A field the galaxies cannot spread far enough

The argument for a magnetic field older than the galaxies has two halves, and only one of them is about the sky. The first half is the observation: blazars that ought to be surrounded by a faint gigaelectronvolt glow, made by the pairs their teraelectronvolt light creates in intergalactic space, are not, and a field in the voids would explain the absence. The second half is an exclusion: nothing that galaxies have done in the thirteen billion years since they formed could have put such a field where it is needed. If the second half fails, the field could be young, blown out of galaxies by their winds, and nothing about the first instant of the universe would follow.

A field made at a phase transition has to survive three hundred thousand years of turbulence to get there, and whether it does depends on how twisted it was. A field from galaxies has a much shorter journey and a much stronger start. Galaxies are magnetised to microgauss levels, their winds carry gas and field out into the intergalactic medium, and the metals found far from any galaxy in the absorption lines of quasar spectra show that the winds reach a long way. The question this essay asks is whether they reach far enough — and the answer turns on what “enough” means for a halo.

A halo counts volume, not mass #

A teraelectronvolt photon from a blazar travels until it meets a photon of the extragalactic background light with enough energy to make a pair with it. That background fills space almost uniformly — it is the accumulated starlight of the whole universe, and on megaparsec scales it does not care whether it is inside a filament or a void — so the place where a photon stops is set by its mean free path, tens to hundreds of megaparsecs, and by chance. It does not care where the matter is either. Pairs are made in proportion to path length, which on average is to say in proportion to volume.

That is the first thing the sightline shows, and it is the thing that makes the galactic explanation hard. The density along the path varies by a factor of a hundred between the knots and the emptiest stretches, and the galaxies, along with everything they could have magnetised, sit in the knots. The pairs ignore the knots. Of sixty pairs made at random along three hundred megaparsecs, four land inside the bubbles the galaxies have blown, and the other fifty-six land in space no galaxy has touched.

The cosmic web makes this worse than a uniform distribution of galaxies would. Most of the universe’s volume is in voids — regions with a fifth to a half of the mean density and expanding faster than the average — and most of its galaxies are in the walls, filaments and nodes between them, which together take a small share of the volume. A teraelectronvolt photon crossing a gigaparsec spends most of its path in voids, and its pairs are made mostly there. A field that is where the galaxies are is a field that is not where the pairs are.

A halo dimmed only by the share of space the field fills #

The second figure turns the sightline into arithmetic. Suppose the field inside the magnetised regions is strong enough to turn every pair it meets out of the beam completely, so that those pairs contribute nothing to the halo. The pairs made outside those regions are untouched. Their halo forms as if no field existed anywhere.

The relation is a straight line, and that is the whole difficulty. A field filling a fifth of the volume removes a fifth of the halo, no more, however strong it is inside that fifth. To make the halo disappear to within the searches’ sensitivity, the field has to fill most of the volume. Simulations of cascades through modelled cosmic webs have made this precise: the published halo limits require a field above about $10^{-16}$ gauss in at least sixty per cent of the volume crossed, and a field confined to the denser regions fails however strong it is made.

This is a different kind of constraint from the one usually quoted. The lower limit on the void field — “at least $10^{-16}$ gauss” — sounds like a statement about strength, and much of the literature on galactic outflows has answered it as one, by asking whether an outflow’s field stays above $10^{-16}$ gauss once it is diluted. That question has an easy answer, which comes later. The constraint that bites is the other one hiding inside the same limit: a minimum share of space.

Most of space is emptier than average #

How much of the volume is anywhere near a galaxy? The answer depends on how lumpy the matter is, and a convenient description is a lognormal distribution — one in which the logarithm of the density is spread like a bell curve — which fits the density of matter smoothed over a few megaparsecs well enough for this purpose.

The asymmetry is the figure’s point. A lognormal distribution has a long tail to high densities, and the dense knots pull the mean up, so the typical point in space is below the mean. Between a fifth and a third of the volume is denser than average, depending on how lumpy the field is; the rest is emptier. A field confined to the regions at or above the mean density — roughly, the walls and filaments where galaxies live — could fill at most that third.

To fill sixty per cent of the volume, the field has to reach every region denser than somewhere between a fifth and three-fifths of the mean. Those are the interiors of voids. Regions at a fifth of the mean density are the emptiest parts of the largest voids, tens of megaparsecs from the nearest galaxy of any size, where the galaxies that do exist are rare dwarfs. A galactic field explanation needs the field there, and needs it there in most voids.

How far a wind reaches #

Galactic winds are driven by the energy of supernovae and, in massive galaxies, by the accreting black hole at the centre. A wind that sweeps up the gas around a galaxy behaves, for a while, like a blast wave, and a blast wave’s radius grows as the fifth root of its energy: the energy goes into a shell whose volume grows as the cube of its radius, while its speed falls as the shell slows, and the two combine into a weak dependence.

The numbers come from putting the energy galaxies are known to have into that law. A supernova releases about $10^{51}$ erg, and a stellar population makes about one per hundred solar masses of stars, so star formation releases $10^{49}$ erg per solar mass formed; a tenth of that driving the wind is a common assumption. A dwarf of a hundred million solar masses of stars then drives $10^{56}$ erg, a galaxy like the Milky Way, with thirty billion, three times $10^{58}$, and a massive galaxy whose central black hole once shone as a quasar may have driven $10^{60}$ erg or more through its outflow. The wind is blown for about a billion years near redshift three, when most stars and most quasar activity happened, into gas a few times denser than the mean, and the bubble it leaves is then carried along by the expansion.

The fifth-root law is merciless. A thousand times more energy buys four times the reach. A dwarf’s bubble is under half a megaparsec in comoving radius; a Milky Way’s a little over one; a quasar host’s two and a half. The surroundings matter less than the energy, but they matter in the same direction: a wind blown into a dense filament stalls sooner than one blown into empty space, and the galaxies with the most energy are the ones in the densest surroundings.

The volume the winds fill #

With radii and numbers, filling fractions follow. If galaxies were scattered at random through space with the densities each population has — a tenth of a dwarf per cubic megaparsec, a hundredth of a Milky Way, a thousandth of a quasar host — the fraction of the volume their bubbles cover would be set by the number of bubbles per unit volume times the volume of each.

The dwarfs are numerous and weak, and their bubbles are small enough that a tenth of a dwarf per cubic megaparsec fills a few per cent of space. The Milky Way analogues fill more, and the quasar hosts, rare but energetic, fill about as much again. With a tenth of the available energy driving the winds, the three populations together fill about fifteen per cent of the volume. Putting every erg of every supernova and every quasar into the wind — which no galaxy does, since most of a supernova’s energy is radiated away within the galaxy — raises that to under half.

And the figure is an overestimate in the most important way. It scatters galaxies at random. Real galaxies are strongly clustered, packed into the filaments and nodes of the web, so their bubbles overlap one another instead of spreading into the voids. Overlapping bubbles fill less volume than the same bubbles placed apart, and the volume they fail to fill is precisely the empty volume where the pairs are made. Cosmological simulations that follow magnetised winds through a realistic web find exactly this: the fields from galaxies fill a few to perhaps twenty per cent of the volume at strengths above $10^{-16}$ gauss, concentrated in the filaments, and leave the void interiors unmagnetised.

What the metals already say #

There is a direct check on how far galactic winds have reached, and it does not involve magnetic fields at all. Winds carry metals — carbon, oxygen, silicon made in the stars of the galaxy that drove them — and metals in intergalactic gas leave absorption lines in the spectra of background quasars. The forest of hydrogen absorption lines that every distant quasar shows comes from gas at every density from a tenth of the mean to a hundred times it, and for each hydrogen line one can look for the matching carbon or oxygen line at the same redshift. Where a wind has been, the gas has metals; where none has been, it has the primordial composition.

The measurements, made by stacking thousands of weak lines too faint to see one at a time, find metals in intergalactic gas down to densities near the mean, at about a thousandth of the Sun’s metallicity, with a large scatter from one line of sight to the next. Below the mean the signal weakens and the scatter grows, and whether the emptiest gas has been enriched at all is not settled. That is what the bubble arithmetic predicts. The winds have reached the filaments and the edges of voids, they have reached them patchily, and the void interiors — which hold most of the volume — are where the metals and the measurements both thin out.

The metals and the field were carried out by the same winds, so the volume the metals fill is an upper bound on the volume the field fills, and a field could fill less if it was dissipated or failed to be carried. A wind that enriched sixty per cent of space with carbon would be evidence that it might have magnetised sixty per cent of space too. Nothing in the absorption-line data suggests that the enriched volume is anywhere near that large.

Strength was never the problem #

The strength of a galactic field is the part of the argument that is easy, and it is worth seeing how easy, because it is so often answered as if it were the hard part.

A magnetic field frozen into a plasma keeps its flux, and if a microgauss field fifty kiloparsecs across is carried out and spread over a sphere of radius $R$, its strength falls as $1/R^2$. At a megaparsec it is a few nanogauss — a field close to what the microwave background allows on that scale — and at ten megaparsecs, far larger than any bubble the energy can blow, it is still $3 \times 10^{-11}$ gauss, a hundred thousand times above the floor. Even allowing for the field being tangled, which raises the floor as the inverse square root of the coherence length, the gap never comes close to closing. The same arithmetic applies to the fields of clusters and groups, which are stronger still, and to the radio lobes that the jets of active galaxies inflate, which carry fields of microgauss strength out to hundreds of kiloparsecs. None of them is short of field. All of them are confined to the densest few per cent of the volume.

So a galaxy’s field, wherever it reaches, is more than strong enough. The halo floor’s strength requirement is not what excludes a galactic origin. The volume requirement is, and the volume requirement is about the cosmic web and the fifth-root law of blast waves, neither of which a stronger or more coherent galactic field can change.

Where the argument could fail #

The exclusion has three weak points, and each corresponds to an assumption the figures make.

The first is that pairs sample volume. That is true on average along any one sightline, but the halo searches stack a handful of bright, hard-spectrum blazars, and a few sightlines could pass through unusually filamentary regions. A sightline that happens to run along a filament for a hundred megaparsecs would see a magnetised path far beyond the average. The stacked analyses try to average this out, and with tens of blazars they mostly do; with the three or four sources that drive the strongest limits they may not.

The second is that the winds stop where the blast-wave law says. Cosmic rays escaping from galaxies can carry energy and, through instabilities they drive in the intergalactic gas, magnetic field further than a thermal wind does, and some proposals generate fields in the intergalactic medium directly — from currents driven by those escaping cosmic rays, or by the ionising radiation of the first galaxies as it swept through the voids. Such fields are not galactic in the sense of having been carried out of galaxies, and they could in principle fill the volume. They are usually weak, $10^{-20}$ to $10^{-18}$ gauss, below the floor, but the estimates are uncertain by orders of magnitude.

The third is the halo itself. If the pair beam’s energy is taken by the plasma before the pairs scatter anything, the halo is absent whatever the field, and the volume requirement disappears along with the strength requirement. That reading needs no field at all, primordial or galactic.

Two measurements that would separate them #

A field blown out of galaxies and a field left from the early universe make different predictions for where the field is, and in principle the gamma-ray sky can tell them apart.

A galactic field makes the halo suppression depend on the sightline. Blazars whose light crosses a dense filament nearby should show weaker halos than blazars whose light crosses mostly voids, and the halo constraint should correlate with the large-scale structure along each line of sight. A primordial field fills the voids too, and suppresses every halo alike. With the galaxy surveys now mapping the web out to the distances of the relevant blazars, the correlation is testable once enough sources have measured halo limits; current samples are too small.

The other route is through the echo of a flare, whose delay measures the field in the region where the pairs from that flare were made. Echoes from blazars at different distances, or along different sightlines, would sample the field in different places, and a field present in some regions and absent in others would show up as echoes from some flares and not from others with the same brightness. That needs bright flares and an instrument watching for the echo, neither of which can be scheduled.

Still open: what fills the voids #

The figures say that galaxies cannot put a field into most of the volume. Their winds are strong enough and their fields more than strong enough, but the fifth-root law limits the reach of a blast wave and the cosmic web confines the galaxies, so the winds fill a quarter of space at best and the voids stay empty. A halo dimmed to a few tenths of its expected strength needs a field in most of the voids.

That leaves three candidates. A field made at the phase transitions of the first second, which needs a twist to survive the electroweak era and needs physics beyond the standard model at the quark–hadron one. A field made in the voids themselves by the radiation or the cosmic rays of the first galaxies, which is volume-filling but probably too weak. Or no field at all, and a plasma that takes the beam’s energy before the halo can form. The volume argument removes the galaxies’ winds from the list; it does not decide among what remains. What would decide is a measurement made inside a void rather than averaged along a sightline — and the only probe that reaches inside a void is a pair cascade, which is where the argument began.