Astronomy & Celestial Mechanics
the sky, computed
Concept

Microwave background — where it appears

The thermal radiation left from the time the universe became transparent, now at a temperature of 2.725 K and filling all space. Its tiny anisotropies record the density fluctuations and sound waves of the early plasma, which is why most precise cosmological parameters come from it.

Named by 3 essays across 2 fields — each of them below, with the objects they name alongside it.

Thirty e-foldings erase the memory of a seed. Field strength against time for three seed fields 8 orders of magnitude apart, amplified at one e-folding every 3·10⁸ years — a galactic dynamo's measured turnover rate — and stopped at the 3·10⁻⁶ gauss the disc actually has. In 10 billion years the budget is 33 e-foldings, which is a factor of 3·10¹⁴. That is the finding: the three tracks reach the same ceiling within 5.5 billion years of one another, so the field a galaxy has today carries essentially no information about the field it started with. Any seed above about 10⁻²⁰ gauss will do, and mechanisms that produce far less than that are the only ones ruled out. The measurement that does constrain a seed has to be made where no dynamo ever ran, which means the voids between clusters — and the limit there comes from gamma rays that never arrived.

The seed that cannot be remembered

A galactic dynamo affords something like thirty e-foldings over the age of a galaxy, which multiplies any seed field above a ten-thousandth of a billionth of a microgauss up to the microgauss actually observed. The field a galaxy has today therefore says nothing about the field it started with, and the only place a seed survives unamplified is the emptiness between clusters.

cosmology · Primordial fields The distance a proton keeps its energy, against the energy. The energy-loss length of a cosmic-ray proton — the distance over which it would lose all its energy at its current rate — against its energy, computed from the photon density of the microwave background at 2.725 K and the cross-section for photoproducing a pion, which peaks at the Δ resonance. The dashed line is the loss to cosmic expansion alone, about 4,283 Mpc. Only above about 6.1·10¹⁹ eV does the combined loss length fall below a gigaparsec, because below that few background photons are energetic enough in the proton's frame to cross the 145 MeV threshold. Above it the loss length collapses: 144,327 Mpc at 3.16·10¹⁹ eV, 155 Mpc at 10²⁰ and 19 Mpc at 10²¹, where every proton is above threshold and the loss is set by the photon density alone. A proton seen above 10²⁰ eV has come from within a hundred megaparsecs or so — a horizon drawn by light at three kelvin. Pair production on the same photons, which costs about a gigaparsec near 10¹⁹ eV, is not drawn.

A horizon drawn by light at three kelvin

A proton above about fifty exaelectronvolts cannot cross the universe, because the microwave background, seen from the proton, is a bath of gamma rays that it loses energy to by making pions. The cut-off in the cosmic-ray spectrum sits where that horizon predicts. But a source that simply cannot accelerate particles any harder would put a cut-off in the same place, and what the particles turn out to be made of says the second explanation may be the right one.

galaxies · Cosmic rays The sky-averaged 21-centimetre signal, and the trough that was claimed. The brightness temperature of neutral hydrogen's 21-centimetre line relative to the microwave background, averaged over the sky, in millikelvin, against observed frequency (the redshift is 1420.4 MHz over the frequency, minus one). In this model the first stars' ultraviolet couples the hydrogen's spin to the gas near redshift 17, X-rays heat the gas near 11, and reionisation is half complete at 7.7. Because the gas has cooled faster than the background since it decoupled, coupling makes it absorb: the trough reaches −171 mK at 71 MHz (redshift 19.1). Heating turns the signal into a weak emission, and reionisation removes it above about 197 MHz. The dashed curve is the deepest absorption standard physics allows at each frequency — gas that has only cooled, fully coupled — and the point is the one claimed detection, −500 mK at 78 MHz: about 1.9 times deeper than that floor.

A shadow cast on the microwave background

Before the first stars lit it up, the neutral hydrogen between the galaxies was colder than the microwave background behind it, and once starlight tied its 21-centimetre line to that cold, it absorbed. The absorption, redshifted to radio frequencies near 70 megahertz, is a thermometer for gas nobody has seen — and the one claimed detection was twice as deep as cooling alone allows, which is either a discovery about dark matter or a lesson about antennas.

cosmology · Reionisation

Named alongside it

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

21-centimetre lineAdiabatic coolingAir showerBiermann batteryBlazarCompositionCosmic dawnCosmic raysDark matterDelta resonanceDynamoEnergy loss length

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