Astronomy & Celestial Mechanics
the sky, computed
Concept

Last scattering surface — where it appears

The shell around every observer from which the microwave background photons last scattered, when the universe became transparent at about 380,000 years old. It is thin but not infinitely so, and its thickness damps the finest structure in the background.

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

One ionising photon per atom, and where that happens. The number of photons energetic enough to ionise hydrogen, per baryon, against temperature — with temperature falling to the right, so the universe ages to the right. The quantity is the fraction of a Planck distribution above 13.6 eV, integrated numerically, divided by the 6.13·10⁻¹⁰ baryons there are per photon. It crosses one at 5,844 K, which is z = 2143, and it falls by 19 orders of magnitude across the plot because it is the tail of an exponential. That crossing is the answer to why recombination waits until three thousand kelvin. At hydrogen's own ionisation temperature of 157,803 K there are two billion ionising photons per atom and the gas has no chance; the temperature has to fall by a factor of forty before the supply runs out, and it runs out suddenly because an exponential tail does. The number that sets the factor of forty is not an energy at all — it is the photon-to-baryon ratio, which is to say the entropy per baryon, which is to say a number fixed long before any of this and measured today from the second acoustic peak and from deuterium alike.

The surface the background actually is

Hydrogen ionises at 157,800 kelvin and the universe became transparent at 3,000. The factor of fifty between them is not an error, and it is not about energy — it is about there being two billion photons for every atom, so the far tail of the distribution can keep the gas ionised long after the typical photon has become useless.

cosmology · Microwave background The polarisation peaks sit in the temperature troughs. A tight-coupling sketch of the two acoustic sources against multipole, each scaled to its own maximum: the temperature, from the compression of the photon–baryon fluid at last scattering plus its Doppler term, and the E-mode polarisation, which is driven by the fluid's velocity gradient. The sound horizon and the distance to last scattering put the acoustic scale at ℓ = 302, the measured phase of the peaks is 0.267 and the damping scale is ℓ = 1400; the baryons' weight, which changes the heights of the temperature peaks and not their places, is left out. The temperature peaks fall at ℓ ≈ 218, 515, 813, 1110, 1408; the polarisation peaks at ℓ ≈ 130, 391, 681, 975, 1272, between them, because a compression is at its extreme when the fluid is momentarily still, and the velocity is largest a quarter of a cycle later. The model has no projection, no decaying potentials and no thickness, so it places the peaks and says nothing about their shapes.

Polarised only where the glow was lopsided

An electron bathed in light from every side scatters it unpolarised, and so does one bathed in light brighter on one side. Only a glow brighter along one axis than across it leaves a polarisation behind, and in the microwave background that glow existed for a short time, in a thin part of a thin shell, because the plasma was moving.

cosmology · Microwave background

Named alongside it

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

Optical depthReionisationThomson scatteringVisibility functionAcoustic peaksE mode polarisationFreeze outMean free pathPhoton to baryon ratioPolarisationQuadrupoleRecombination

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