Astronomy & Celestial Mechanics
the sky, computed
Concept

Kinematic dipole — where it appears

The pattern imposed on the whole sky by an observer's own motion: brighter and hotter towards the direction of travel and fainter behind. The microwave background's dipole is about a thousandth of its temperature and gives the Sun's speed relative to it, 370 kilometres a second.

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

The dipole a 370 km/s motion has to put into counts of distant sources. The amplitude of the dipole in the number of sources per unit solid angle expected from the Sun's motion at 369.82 km/s relative to the microwave background, β = 1.234e-3, split into its two parts: aberration, 2β, which crowds sources towards the direction of motion, and the Doppler boost, x(1 + α)β, which brightens sources there and lifts fainter ones above the flux limit. For radio sources, with counts steepening as S^(−1) and spectra falling as ν^(−0.75), the expected dipole is 0.0046; for mid-infrared quasars, with counts steepening as S^(−1.7) and spectra falling as ν^(−1.26), the expected dipole is 0.0072, and the measured one is 0.0155 — 2.16 times larger, which would need a speed of 797 km/s. A dipole of a few parts in a thousand needs a catalogue of more than a million sources to see at all. The disagreement is not with the direction, which lies close to the microwave background's, but with the size, and it is not yet explained: either the samples carry a systematic nobody has found, or the matter and the radiation do not share one rest frame on these scales — in which case the assumption that the universe looks the same from everywhere is wrong in a way it has never been caught being wrong before.

The Sun's speed counted in quasars comes out twice too large

The microwave background is warmer in one direction by a part in a thousand, and that dipole is read as the Sun's motion through it at 370 kilometres per second. The same motion must crowd the counts of distant galaxies and quasars towards the same direction by an amount that can be calculated exactly. When a million quasars were counted, the direction agreed and the size came out more than twice too large — as though the Sun were moving at 800 kilometres per second relative to the matter.

cosmology · Expansion The spectrum ahead is the spectrum behind, shifted. The difference between the local power spectrum of the microwave background measured in the direction of the observer's motion and in the opposite direction, as a percentage of the average, against multipole, at 369.8 km/s. Ahead, the pattern is compressed and every feature moves to a higher multipole by a factor 1 + β; behind, to a lower one by 1 − β, with β = 1.234e-3. The difference is largest where the spectrum is steepest — 2.30 per cent at most in this range — and passes through zero at every peak and trough, where a small shift changes nothing. The spectrum is an interpolation through the measured peaks and troughs, so its steepness between them is known only to that resolution. A per cent of a quantity estimated from millions of independent modes is a measurable number.

A speed read from the finest spots in the map

The dipole in the microwave sky is taken to be the observer's motion and subtracted. The same motion also squeezes the small-scale pattern towards the direction of travel by a part in a thousand, and that squeeze measures the speed a second time without using the dipole at all — which is the only way to ask how much of the dipole is the universe's own.

cosmology · Microwave background

Named alongside it

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

AberrationCMB dipolePeculiar velocityAngular power spectrumBoostCosmic varianceCosmological principleDamping tailDoppler boostingIsotropyMultipolePoisson noise

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