Astronomy & Celestial Mechanics
the sky, computed
Concept

Foreground removal — where it appears

The subtraction of emission from the Milky Way and other sources lying between an observer and a faint cosmological signal. It relies on the foregrounds' different frequency spectra, so maps at several frequencies are fitted together.

Named by 3 essays across 2 fields — 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 Polarised dust, synchrotron and the signal between them. The amplitude of B-mode polarisation at angular multipole 80, in microkelvin of CMB temperature on a logarithmic scale, against frequency from 20 to 450 GHz, for a patch of sky as clean as the cleanest large field observed. Dust is a modified blackbody with emissivity index 1.53 at 19.6 K, normalised to 4.6 µK² at 353 GHz; synchrotron falls as frequency to the power −3.1 in antenna temperature, normalised to an illustrative 1 µK² at 23 GHz. The horizontal lines are a primordial signal with tensor-to-scalar ratio 0.01, about 0.048 µK, and the lensing B-modes, about 0.071 µK. The foregrounds together are faintest at 81 GHz, at 0.038 µK, 0.8 times the signal. At 150 GHz the dust alone is 0.105 µK, the amplitude a tensor ratio of 0.046 would produce; at 353 GHz it is 2.23 µK, 47 times the signal. No frequency has the signal above the foreground.

A foreground drawn by the field it traces

The grains that polarise starlight along the Galaxy's magnetic field glow, at millimetre wavelengths, with light polarised across it — and that glow is brighter than the primordial signal cosmologists are looking for at every frequency above eighty gigahertz and in every patch of sky. Its pattern on the sky is set by how loosely the interstellar filaments follow the field, and removing it rests on a bet that the clouds along each line of sight share one temperature.

galaxies · Dust polarisation The trough a smooth fit leaves behind. A trough 150 mK deep, centred at 75 MHz and 15 MHz wide at half depth (dashed), and what remains of it after the same foreground fit that removes the sky, with 3, 5, 7 terms. The fit cannot tell which part of the spectrum is sky and which is signal, so it absorbs whatever part of the trough looks smooth: what remains is 197, 62, 71 mK deep at its lowest, narrower than the injected trough and flanked by bumps above zero that were never in the sky. Measured jointly with the foreground, the trough is worth, in signal-to-noise, a trough 48, 29, 15 per cent as deep with no foreground to remove. What a global experiment measures is not the trough but its projection onto whatever the foreground fit leaves free.

A depth that belongs to the fit as much as the sky

The trough the first stars should have cast is found by subtracting a smooth function from a sky ten thousand times brighter, and a smooth function flexible enough to remove that sky also removes most of any trough as wide as the models predict. What a global 21-centimetre experiment reports is not the trough but the part of it the fit could not imitate, and that part depends on how many terms the fit was given.

cosmology · Reionisation

Named alongside it

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

Synchrotron radiationAberrationAnisotropyB-modesBeam chromaticityBlackbodyBoostCMB dipoleCosmic dawnDust polarisationE-modesGlobal signal

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