Astronomy & Celestial Mechanics
the sky, computed
Concept

Neutron lifetime — where it appears

The mean time a free neutron survives before decaying into a proton, an electron and an antineutrino, about 880 seconds. It fixes the rates that set the helium made in the early universe, and bottle and beam measurements disagree by about nine seconds.

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 helium the first three minutes make, against the neutron's lifetime. The primordial helium mass fraction against the free-neutron lifetime, integrated through the first three minutes with the weak conversion rates normalised on that lifetime and free decay at the same rate, at the baryon density the microwave background gives. The line rises by 1.96 parts in ten thousand per second: a longer-lived neutron means slower conversions, an earlier freeze-out and less decay before the neutrons are locked into helium. The two laboratory lifetimes — 877.75 s from storing ultracold neutrons in a bottle, 887.7 s from counting protons in a beam — give 0.2468 and 0.2487, a difference of 19 in the fourth decimal place. The band is helium in metal-poor galaxies (Aver et al. 2015), 0.2449 ± 0.004; read back through the line it says the neutron lives 869 s, anywhere from 848 to 889 — a measurement of a laboratory constant from galaxies, good to about 20 seconds, and twice too coarse to referee a ten-second disagreement. The absolute level of the line is set to a full network's value for the bottle lifetime; the slope is computed.

The first three minutes use two lifetimes

A free neutron lives 877.75 seconds in a bottle and 887.7 in a beam. Nucleosynthesis uses the lifetime twice — once to set how fast neutrons and protons interconvert, once to set how fast the leftovers decay — and if a neutron can decay into something invisible, those are the two different numbers the laboratories measure.

cosmology · Nucleosynthesis

Named alongside it

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

Baryon-to-photon ratioBig bang nucleosynthesisBeta decayDetailed balanceDeuterium bottleneckEffective number of neutrino speciesFreeze outHelium abundanceNeutron proton ratioNeutron starPrimordial abundancePrimordial helium

All concepts