Astronomy & Celestial Mechanics
the sky, computed
Concept

Central temperature — where it appears

The temperature at the centre of a star, where it is highest and where fusion runs. It is set by the balance of gravity and pressure, so it rises with mass and with compactness; the reactions available decide where a star's contraction stops.

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

A flux that measures a temperature to 0.12 per cent. Neutrino flux against central temperature, in units of the standard model's, for the three main solar channels. The exponents are not arbitrary: each reflects how far up the Gamow peak the reaction has to reach, so the channel with the largest Coulomb barrier is the steepest. The boron-8 flux goes as roughly the twenty-fourth power, which means a measurement good to 3 per cent constrains the Sun's central temperature to 0.12 per cent — better than any other technique by an order of magnitude. The same steepness is why the flux is useless as a check on anything else: a stellar model whose central temperature is uncertain at the half-per-cent level predicts this flux to within a factor, and the disagreement between two model families is far larger than the measurement.

A flux that is a thermometer to a tenth of a per cent

The boron-8 neutrino flux from the Sun's core rises as roughly the twenty-fourth power of the central temperature. That makes it the sharpest thermometer in astrophysics and simultaneously the most fragile prediction — a model uncertain in its central temperature by half a per cent predicts the flux to within a factor.

stars · Solar neutrinos The carbon a star makes, and the carbon it needs. For a 30 solar-mass star born with no carbon, two quantities against its central temperature, on logarithmic scales: the carbon fraction its core needs for the CNO cycle to carry its luminosity (falling steeply, because a hotter core needs less catalyst), and the carbon the triple-alpha process makes in the hundred thousand years the core takes to contract (rising even more steeply). They meet at 108 million kelvin and a carbon fraction of 1.7 × 10⁻¹⁰: 1.7 parts in ten billion by mass, made by the star itself, are enough to switch on the cycle that runs every massive star of the present day. The contraction stops there.

A star that has to make its own catalyst

Every massive star now forming burns hydrogen through a cycle of reactions that carbon, nitrogen and oxygen catalyse, and the first stars had none of those elements. A massive star made of hydrogen and helium alone contracts and heats until its core reaches a hundred million kelvin, where helium begins to fuse into carbon; a few atoms of carbon in ten billion are enough to start the cycle, and the star settles there — three times hotter at its centre than any star of the same mass today, and smaller, and bluer.

stars · The mass–luminosity relation

Named alongside it

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

Abundance problemCNO cycleCross-sectionFirst starsGamow peakHelioseismologyHomologyIonising radiationMetallicityOpacityPopulation IIIProton proton chain

All concepts