Astronomy & Celestial Mechanics
the sky, computed
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The cmb-blackbody generator

A blackbody at 2.7255 kelvin, filling the sky
A blackbody at 2.7255 kelvin, filling the sky. The Planck function at 2.7255 K in the units the measurement is reported in, with the peak marked where Wien's law in frequency puts it: x = hν/kT = 2.8214, so ν = 160.2 GHz and the intensity there is 384 MJy per steradian. The points are drawn at the twenty-one frequencies across the FIRAS band, displaced from the curve by a Gaussian of 50 parts per million of the peak, which is the root-mean-square deviation the instrument actually reported. At the scale of this plot that displacement is a fifth of a pixel and the points sit on the line — which is the entire finding. Nothing else in astronomy is a blackbody to a part in twenty thousand: a stellar spectrum is a blackbody with absorption lines cut into it and a continuum that is the wrong shape at both ends. A thermal spectrum this exact requires that the radiation was once in equilibrium with matter, which requires that the universe was once opaque, which requires that it was once hot and dense.

The Planck function at 2.7255 K in the units the measurement is reported in, with the peak marked where Wien's law in frequency puts it: x = hν/kT = 2.8214, so ν = 160.2 GHz and the intensity there is 384 MJy per steradian. The points are drawn at the twenty-one frequencies across the FIRAS band, displaced from the curve by a Gaussian of 50 parts per million of the peak, which is the root-mean-square deviation the instrument actually reported. At the scale of this plot that displacement is a fifth of a pixel and the points sit on the line — which is the entire finding. Nothing else in astronomy is a blackbody to a part in twenty thousand: a stellar spectrum is a blackbody with absorption lines cut into it and a continuum that is the wrong shape at both ends. A thermal spectrum this exact requires that the radiation was once in equilibrium with matter, which requires that the universe was once opaque, which requires that it was once hot and dense.

3 essays call cmb-blackbody. The drawing above is what it returns with no arguments at all; every call below passes it something, because a placement that passes nothing draws whichever member of the family the generator happens to default to rather than the one its essay argues about.

Where it is called

Every figure listed here is the same construction drawn at different numbers, so a correction to one is a correction to all of them.

A blackbody at 2.7255 kelvin, filling the sky. The Planck function at 2.7255 K in the units the measurement is reported in, with the peak marked where Wien's law in frequency puts it: x = hν/kT = 2.8214, so ν = 160.2 GHz and the intensity there is 384 MJy per steradian. The points are drawn at the twenty-one frequencies across the FIRAS band, displaced from the curve by a Gaussian of 50 parts per million of the peak, which is the root-mean-square deviation the instrument actually reported. At the scale of this plot that displacement is a fifth of a pixel and the points sit on the line — which is the entire finding. Nothing else in astronomy is a blackbody to a part in twenty thousand: a stellar spectrum is a blackbody with absorption lines cut into it and a continuum that is the wrong shape at both ends. A thermal spectrum this exact requires that the radiation was once in equilibrium with matter, which requires that the universe was once opaque, which requires that it was once hot and dense. Cosmology

The most perfect blackbody ever measured

The whole sky glows at 2.7255 kelvin, and its spectrum matches the Planck curve to fifty parts in a million. Nothing else in astronomy is thermal to a part in twenty thousand, and a spectrum that exact is not a description of the radiation — it is a constraint on the history of everything that could have disturbed 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. Cosmology

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.

 A dipole 187 times the signal, and its own harmonics under it. The amplitude of each harmonic of the observer's own motion imprinted on the microwave sky, against the anisotropies of the sky itself. Moving at 369.8 kilometres a second through a blackbody field makes it hotter ahead and cooler behind by a fraction β = v/c, giving a dipole of 3.36 millikelvin — 187 times the 18 microkelvin anisotropies. Each further harmonic is smaller by another factor of β, so the kinematic quadrupole is 4.15 microkelvin, which is comparable to the real quadrupole and has to be subtracted separately. The dipole is not a nuisance in one respect: it is the measurement of the solar system's motion with respect to the radiation, and it is the most precisely known velocity in astronomy. Cosmology

A dipole a hundred times the signal

The largest structure in the microwave sky is the observer. Moving through a blackbody radiation field makes it hotter ahead and cooler behind by three and a third millikelvin — nearly two hundred times the anisotropies that all of cosmology is read from — and removing it is the first operation on any map.

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