Astronomy & Celestial Mechanics
the sky, computed
Concept

Solar neutrinos — where it appears

Neutrinos produced by the nuclear reactions in the Sun's core, which leave it in about two seconds and carry a direct record of the core's conditions. Their measured deficit in electron flavour was the first evidence that neutrinos change flavour and so have mass.

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 A survival probability with a step in the middle of the spectrum. The probability that an electron neutrino made in the core of the Sun is still an electron neutrino at the Earth, against its energy, from the resonant conversion it undergoes in the Sun's own electrons: mixing angle sin²θ₁₂ = 0.307, splitting Δm² = 7.4·10⁻⁵ eV², and an electron density at the point of production of 90 moles per cubic centimetre. At low energy the matter potential is small beside the vacuum term and the probability is the vacuum average, 0.54 at 0.3 MeV (the flat limit is 0.55). At high energy the matter term dominates, the neutrino is born almost entirely in the heavier mass state, and the probability falls to 0.32 at 10 MeV, close to sin²θ₁₂. The two terms are equal at 2.1 MeV, which falls in the gap between the ⁷Be line and the bulk of the ⁸B spectrum. The points are the measured survival probabilities for each source separately — pp, ⁷Be, pep and ⁸B from Borexino, and ⁸B from SNO — and every one of them lies within about two standard deviations of the curve: low-energy neutrinos survive about half the time, high-energy ones about a third.

A survival that depends on the energy

A low-energy neutrino from the Sun reaches the Earth still an electron neutrino about half the time, and a high-energy one about a third of the time. The difference is made by the Sun's own electrons, and the energy at which it switches over — near two million electronvolts — sits in the gap between the neutrinos that never meet a resonance and the ones that all do.

stars · Solar neutrinos

Named alongside it

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

Standard solar modelAbundance problemAdiabatic invariantCentral temperatureCross-sectionDay night asymmetryElectron densityFlavourGamow peakHelioseismologyMass orderingMsw effect

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