Astronomy & Celestial Mechanics
the sky, computed
Concept

Deuterium bottleneck — where it appears

The delay in big-bang nucleosynthesis while deuterium is still being photodissociated by the tail of the photon distribution. It ends at about 85 keV, far below deuterium's binding energy, because there are a billion photons for every baryon — and it sets how many neutrons have decayed before the network fires.

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

The helium abundance as a count of neutrino species. The primordial helium mass fraction against the number of light neutrino species, integrated at a deuterium-bottleneck temperature of 0.0855 MeV and a neutron lifetime of 877.75 s. The curve rises at 0.01348 in Y_p per species near the standard model, and it is not quite a line: freeze-out temperature goes as the sixth root of g_*, so a species added at N_eff = 4.5 buys 25 per cent less helium than one added at 2 — a slope ratio of 0.749 against the 0.769 that scaling requires. The reading below is therefore taken off the drawn curve rather than off a slope. The horizontal band is the measurement — ⁴He (Aver 2015), Y_p = 0.2449 ± 0.004, taken from recombination lines in metal-poor dwarf galaxies and extrapolated to zero metallicity. Where the band crosses the line is the answer: N_eff = 2.84, with the ends of the observed interval giving 2.56 to 3.13. The standard model has three, and 3.046 rather than 3 because the neutrinos are not quite decoupled when the electron–positron pairs annihilate and take a sliver of the heat. The strength of this is not its precision, which is a third of a species and worse than the microwave background's; it is that the two constraints come from utterly different epochs, and that this one is a laboratory result about particle content obtained from an emission line in a galaxy.

A particle count taken from a dwarf galaxy

Nearly every neutron that survives the first three minutes ends inside a helium nucleus, so the primordial helium abundance is not chemistry — it is the reading of a race between the weak interaction and the expansion. The expansion rate carries the square root of the number of relativistic species, which is why an emission line in a metal-poor galaxy counts neutrinos.

cosmology · Nucleosynthesis 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

Named alongside it

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

Baryon-to-photon ratioBig bang nucleosynthesisFreeze outBaryon densityColumn densityCurve of growthDetailed balanceDeuterium abundanceEffective number of neutrino speciesGamow peakIsotope shiftNeutron lifetime

All concepts