Astronomy & Celestial Mechanics
the sky, computed
Concept

Blazar — where it appears

An active galactic nucleus whose relativistic jet points within a few degrees of the line of sight, so its emission is beamed and boosted by factors of tens. Blazars are the brightest extragalactic sources above 100 GeV, and the absorption bitten out of their spectra is how the background light is weighed.

Named by 7 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 The sky's darkness, measured as an opacity. Optical depth to electron–positron pair production against gamma-ray energy, for sources at redshifts 0.03, 0.1, 0.3, 1, both axes logarithmic. A gamma ray of energy E is absorbed most readily by background photons near twice the square of the electron rest energy divided by E: at 1 TeV that is 2.37 µm and at 100 GeV it is 0.24 µm, so the energy axis is a wavelength axis for the background light, running backwards — and the background it is evaluated against is the same two-component spectrum the star formation history produced, not a flat number. Above the marked τ = 1 the universe is opaque. The depth is computed in the delta-function approximation, the cross-section replaced by 0.2 of the Thomson value over a bandwidth of order the energy, with the background's comoving density evolving as (1+z)^1.2. That is a factor-of-two calculation and the shape is what it gets right: the horizon closes from z = 0.59 at 100 GeV to z = 0.16 at 1 TeV. The measurement runs the other way. A blazar's spectrum is observed, the absorbed part is the difference between it and the spectrum the source is believed to have emitted, and that difference gives the background — in the near infrared, where no direct measurement can subtract the zodiacal light well enough to compete.

A background weighed by what it stops

The faintest light in the universe cannot be photographed from inside the Solar System, because the zodiacal foreground is a hundred times brighter. It can be weighed instead, by the bite it takes out of a blazar at a trillion electronvolts.

cosmology · Olbers's paradox 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 An electroweak field decays toward one line, and helicity decides where it meets it. The comoving strength of a magnetic field against its coherence length, both on logarithmic scales. A field made at the electroweak transition, at 100 GeV, starts on a hundredth of the Hubble length then (1 AU today) with a tenth of the radiation's energy density (1 × 10⁻⁶ G), and decays as its turbulence is processed until the largest eddy is the one an Alfvén wave can cross by recombination — the straight line, 10⁻⁸ G at 1 Mpc. With no net helicity it falls as λ^−5/2 and stops at 0.038 pc and 4 × 10⁻¹⁶ G. Maximally helical, it falls only as λ^−½ and stops at 4.7 kpc and 5 × 10⁻¹¹ G. The shaded floor is what the missing gamma-ray halos exclude: a field coherent over more than a megaparsec must exceed 9 × 10⁻¹⁷ G, and the bound rises as the inverse square root of the coherence length below the leptons' cooling length of 0.6 Mpc. The non-helical field ends 3.0 decades below it; the helical one 4.6 decades above it. Above 10⁻⁹ G at a megaparsec the microwave background excludes the field.

A twist that decides where the field ends

A magnetic field made in the first trillionth of a second starts strong and absurdly small, and its turbulence spends the next three hundred thousand years trading strength for size. How far it gets depends on one conserved quantity — how twisted its field lines are — and for a field made at the electroweak transition, that twist is the difference between failing the void bound by three decades and clearing it by five.

cosmology · Primordial fields A sightline through the web, and where its field would be. The density of matter along a 300-megaparsec sightline through a model cosmic web, relative to the mean, on a logarithmic scale: a lognormal field whose logarithm has a width of 1.2. Galaxies sit at the 8 density peaks above the mean, and each has blown a magnetised bubble 1.4 Mpc in radius (shaded columns). Together they cover 7% of the sightline. The dots along the bottom are where 60 teraelectronvolt photons, stopped at random along the path, made their pairs: a photon stops where it stops, regardless of what is there, so the pairs fall on the empty stretches as often as on the crowded ones. Four of the 60 are made inside a bubble and are turned by its field. The other 56 are made in unmagnetised space, and their light forms a halo at full strength whatever the bubbles hold.

A field the galaxies cannot spread far enough

The missing gamma-ray halos are read as a field older than the galaxies because the galaxies seem unable to have put one there. The reason is not strength. A galaxy's wind carries a field that, spread over a megaparsec, is still ten million times stronger than the halos require. What it cannot do is reach the empty volume where most of the pairs are made — and a halo is dimmed only by the share of space the field fills.

cosmology · Primordial fields

Named alongside it

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

Pair cascadePrimordial fieldsCoherence lengthVoidsExtragalactic background lightMagnetogenesisFlux freezingIntergalactic mediumInverse Compton scatteringPhase transitionPlasma instabilityAlfven speed

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