Astronomy & Celestial Mechanics
the sky, computed
Concept

Electron density — where it appears

The number of free electrons per unit volume in a plasma or ionised gas. It sets how radio waves are dispersed and refracted, and for neutrinos crossing the Sun it sets the matter potential that makes flavour conversion depend on energy.

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

A path length recovered from two integrals of one cluster. The two line-of-sight integrands through an isothermal β = 0.67 cluster, each normalised to its own centre, against distance along the line of sight in core radii. The upper curve is electron density, which the Compton parameter integrates; the lower is density squared, which the X-ray surface brightness integrates. They are integrals of the same gas along the same line and they weight it differently — the half-width is 1.00 core radii for the linear one and 0.64 for the quadratic, and one core radius either side of the centre holds 51 per cent of the pressure signal against 82 per cent of the X-ray. That difference is the whole method. Two integrals with different powers of one unknown density, down one unknown path, are two equations in two unknowns: y₀ = 1.5·10⁻⁴ and a central X-ray surface brightness of 1.63·10⁻⁵ erg cm⁻² s⁻¹ sr⁻¹ give back a central density of 0.006 cm⁻³ and a physical core radius of 0.250 Mpc. Divide that length by the angular core radius the same cluster subtends, 54.2 arcseconds, and the answer is an angular-diameter distance of 952 Mpc — against the 952 Mpc the cluster was built at, which is the round trip this figure exists to close. Nothing in that chain is calibrated on a Cepheid, a supernova or a parallax. It is a length in centimetres measured against an angle.

A length in centimetres, measured against an angle

A cluster's hot gas offers two line integrals of the same electrons — one linear in density, one quadratic. Two equations in two unknowns give back the path length in centimetres, and a length divided by the angle it subtends is a distance that leans on no other distance measurement.

cosmology · Sunyaev zeldovich 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.

Adiabatic invariantAngular-diameter distanceBeta modelBremsstrahlungCompton parameterDay night asymmetryFlavourGas clumpingHubble constantIntracluster mediumLine of sight integralMass ordering

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