Astronomy & Celestial Mechanics
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Concept

Lithium problem — where it appears

The factor of about three between the primordial ⁷Li abundance big-bang nucleosynthesis predicts and the value measured in the oldest stars. It has stood since 1982, it is the only failure among the four light elements, and what prices every proposed resolution is the flatness of the observed plateau rather than its height.

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

Four abundances, one free parameter. The abundances big-bang nucleosynthesis predicts, against the one number it is free to choose: η₁₀, the ratio of baryons to photons in units of 10⁻¹⁰. Four curves spanning nine decades, from a helium mass fraction of about a quarter down to a lithium abundance of one atom in ten billion, and they are not four independent predictions — they all come out of the same reaction network run at the same density. The horizontal bands are what is measured in the sky, each at its published one sigma. The measurement that matters is deuterium, because its curve is the steep one: inverting the drawn curve at D/H = 2.527e-5 gives η₁₀ = 6.11, and the ends of the observed interval give 6.06 to 6.15. The vertical band is what the microwave background gives, 6.13 ± 0.04, from the height of the second acoustic peak relative to the first. Those two agree to 0.4 per cent, and they have nothing whatever in common: one is a nuclear-reaction network run in the first three minutes and read off a quasar absorption line, the other is a fluid oscillation at four hundred thousand years read off a sky map. Lithium is the exception and it is not a small one — the network predicts 4.70e-10 at the microwave background's density and the halo stars show 1.60e-10, a factor of 2.9 too much, which is unresolved.

Four abundances and one free parameter

In the first three minutes the universe ran a nuclear reaction network with exactly one adjustable number in it. That number predicts four abundances spanning nine orders of magnitude, three of them are observed and match, and the fourth is wrong by a factor of three and has been for twenty-five years.

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 A lumpy universe makes more of both, and one of them was already too much. The deuterium–lithium plane, with the curve a homogeneous universe traces as its baryon density varies and the points a two-zone universe reaches at a fixed mean density of η₁₀ = 6.13. The dense zone occupies 15 per cent of the volume, and the contrast between the zones runs from 1 — which is the homogeneous case — to 100. Every mixture lies up and to the right of its own homogeneous point, and that is not a modelling choice: an abundance is measured per baryon, so what a telescope averages is η times the abundance — and for both deuterium and lithium that product is a convex function of the density, whose average therefore exceeds its value at the average. The excess is large. At a contrast of 100 the mixture gives D/H = 1.13e-4 against 2.51e-5 smooth, and ⁷Li/H = 1.77e-8 against 4.70e-10, a factor of 37.7. The extra deuterium is exactly what the proposal was for: it lets the mean baryon density be raised while the observed D/H is still matched, which in the 1980s was the one way to make the baryons account for all the matter that dynamics required. The extra lithium is what it costs. The measured abundance was already a factor of 2.9 below the homogeneous prediction, and every step toward the lumpy universe that fixes the density makes that discrepancy worse — which is why the answer to "the baryons are lumpy" turned out to be that the extra matter is not baryons.

The universe that was lumpy at one second

If the baryons were unevenly spread when the network fired, each region ran its own nucleosynthesis and what is observed is an average. For a decade that was the one way to make ordinary matter account for all the matter — and the reason it fails is a theorem about convex curves.

cosmology · Nucleosynthesis

Named alongside it

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

Baryon-to-photon ratioBig bang nucleosynthesisDeuterium abundanceBaryon densityPrimordial abundanceBinding energyConvective envelopeConvexityCritical densityCross-sectionDark matterDiffusion length

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