Astronomy & Celestial Mechanics
the sky, computed
Concept

Neutral fraction — where it appears

The proportion of intergalactic hydrogen that is not ionised. It fell from one to about one part in a hundred thousand during reionisation, and the Lyman-alpha forest saturates so early in that fall that it constrains only the very end.

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

A neutral fraction of 2.4·10⁻⁶ is already opaque. The Gunn–Peterson optical depth against the neutral fraction of the intergalactic medium, at z = 3, 5, 6.3, for Ω_b = 0.0493 and h = 0.674. Note the range of the vertical axis. A fully neutral medium at z = 6.3 gives τ = 4.1·10⁵, which is not absorption but extinction of everything; the medium reaches τ = 1 — the point at which it stops transmitting most of the light — at neutral fractions of 6.1·10⁻⁶ at z = 3, 3.3·10⁻⁶ at z = 5, 2.4·10⁻⁶ at z = 6.3. That is why the argument runs from the flux that survives rather than from the flux that does not. A spectrum showing any transmission at all between Lyman α and Lyman β is a measurement that the medium is ionised to better than one part in 164,727, and no fit to any absorption line is needed to establish it.

A trough that proves the forest survived

A uniform neutral medium at redshift six would absorb Lyman alpha with an optical depth of four hundred thousand. So the existence of any transmitted light in a quasar's spectrum is a measurement — of a neutral fraction below one part in ten thousand — made from a detection rather than from an absorption.

cosmology · Reionisation A 5 per cent continuum error, and an optical depth wrong by 1.1. The mean transmitted flux of the Lyman-alpha forest against redshift, with a 5 per cent uncertainty in the quasar continuum drawn as a band. The continuum is not observed: at these redshifts every part of the spectrum blueward of the emission line is absorbed, so the level has to be extrapolated from the red side across a region where the quasar's own spectrum has structure. A fractional error in that level is a fractional error in the flux, and since the optical depth is minus the logarithm of the flux, the resulting error in the optical depth is the fractional error divided by the flux — which grows without bound as the forest goes black. At z = 2 it is 0.06; at z = 6.2 it is 1.1. That is why measurements of when reionisation ended are quoted as limits rather than values above about redshift six.

A forest with no continuum left

Measuring how much neutral hydrogen sits between here and a distant quasar means measuring the fraction of its light that survives, which means knowing how much light there was. At high redshift nothing survives at the wavelengths that would show it, so the level is extrapolated across the region being measured — and the optical depth is the logarithm of a number divided by a guess.

cosmology · Reionisation

Named alongside it

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

The Gunn–Peterson troughThe Lyman-α forestOptical depthSaturationContinuum placementEffective optical depthIntergalactic mediumIonising backgroundMean transmitted fluxPrincipal component analysisQuasar absorptionQuasar spectrum

All concepts