Astronomy & Celestial Mechanics
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Cosmology

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.

Assumes Expansion and Microwave background.

18 min read 10 figures Scales that defeat intuitionMeasuring the unreachable

Every galaxy that has been looked at is magnetised, at a few microgauss, ordered on kiloparsec scales. So are clusters of galaxies. So, probably, are the filaments between them. The question of where those fields came from is one of the oldest unanswered questions in cosmology, and it has an unusual structure: the observation that ought to answer it has been rendered useless by the very process that produces the field.

The reason is that a dynamo is an exponential.

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.
Fig. 1 Field strength against time for three seed fields eight orders of magnitude apart, amplified at one e-folding every three hundred million years and stopped at the field a galactic disc actually has. All three reach the ceiling within a billion years of one another, so the field observed today carries no information about where it started.

Why the memory is gone

A galactic dynamo works by taking the differential rotation of a disc and the helical turbulence within it and converting one field component into another and back, with a net gain per cycle. The gain is what makes it a dynamo, and the cycle time is a fraction of a galactic rotation — a few hundred million years.

An e-folding time of three hundred million years over ten billion years is about thirty e-foldings. That is a factor of ten to the thirteen.

The field a disc actually has is a few microgauss, and it is set by saturation rather than by time: the dynamo stops growing when the field’s energy approaches the turbulent energy driving it, which happens at a few microgauss in a normal disc — comparable, and not by accident, to the other pressures holding the gas layer open. So the observed value is a property of the saturation, not of the growth.

Put the two together and the conclusion is immediate. Any seed above about ten to the minus twenty gauss reaches saturation well within a galaxy’s life. Two seeds a million times apart in strength arrive at the same answer, differing only in how long they took. The field measured today is a measurement of the saturation condition and of nothing else.

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 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 100 e-foldings, which is a factor of 3·10⁴³. That is the finding: the three tracks reach the same ceiling within 1.8 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.
Fig. 2 The same three seeds amplified three times faster, at one e-folding per hundred million years. The convergence is correspondingly sooner — all three reach the ceiling within a few hundred million years of each other rather than a billion — and the conclusion is unchanged and strengthened. The erasure does not depend on the e-folding time being what it is; it depends only on the number of e-foldings exceeding the logarithm of the range of possible seeds, and thirty exceeds forty-six only narrowly while a hundred exceeds it comfortably.

That is a rare situation in astrophysics — an exponential that runs for long enough to destroy the initial condition — and it is worth naming what it costs. The most abundant, best-measured magnetic data in the universe are useless for the question they seem designed to answer.

The contrast with the other conserved-quantity problems in this collection is sharp and instructive. A collapsing cloud’s field is frozen in, so its history is written all over its present value and the whole difficulty is that the value is too large. A galaxy’s field is regenerated, so its history is gone and the value is whatever the saturation says. Freezing preserves memory and a dynamo destroys it, and the two problems that look alike from a distance are opposites.

There is a further wrinkle that makes the erasure even more complete. Before the large-scale dynamo has done anything at all, a small-scale dynamo operates: turbulence alone, with no rotation and no helicity, amplifies a field on the scale of the turbulence itself, and it does so on the eddy turnover time rather than the rotation time — millions of years rather than hundreds of millions. So the seed is amplified to near equipartition on small scales almost immediately, and the slow dynamo’s job is only to organise that tangle into something large-scale. Two exponentials in series, both erasing.

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 13 billion years the budget is 43 e-foldings, which is a factor of 7·10¹⁸. 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.
Fig. 3 The same construction run for thirteen billion years rather than ten, which is the age a galaxy that formed early actually has. Three more e-foldings are three more factors of ee of erasure, and the tracks are converged for the whole of the last two thirds of the plot. What the extension makes visible is that the epoch of convergence is the only thing the seed affects: a larger seed saturates earlier, and a measurement of when galaxies became magnetised is therefore a measurement of the seed in a way that a measurement of how magnetised they are is not.

What could have made a seed

There is no shortage of mechanisms and no way of choosing between them, which is the usual signature of a question with no discriminating observation attached.

The most conservative is the Biermann battery, and it requires nothing beyond ordinary plasma physics. If the density gradient and the pressure gradient in an ionised gas are not parallel, electrons and ions are pushed differently and a current flows, generating a field from nothing. That happens at any curved ionisation front, at any oblique shock, and at the edges of the first ionised regions. It reliably produces about ten to the minus twenty gauss, which is comfortably above the threshold and comfortably below anything measurable.

The battery’s virtue is that it cannot be avoided. It requires no new physics, no coupling, no phase transition — only that a real astrophysical plasma has gradients that are not everywhere parallel, which is guaranteed. So the seed question is not whether a seed existed but whether anything made a larger one, and the observational programme is a search for an excess over a floor that is certainly there.

More exotic mechanisms produce more. A phase transition in the early universe — the electroweak transition at a hundred gigaelectronvolts, or the quark–hadron transition at a few hundred megaelectronvolts — involves bubbles nucleating, colliding and stirring a plasma, and turbulence in a conducting plasma makes fields. The trouble is the coherence length: a field made at the electroweak epoch is coherent on the horizon scale at that time, which redshifts to something like an astronomical unit today. That is uselessly small on any galactic scale.

Something can be recovered from it, and the mechanism is worth a sentence because it is counterintuitive. A tangled magnetic field in a turbulent, decaying plasma does not simply dissipate; if it has net magnetic helicity — a measure of how linked the field lines are — the helicity is conserved far better than the energy, and the field is forced to transfer its energy to progressively larger scales as it decays. That is an inverse cascade, and it can grow the coherence length by many orders of magnitude between the electroweak epoch and recombination. Whether the primordial field is helical is therefore a question with observational consequences, and a helical field has a parity-violating signature in the microwave background that a non-helical one does not.

Inflation is the mechanism that solves the coherence problem and creates a different one. A field generated during inflation is stretched to arbitrarily large scales, which is exactly what is wanted. But electromagnetism is conformally invariant, and in a conformally flat expanding universe a conformally invariant field is simply diluted rather than amplified — so producing anything requires breaking that invariance, which means adding a coupling that has no independent motivation.

The two constraints from the microwave background

If a coherent field existed before recombination it would have left traces, and the absence of those traces is where the upper limits come from.

The first constraint is dynamical. A magnetic field carries energy and exerts anisotropic stress, so a primordial field perturbs the photon–baryon fluid and changes the acoustic peaks. It also generates its own vector and tensor modes, which produce polarisation patterns that scalar perturbations cannot. Fitting the observed spectra with a magnetic component included bounds a scale-invariant primordial field at a few nanogauss.

The second is Faraday rotation, on the last scattering surface itself. A field there would rotate the polarisation of the microwave background by an amount going as the square of the wavelength, mixing the two polarisation patterns into each other in a frequency-dependent way. The bound from that is comparable.

The field a collapse would arrive with, and the one it has. Field strength against hydrogen density, both logarithmic, over the eight decades between diffuse gas and a protostellar core. The steeper line is what perfect flux freezing demands: a sphere collapsing conserves both mass and flux, so B goes as R⁻² while ρ goes as R⁻³, and therefore B goes as the two-thirds power of the density exactly — an exponent with no free parameter in it. The shallower locus is what Zeeman measurements find: a flat branch at about 10 µG up to 300 per cubic centimetre, where the density is rising and the field is not, and a rise as the 0.65 power of the density above it. By the density of a core the two differ by a factor of 1, and a star built at the frozen-flux value would carry a field four orders of magnitude beyond anything measured on one. The flat branch is the important half: it says the gas is moving along field lines without dragging them, which is what gravity does to a cloud that is still magnetically supported, and it locates where the freezing has to break.
Fig. 4 Why a seed cannot simply be scaled up from what is measured now. Flux freezing ties the field to the gas, so compressing a cloud by a factor in density raises the field by that factor to a power near two thirds — and running that backwards from a galaxy’s microgauss field to the density of the intergalactic medium gives a seed of order 10−2010^{-20} gauss. Any seed at least that large is compatible with everything observed, and so is any seed twenty orders of magnitude smaller if a dynamo has had time to run. The measurement constrains the product, not the factors.

A few nanogauss sounds small and is enormous. Diluted by expansion and then amplified by a dynamo, a nanogauss seed would give a galactic field far above what is observed — so the microwave background bound is not close to being restrictive for the seeds that matter. It rules out the top of the range and leaves twelve orders of magnitude below it untouched.

The energy at which the sky begins to point. Gyroradius against energy for a singly charged particle, in three field strengths, with the thickness of the galactic disc and the size of its halo marked. A cosmic ray is not an image of anything: its path is a helix about a field line, and by the time it arrives the direction it came from has been erased. The erasure is quantitative. At 1 µG a proton's gyroradius equals the disc's half-thickness at 1.4·10¹⁷ electronvolts and the halo's radius at 1.4·10¹⁹, so below the first the particle is stored and stirred for tens of millions of years, and only above the second does it travel in something like a straight line. The measured spectrum has a break — the knee — at about 3×10¹⁵ eV, which is within a factor of a few of the first of those; the sky only starts showing structure above 10¹⁹, which is the second. Two features of a spectrum measured on the ground, both located by one straight line on this plot.
Fig. 5 The length scale on which any of the bounds above are statements about a fluid. A charged particle’s gyroradius at a hundredth of a microgauss — the intergalactic regime — is enormous by laboratory standards and is still minute compared with a megaparsec, so even a void’s field is a fluid property rather than a set of trajectories. That is what licenses the induction equation everywhere in this essay, and it is why the one place the framework fails — the highest-energy cosmic rays, whose gyroradii approach the size of the Galaxy — is a separate subject with separate methods.

There is a third constraint from the same era that is independent of the other two and is worth recording. A magnetic field present during primordial nucleosynthesis changes the expansion rate slightly, changes the electron phase space, and therefore changes the helium abundance. The bound from that is weaker than the microwave background’s, but it applies at a much earlier time and to a field of any coherence length, including one far too small to affect the acoustic peaks. Three bounds at three epochs, all null, all at roughly the same level.

Where a seed survives

The escape from the dynamo problem is to look where no dynamo ever ran, and that means the voids.

A void is a region tens of megaparsecs across containing almost no galaxies and almost no gas. There has been no differential rotation there, no turbulence worth the name, and nothing to amplify anything. Whatever field a void contains is close to whatever the primordial field was, diluted by expansion and otherwise untouched.

The difficulty is obvious: there is nothing there to measure. No synchrotron emission, because there are no relativistic electrons; no Faraday rotation worth measuring, because there are no thermal electrons; no aligned dust, because there is no dust.

The measurement that has been made instead is beautifully indirect and its interpretation is contested.

It is worth appreciating the emptiness first. A void has a density perhaps a fifth of the cosmic mean, over a region large enough to hold a hundred galaxy groups. Structures that large have not had time to collapse, so a void is a piece of the early universe preserved at low density — expanded, cooled, and otherwise unprocessed. Homogeneity above a hundred megaparsecs is what guarantees that voids are a fair sample rather than an oddity.

The cascade that did not arrive

A blazar is an active galactic nucleus pointed at the observer, and it emits gamma rays up to teraelectronvolt energies. Those gamma rays do not reach here unimpeded: they collide with the extragalactic background light and produce electron–positron pairs, over a path of a few hundred megaparsecs.

The pairs then scatter microwave background photons up to gigaelectronvolt energies. So a teraelectronvolt source should be accompanied by a gigaelectronvolt halo — reprocessed light, arriving slightly later and slightly off-axis, with a total energy comparable to what was absorbed.

The halo is not seen. The gigaelectronvolt flux from several blazars is well below what the cascade requires. One explanation is a magnetic field in the voids. The pairs are charged, and even a fantastically weak field deflects them enough to spread the reprocessed emission over a larger angle or to delay it beyond the observing window. Requiring the deflection to be large enough gives a lower bound on the void field, at around ten to the minus sixteen or ten to the minus seventeen gauss.

That would be the first detection of a genuinely primordial field, and it is exactly the kind of measurement that ought to be treated with suspicion. The alternative explanation is that the pairs lose their energy some other way — to plasma instabilities in the intergalactic medium, which would heat the gas rather than upscatter photons. Whether those instabilities operate fast enough is a plasma physics question with no laboratory analogue, and it has been argued both ways for fifteen years. The situation resembles the trough that proved the forest survived: an absence is being asked to carry a quantitative conclusion, and the strength of the conclusion depends entirely on how well the alternative explanations are bounded.

Why the answer would matter

It would be reasonable to ask why a field of ten to the minus sixteen gauss is worth this much effort, and the answer is that its existence is the whole content rather than its size.

A field in a void cannot have been made by anything in a void, because nothing is there. It cannot have been made by a galaxy and expelled, because the transport times are far too long and the geometry is wrong. So it has to have been made before structure existed, which means before recombination, which means in the early universe — and the mechanisms available there are all speculative physics beyond the standard model. A detection would therefore be a measurement of the early universe by an entirely new route, comparable in kind to the abundance of light elements or the acoustic peaks. It would also, incidentally, close the origin question for galactic fields by supplying a seed of known strength. There is a second reason the question matters, and it is closer to home. If the seed is large — nanogauss rather than ten to the minus twenty — then the field was dynamically significant during structure formation itself, adding pressure to the collapsing gas and altering when and where the first stars formed. That is a testable difference and it is one of the things the earliest galaxies may eventually decide.

The leak that lets a cloud go. Two timescales against the fractional ionisation of a dense core. The rising line is the ambipolar diffusion time — how long the neutral gas takes to drift through the ions that are tied to the field — and it is proportional to the ionisation fraction, because a rarer ion is collided with less often and holds the neutrals less firmly. The flat line is the free-fall time at 10⁴ molecules per cubic centimetre, which knows nothing about the field. They cross at an ionisation of 1.8e-6. Cosmic rays keep the ionisation of a shielded core near 1e-7, which puts the drift time 0 times the free-fall time — slow enough that the core is supported and fast enough that it is not supported for ever. That is the resolution of the flux problem and it is a quantitative one: the field leaks out on a schedule set by how many ions the cosmic rays make, so the star formation rate of a magnetised cloud is set by a particle flux arriving from outside the galaxy.
Fig. 6 The one place a field can be lost rather than amplified. In a weakly ionised gas the neutrals are not tied to the field at all — only the ions are — so the field drifts through the neutral gas at a rate set by the ionisation fraction, and at a part in ten million that drift is fast enough to matter over the life of a cloud. Ambipolar diffusion is the only term in this essay that removes flux, and it operates exactly where a seed might otherwise have been preserved.

Clusters, which are neither

Between a galaxy and a void sits a third environment, and it is the one where the argument is least settled.

The gas in a cluster of galaxies is hot, ionised, and magnetised at a few microgauss — comparable to a galactic disc, over a volume a thousand times larger. It is measured by rotation measures of radio sources seen through the cluster, and by the diffuse synchrotron haloes that some clusters have. Whether a cluster field is amplified or inherited is genuinely open. Cluster gas is turbulent — stirred by mergers and by the galaxies moving through it — so a small-scale dynamo can operate; but the turnover times are long, the number of turnovers over a Hubble time is modest, and the amplification available may be only a few orders of magnitude rather than thirteen. If so, a cluster field retains some memory of its seed, and the required seed is much larger than a Biermann battery gives.

A radial wind from a rotating star draws a spiral. The interplanetary field out to 5 astronomical units, drawn as the Archimedean spiral it is. Nothing here rotates: the plasma moves radially outward at 400 kilometres a second and the field is frozen into it, so each parcel remembers the longitude it left from and the pattern winds up while the material does not. The pitch angle is arctan(Ωr/v), which is 47° at one astronomical unit — the radius where the star's rotation has carried the footpoint through one radian in the time the wind takes to arrive. The practical consequence is a matter of hours: a flare's particles follow the field rather than the line of sight, so the ones that reach a given planet left a longitude about 61° to the west of it. A magnetically well-connected flare on the western limb delivers a particle storm and a larger one at disc centre does not, and the difference is this geometry rather than anything about the flare.
Fig. 7 The other thing a magnetised flow does with a rotation, and the reason a cluster is a harder case than a disc. A radial wind from a rotating body winds its field into a spiral, and the winding is what a large-scale dynamo has to work against and with — an organising influence that a galactic disc’s differential rotation supplies and a cluster’s chaotic, merger-driven motions do not. A cluster is turbulent without being systematically sheared, so the small-scale dynamo operates and the large-scale one has nothing to organise the tangle with. That is why cluster fields are strong and disordered while disc fields are comparable and coherent.

That makes clusters the most promising place to look for an excess over the floor, and the least clean. The measurement is a rotation measure through a medium whose density is known from X-rays and whose turbulence is not, and the systematic uncertainty is the correlation between the two.

What a galaxy’s field does say

The dynamo has erased the seed, but it has not erased everything, and it is worth recording what the galactic measurements are still good for.

They measure the saturation condition, which is a statement about the turbulence and the rotation rather than about history. They measure the geometry — whether the large-scale field reverses across the disc — and different dynamo modes predict different geometries, so the sign pattern is a test of the dynamo rather than of the seed, and it is read off the same catalogue of background sources that measures everything else about the galactic field in projection. And they measure timing. A dynamo takes billions of years to saturate, so a galaxy observed at high redshift with a fully ordered microgauss field is a problem: there has not been time. Rotation measures of a handful of galaxies at redshifts around one to two do suggest fields as strong as today’s, which is uncomfortable for the slow dynamo and is one of the better arguments for a larger seed or a faster small-scale dynamo operating first.

The energy at which the sky begins to point. Gyroradius against energy for a singly charged particle, in three field strengths, with the thickness of the galactic disc and the size of its halo marked. A cosmic ray is not an image of anything: its path is a helix about a field line, and by the time it arrives the direction it came from has been erased. The erasure is quantitative. At 3 µG a proton's gyroradius equals the disc's half-thickness at 4.2·10¹⁷ electronvolts and the halo's radius at 4.2·10¹⁹, so below the first the particle is stored and stirred for tens of millions of years, and only above the second does it travel in something like a straight line. The measured spectrum has a break — the knee — at about 3×10¹⁵ eV, which is within a factor of a few of the first of those; the sky only starts showing structure above 10¹⁹, which is the second. Two features of a spectrum measured on the ground, both located by one straight line on this plot.
Fig. 8 And the length scale on which any of this is meaningful. A charged particle spirals about a field line with a radius set by its momentum, and in every regime discussed here that radius is minute compared with the system — so “the field” is a fluid property rather than a set of trajectories, and the induction equation is the right description. Where the gyroradius approaches the system size the whole framework fails, which is why the highest-energy cosmic rays are a separate subject.

What would settle it

Three measurements would move the subject, and all three are being attempted.

A rotation-measure survey of the diffuse filaments between clusters would reach the intergalactic field where it is not quite zero and not yet amplified. The signal is a fraction of a radian per square metre against a galactic foreground of tens, so it requires both a very large sample and a very good model of the foreground — which is why it is a project for the next generation of low-frequency arrays rather than for the present one.

The field a collapse would arrive with, and the one it has. Field strength against hydrogen density, both logarithmic, over the eight decades between diffuse gas and a protostellar core. The steeper line is what perfect flux freezing demands: a sphere collapsing conserves both mass and flux, so B goes as R⁻² while ρ goes as R⁻³, and therefore B goes as the two-thirds power of the density exactly — an exponent with no free parameter in it. The shallower locus is what Zeeman measurements find: a flat branch at about 3 µG up to 300 per cubic centimetre, where the density is rising and the field is not, and a rise as the 0.65 power of the density above it. By the density of a core the two differ by a factor of 1, and a star built at the frozen-flux value would carry a field four orders of magnitude beyond anything measured on one. The flat branch is the important half: it says the gas is moving along field lines without dragging them, which is what gravity does to a cloud that is still magnetically supported, and it locates where the freezing has to break.
Fig. 9 The same scaling run down from a weaker diffuse field, which is the sensitivity of the seed estimate to the one measurement it starts from. Three microgauss rather than ten shifts the whole relation and moves the inferred seed by the same factor — a factor of three, against the twelve orders of magnitude the bounds span. That is worth drawing because it says where the uncertainty is not: the flux-freezing extrapolation is the reliable part of the argument, and everything unsettled is in what the dynamo did afterwards rather than in what the compression did before.
The one number that decides whether a field is a fluid. The magnetic Reynolds number, vL/η, for five plasmas, on a logarithmic axis spanning 22 decades. It is the ratio of the term in the induction equation that carries a field with the flow to the term that lets it slip through, so a large value means a field line is a material line — it moves with the gas, it cannot break, and its flux through any surface carried along with the fluid is conserved. Astronomical values run from 10⁹ to 3·10²⁰; the laboratory value is 100, which is why the behaviour that dominates every plasma in this collection is the one that is hardest to arrange on a bench. The size of the number is doing the work: at 10¹⁶ the diffusion time across a molecular cloud is ten million times the age of the universe, so freezing is not an approximation to be checked but a constraint to be worked around, and the interesting question everywhere below is where and how the coupling is allowed to fail.
Fig. 10 And why the dynamo is available everywhere. The magnetic Reynolds number is the ratio of field advection to field diffusion, and in every astrophysical plasma — a protogalaxy, a disc, a cluster — it exceeds unity by ten or twenty orders of magnitude. So the field is frozen to the flow and cannot decay away on any relevant timescale, which is what makes exponential amplification the default rather than a special case. The seed is forgotten because the amplification is efficient, not because the field is fragile.

A definitive resolution of the blazar cascade argument would require settling whether plasma instabilities drain the pairs. That is a plasma physics calculation rather than an astronomical measurement, and it is the kind of question that laboratory experiments on relativistic beams may eventually reach.

And a detection of parity violation in the microwave background’s polarisation would establish a helical primordial field directly. The signal is a correlation between two polarisation patterns that ordinary physics forbids, so a detection would be unambiguous — and current data are consistent with zero.

The honest state of the subject is this. Galactic fields are ubiquitous, well measured, and uninformative about their own origin. The early universe offers a dozen mechanisms and no way to choose. One indirect measurement suggests a primordial field at the level a Biermann battery would give, and its interpretation depends on plasma physics nobody can test. The strongest statement that can be made without controversy is negative: whatever made the seed, it made at least ten to the minus twenty gauss and no more than a few nanogauss, and twelve orders of magnitude is the width of current knowledge. That is a wide interval, and it is worth ending on what makes it tolerable: the two ends are bounded by real measurements rather than by taste, and the mechanism that erased the evidence is understood well enough to say exactly what was lost and why. A question with a known reason for being hard is in better shape than one that is merely open, which is roughly the position the coincidence problems of the early universe were in before inflation gave them a mechanism to be argued about.

It is worth ending on what the erasure does not destroy, because the situation is not quite as bleak as the exponential makes it sound. A dynamo erases the seed’s magnitude; it does not erase everything about the initial conditions. The geometry of the resulting field depends on which mode grew fastest, which depends on the disc’s rotation and turbulence rather than on the seed — so geometry reports on the dynamo. The helicity is better still: it is far better conserved than the energy, so a primordial field with net helicity leaves a signature that amplification does not remove, and searching for parity violation in the microwave background’s polarisation is a search for exactly that residue.

The other survivor is timing. A dynamo takes a calculable number of e-folding times to saturate, and the e-folding time depends on the galaxy’s rotation rather than on the seed — so the epoch at which galaxies became magnetised is a prediction, and one that observations at high redshift can test. Finding ordered microgauss fields at redshift two, as a handful of measurements suggest, either shortens the e-folding time or lengthens the seed.

That is a considerably better position than “twelve orders of magnitude and no way in”. The magnitude is gone; the geometry, the parity and the schedule are not. Which of the three eventually decides the question is not obvious, and all three are being pursued by different instruments for different reasons. That diversity is a strength: a question approached from one direction is a question with one systematic, and this one has three.

Where this goes next

A slope, not an angle. Above: the polarisation angle of a background source against the square of the observing wavelength, at the five wavelengths a radio survey actually uses. The plane rotates as it passes through magnetised plasma, by an amount proportional to the integral of the electron density times the field along the path — and to λ². The intercept is the angle the source emitted at, which nobody knows, so a measurement at one wavelength contains no information whatever; the slope is the rotation measure, here 42 radians per square metre, and it needs no knowledge of the source at all. Below: the fractional polarisation that survives. A telescope beam covers many lines of sight with slightly different rotation measures, their angles disagree by more at longer wavelengths, and the vector sum collapses — which is why the useful band has a long-wavelength edge that has nothing to do with sensitivity. Divide the rotation measure by the dispersion measure of the same path, 26.8 in the usual units, and the electron density cancels: the mean line-of-sight field is 1.93 µG, obtained without knowing the distance, the density, or where along the path the field was. A slope that needs no source Polarised light passing through magnetised plasma has its plane rotated, by an amount proportional to the square of the wavelength. A single measurement of the angle is worthless, because nobody knows the angle the source emitted at. A measurement of the slope against wavelength squared does not need to know. A slice 1,000 megaparsecs across. 872 galaxies in a wedge 1000 comoving megaparsecs deep, generated as a Thomas process — Poisson centres at 0.00012 per square megaparsec, 13 galaxies each on average, scattered about their centre with a Gaussian of 22 Mpc. That is not a simulation of how structure formed and does not pretend to be; it is the simplest clustered process whose correlation function is known exactly, which is what lets the next figure check a measurement against something rather than against itself. What it does reproduce is the impression: at this scale the distribution is obviously not uniform, there are groups and there are gaps, and the eye finds patterns in it readily — including several that are not there, because the eye finds patterns in a Poisson field too. The question the next two figures ask is the only one that settles it: at what separation does the clustering stop, and is there a scale above which a box of this universe looks like any other box? Homogeneous above a hundred megaparsecs Every cosmological calculation in this field assumes the universe is the same everywhere. Looked at on any scale a person can picture, it plainly is not — it is stars in galaxies in groups in clusters in filaments around voids. The assumption is not a claim about appearance; it is a claim about a statistic, and the statistic has a scale attached. One length, leaving and returning. The comoving Hubble radius c/aH against the scale factor, both logarithmic. Everything to the right of the kink is exact and is the same cosmology as every other figure here: after inflation the comoving Hubble radius grows, as a in the radiation era and as √a in the matter era, then turns over once Λ takes hold. Everything to the left is a schematic — the energy scale of inflation is unmeasured, so neither the height of the plateau nor the 62 e-folds drawn is a number anybody has — but the shape is not negotiable: in any accelerated expansion H is nearly constant, so c/aH falls as 1/a. The consequence is the mechanism. The solid horizontal line is a fixed comoving length of 209 Mpc: it starts inside the Hubble radius, is carried outside during inflation, sits frozen while nothing can act across it, and re-enters at z = 1090, which is last scattering — it is the scale the first acoustic peak is made of. The dashed line above it is the comoving size of the whole observable universe, 14148 Mpc, and the figure's quiet second finding is that it is still outside the Hubble radius: the very largest angular scales in the microwave background have never re-entered, which is why they show the primordial spectrum with no acoustic processing on it at all. One crossing does two jobs: it makes the sky uniform, because everything now visible was once in causal contact, and it makes it not quite uniform, because a quantum fluctuation stretched beyond the horizon has nothing left that can smooth it out. Two coincidences with one mechanism Opposite sides of the microwave sky were never in causal contact and have the same temperature to one part in a hundred thousand. The total density sits on the knife edge of flatness, which is an unstable equilibrium. Two fine-tunings of quite different kinds, and one epoch of accelerated expansion removes both.

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Biermann batteryBlazarDynamoFlux freezingInflationMagnetogenesisMicrowave backgroundPair cascadePhase transitionPrimordial fieldsVoids