Astronomy & Celestial Mechanics
the sky, computed
Concept

Primordial fields — where it appears

Magnetic fields generated in the very early universe and present before the first stars formed. Fields of about a nanogauss would alter recombination and the microwave background, which is how their strength is bounded.

Named by 5 essays across one field — 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 A clumped plasma recombines earlier. The fraction of hydrogen still ionised against redshift, decreasing to the right, on a logarithmic axis, from Peebles's three-level atom: for a smooth plasma (solid), and for one whose baryons are clumped into two equal volumes at 1.71 and 0.29 times the mean density, a clumping factor of 0.5 (thick dashed, averaged by mass; thin dashed, each zone alone). Recombination goes as the density squared, so the dense zone recombines first and carries most of the mass; the average ionisation falls through one half at redshift 1292 instead of 1273, and at redshift 1100 it is 0.123 against 0.145. The photons cannot see the individual patches, which are smaller than their mean free path; they see only the average, and the average recombines earlier.

A field that would have moved the ruler

A magnetic field left over from the early universe, too weak to matter to any galaxy, could still have pushed the baryons into small clumps before the universe became transparent. Clumped hydrogen recombines earlier, the sound waves in the plasma stop sooner, and the ruler that the microwave background is read with comes out shorter — which raises the Hubble constant the background implies, in the direction of the disagreement that has resisted every other explanation.

cosmology · Primordial fields How far a void field turns the leptons that make each cascade photon. The deflection angle of a cascade lepton over its cooling length, in radians on a logarithmic scale, against the energy of the cascade photon it produces, for fields of 10⁻¹⁸ G, 10⁻¹⁷ G, 10⁻¹⁶ G, 10⁻¹⁵ G, 10⁻¹⁴ G coherent over at least that length. The angle falls as the square of the lepton energy, so as the inverse of the photon energy: the gigaelectronvolt halo is made by the slowest leptons, which are turned most. At 1 GeV the deflections are 1e-3, 0.01, 0.11, 1.06, 10.62 rad. The dashed line is the jet's half-opening angle, 0.1 rad; a lepton turned further than that sends its photons away from the observer, and the halo at that energy disappears.

A lower limit made of three lengths and a missing echo

The only measurement of a magnetic field in the empty space between galaxies is a lower limit, and it comes from light that did not arrive. Teraelectronvolt gamma rays from distant blazars make electron pairs in intergalactic space, the pairs should re-emit the energy at gigaelectronvolts in a halo around each source, and the halos are missing. Whether that absence weighs a field of a ten-thousandth of a billionth of a microgauss depends on three lengths, the field's own tangle, and how long the blazar has been shining.

cosmology · Primordial fields The intergalactic temperature against density, with and without blazar heating. The temperature of the intergalactic gas against its density relative to the cosmic mean, both logarithmic, near a redshift of two. Photoheating by the ultraviolet background alone (dashed) gives a power law with denser gas hotter, T = 12,000 K at mean density rising as the density to the 0.6. Heating by the pair beams of distant blazars, if they lose their energy to the plasma rather than to scattering, is deposited per unit volume, so each particle in a void gets more of it: adding increments of 3,000, 10,000, 30,000 K at mean density turns the relation over below densities of 0.58, 1.23, 2.44 times the mean, and the emptiest gas becomes the hottest. That inversion is what a void heated from the inside looks like, and it would happen whether or not the void holds a magnetic field.

A void heated from the inside

The missing gamma-ray halos around distant blazars are read as a magnetic field in the voids — unless the electron–positron pairs that should make the halos lose their energy to the plasma first. Then the voids are being heated, the heat goes preferentially to the emptiest gas, and the intergalactic medium's temperature–density relation turns over, with the voids hotter than the filaments. The field and the heating predict different skies, and the Lyman-α forest is where they part.

cosmology · Primordial fields The echo of a one-day flare, for four void fields. The 1–10 GeV flux of the cascade echo against the time since the start of a one-day teraelectronvolt flare of 10 Crab-days, from a blazar 500 Mpc away, both on logarithmic scales, for void fields of 10⁻²¹ G, 10⁻²⁰ G, 10⁻¹⁹ G, 3 × 10⁻¹⁹ G. The echo carries 1.0 × 10⁻⁴ erg cm⁻² in the band whatever the field — the field decides only when it arrives, and so how thinly it is spread. Half of it has arrived 14 hours after the flare began in the weakest field and 4.1 years in the strongest, and the flux at that moment falls from 1.1 × 10⁻⁹ to 1.3 × 10⁻¹³ erg cm⁻² s⁻¹. The dashed curve is the flux a space telescope needs to detect a source averaged over that long, falling as the square root of the time to a floor of 10⁻¹² erg cm⁻² s⁻¹. Counting only what arrives after the flare has ended, three of the four echoes clear it.

An echo heard only from the weakest fields

A missing gamma-ray halo gives the field in the voids a lower limit and nothing more. A flare's echo could give it a value — the gigaelectronvolt light that arrives late because the void field bent its path. But the echo carries a fixed amount of energy and the field decides only how long it is spread over, so it can be heard only from fields weak enough to deliver it quickly, and only after flares brighter than almost any yet seen from a blazar far enough away to make one.

cosmology · Primordial fields

Named alongside it

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

BlazarPair cascadeVoidsCoherence lengthExtragalactic background lightInverse Compton scatteringMagnetogenesisPlasma instabilityAcoustic peaksBaryon clumpingBiermann batteryDynamo

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