Astronomy & Celestial Mechanics
the sky, computed
Concept

Radiative capture — where it appears

A nuclear reaction in which two nuclei fuse and the excess energy leaves as a photon. It is far slower than a reaction whose products are two nuclei, so it dominates only once the abundances of everything else have fallen away — which is why D(p,γ)³He rather than D+D sets the surviving deuterium.

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

The deuterium burning rate against the expansion, at three baryon densities. The rate at which a deuteron is destroyed, divided by the expansion rate, against temperature. Temperature falls to the right, so the picture reads left to right as time, and the horizontal line at one is where the burning stops mattering: above it a deuteron is destroyed many times over before the universe doubles in size, below it the reaction has effectively ceased. The rate drawn is D(p,γ)³He at the NACRE parameterisation, multiplied by the free-proton density — three quarters of the baryons by number once ⁴He has taken the rest — and the expansion rate is the same 1.66√g* T²/mPl the freeze-out calculation raced the weak interactions against. The three curves differ in one number and one only: the baryons per photon, 3, 6, 12 in units of 10⁻¹⁰. They are therefore vertical translations of each other, exactly in proportion to η, because the reaction is two-body and the expansion is not. That is the entire mechanism by which an abundance measures a density. A denser universe crosses the line later — 21.4 keV at η₁₀ = 3, 16.0 keV at η₁₀ = 6, 12.3 keV at η₁₀ = 12 — and every extra second below the crossing is deuterium that does not survive. What the figure does not do is predict the abundance itself: the residue depends on the whole reaction network and on the ⁷Be and ³He channels that feed back into it, and the curve the abundance is read off is a fit to that network rather than to this.

The residue that failed to burn

Deuterium's abundance is not a measure of what the first three minutes made. It is a measure of what escaped being used — a two-body destruction rate losing a race to a one-body expansion, which is why its curve against the baryon density is steep and helium's is flat.

cosmology · Nucleosynthesis A factor of 2.9, and the density that would remove it. The predicted ⁷Li abundance against the baryon density, with the halo-star measurement as a horizontal band and the microwave background's density as a vertical one. At η₁₀ = 6.13 the network gives 4.70e-10 and the stars show 1.60e-10, a factor of 2.94 — 0.47 in the logarithm, which is the number every proposed resolution has to produce. The obvious cure is drawn as the second marker: ⁷Li rises as η², so the density that would reproduce the observation is η₁₀ = 3.58, a third below the measured one. That is where the cure fails, and it fails on a different element. Deuterium falls as η^(−1.6), so at 3.58 the predicted D/H is 5.946e-5 against the 2.527e-5 measured in quasar absorbers — 2.35 times too much, and 114 times deuterium's own error bar. Helium, meanwhile, moves to 0.2445 and stays inside its measurement, because its curve is flat. The three light elements do not fail together, and that is what rules out a single wrong parameter: whatever is wrong is wrong about mass seven specifically.

A factor of three, and the flatness that prices every cure

The oldest stars in the Galaxy show a third of the lithium the first three minutes should have left. Three kinds of resolution have been offered, and the datum that rules on all three is not how much lithium is missing but how uniformly it is missing.

cosmology · Nucleosynthesis

Named alongside it

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

Baryon-to-photon ratioBig bang nucleosynthesisDeuterium abundanceBaryon densityColumn densityConvective envelopeCross-sectionCurve of growthDeuterium bottleneckElectron captureFreeze outGamow peak

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