Astronomy & Celestial Mechanics
the sky, computed
Concept

Boost — where it appears

The change of a measured quantity when the observer moves relative to the source, combining the Doppler shift with the bending of directions by aberration. An observer's motion through the microwave background boosts its temperature into a dipole and distorts its fine structure on every scale.

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

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.

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.

cosmology · Microwave background 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 velocityRest-frameAngular power spectrumAnisotropyBlackbodyCosmic varianceDamping tailForeground removalKinematic dipoleKinematic quadrupole

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