piles up in them. The model's peaks sit at mass numbers 88, 138, 208 — strontium and zirconium, barium, and lead — the three s-process peaks of the solar system's abundances. The peak at barium stands 7 times above the abundances just below it. The abundance pattern of the heavy elements is a record of nuclear structure: the magic numbers of the shell model are written into the composition of every star, by a process that happened in other stars before the Sun formed.

A flow that piles up at the magic numbers

Half the elements heavier than iron were built one neutron at a time, in ageing stars, over thousands of years. The flow of matter up the chart of nuclei settles into a balance in which each nucleus is as abundant as it is reluctant to capture — and it jams at the closed neutron shells, leaving the peaks at strontium, barium and lead that every star's spectrum records.

stars · Fusion

Named alongside it

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

Asymptotic giant branchBinding energyBlack holeChemical evolutionCluster turnoffCross-sectionDegeneracyFusionHelium flashHoyle stateInitial mass functionMagic numbers

All concepts