A void heated from the inside

The only measurement of a magnetic field in the emptiest space between galaxies is a lower limit read from light that did not arrive. Teraelectronvolt gamma rays from distant blazars make electron–positron pairs on the extragalactic background light that the same gamma rays are used to weigh, the pairs should scatter the microwave background up to gigaelectronvolts and fill a halo around each blazar, and the halos are missing. A field of about $10^{-16}$ gauss, bending the pairs out of the beam, would explain the absence. So would a different fate for the pairs: losing their energy, before they scatter anything, to the tenuous plasma they are travelling through.

That alternative was set aside in the essay on the missing echo with the remark that it would heat the voids measurably. This essay takes the remark seriously, because a heated void is not a failure to measure the field — it is a different universe, with its own signature, and the signature is in the gas that fills most of the volume of the cosmos and holds most of its ordinary matter.

A beam in a plasma #

A blazar’s pair beam is a stream of relativistic electrons and positrons, all moving in nearly the same direction, through intergalactic gas that is fully ionised and extraordinarily thin — a few protons per cubic metre, a millionth of the density of the best laboratory vacuum. A beam moving through a plasma is a source of free energy: if the plasma’s own oscillations can be made to grow by taking energy from the beam, the beam slows and the plasma warms. The question is how fast that happens compared with the competing loss, inverse-Compton scattering of the microwave background, which takes about a million years and a hundred kiloparsecs for these pairs.

The linear theory says the instabilities grow fast — in hours rather than millions of years — because the beam, though dilute, is extremely energetic and narrowly collimated. Broderick, Chang and Pfrommer argued in 2012 that the growth would drain the beam long before the pairs could scatter anything, so that most of the energy blazars emit above a teraelectronvolt goes into heating the intergalactic gas. The argument depends on how the instabilities saturate, which is nonlinear plasma physics in a regime no laboratory reaches: the beam is a million times less dense than a laboratory plasma’s tenuous end, and the region it crosses is megaparsecs long.

Enough energy to matter #

The idea is worth taking seriously only if the beams carry enough energy, and the arithmetic is short. Raising the temperature of ionised intergalactic gas by ten thousand kelvin takes about three electronvolts per baryon, counting the electrons that share the heat. The light all the galaxies and active nuclei have ever emitted, now spread through the universe as the extragalactic background, amounts to some tens of thousands of electronvolts per baryon. The blazars’ output above a teraelectronvolt is a small fraction of the active nuclei’s light — a tenth of a per cent or so — but a tenth of a per cent of tens of thousands is tens of electronvolts, ten times what is needed. Most of the intergalactic gas has never received any energy except from the ultraviolet background that keeps it ionised, at a few electronvolts per baryon; a second source of comparable size, delivered differently, would not be a small correction.

Heat delivered per volume, not per particle #

The consequence that makes the alternative testable is geometric. The beams from all the blazars in the sky criss-cross intergalactic space almost uniformly, so the heating rate per unit volume is nearly the same in a void as in a filament. Per particle it is not: a void has a tenth of the mean density, so each of its protons and electrons receives ten times the share of heat. Photoheating by the ultraviolet background is the opposite — it is delivered per atom, and the denser gas, which also cools less effectively by expansion, is hotter. The two together make the temperature

$$T(\Delta) = T_0\,\Delta^{\gamma - 1} + T_b\,\Delta^{-1},$$

with $\Delta$ the density relative to the mean, $T_0 \approx 12{,}000$ K and $\gamma - 1 \approx 0.6$ from photoheating, and $T_b$ the blazar heating’s increment at mean density. Below the density where the two terms’ slopes balance the relation turns over: the emptiest gas is the hottest.

The index γ is what the forest measurements actually quote, and the figure shows how sensitive it is in the voids. A blazar heating of only a thousand kelvin at mean density — less than a tenth of the photoheating — is enough to make γ fall to one in gas at a third of the mean, and a few thousand kelvin makes it fall well below. The heating proposed in the original calculations was several thousand to ten thousand kelvin by a redshift of two, which would invert the relation in all the underdense gas.

What the forest would show #

The intergalactic gas is seen in the Lyman-α forest: the thicket of absorption lines in a distant quasar’s spectrum, each made by neutral hydrogen at a different redshift along the line of sight, and the depth of each set by the density and temperature of the gas. The forest is where the reionised universe’s gas is studied, and its temperature has been measured from it for twenty years — from the widths of the narrowest lines, which are set by thermal motions, and from the distribution of transmitted flux.

The visible effect is not where the heat is. Hotter gas recombines more slowly, so it holds less neutral hydrogen and absorbs less, but the voids already transmit nearly all the light, and making them a little more transparent changes little that can be measured. The largest change in transmission is near mean density, where absorption is partial and most sensitive to temperature. The inverted relation’s fingerprint is therefore a modest brightening spread through the forest, together with a change in the shape of the distribution of transmitted flux at its bright end — exactly the statistic that is hardest to measure, because it depends on how well the quasar’s unabsorbed continuum is known.

Some analyses of that statistic in the 2000s found the flux distribution easier to fit with an inverted relation at redshifts of two to three, and blazar heating was proposed partly to explain them. Later analyses with better continuum modelling and simulations found the inversion was not required, and the measured γ in the forest is now generally close to the photoheating value with large uncertainties at the lowest densities. The data neither require the heating nor exclude it at the level the original calculations proposed.

How a temperature is read from absorption lines #

The forest’s temperature is measured from shapes, and each method weighs the gas differently. The narrowest absorption lines are as narrow as the thermal motion of the hydrogen allows, so the lower edge of the distribution of line widths gives a temperature — mostly for gas a little above mean density, which makes lines deep enough to fit. The curvature of the transmitted flux, a measure of how smooth the absorption is on small scales, responds to temperature through the same broadening and samples similar densities. The distribution of transmitted flux itself, and especially its bright end, is the only statistic that reaches the voids, and it is the one most entangled with the quasar’s continuum and with the forest’s own normalisation.

So the measurement is strongest where the heating is weakest, and weakest where the heating is strongest. The temperature at mean density is now known to about ten per cent at redshifts from two to five; the slope γ is known to perhaps twenty per cent; the temperature of gas at a third of the mean density, where an inversion would show most clearly, is barely constrained. That is the observational reason the hypothesis has survived for a decade: it predicts its largest effect in the part of the forest that is hardest to read.

A competing heater at the same time #

The blazars are not the only thing that heated the intergalactic gas between redshifts two and four. The ultraviolet background’s hardest photons, from quasars, ionised the last of the helium’s second electron around redshift three, and that event — helium’s reionisation — deposited heat as the ionisation front passed, raising the gas temperature by several thousand kelvin and, because the hardest photons travel furthest and heat the low-density gas they reach, flattening the temperature–density relation towards isothermal. Measurements of the temperature at mean density show a peak near redshift three, the signature of helium reionisation.

That is a confusion the forest data have to break. Helium reionisation flattens γ towards one; blazar heating pushes it below one. Both are strongest at redshifts two to three. The difference is in the details: helium reionisation’s heating is patchy, following the ionisation fronts from individual quasars, and it ends when helium is fully ionised, while blazar heating is smooth and continues after. A relation that stays flat or inverted at redshift two, after helium reionisation is complete and the gas has had time to cool back to the photoheating slope, would favour the blazars; one that steepens again would not.

A heating with a history #

Blazars were not always there to heat anything, and their numbers peaked when the universe was a few billion years old.

The heating rises with the blazar population, peaks a little after it, and then declines as expansion cools the gas faster than the dwindling blazars can heat it. That gives the hypothesis a distinctive time signature. At redshifts above three or four, before the population rose, there should be no inversion at all; at redshifts between one and three, where the forest is observed from the ground, the effect should be strongest; at low redshift, where the forest is seen only from space in the ultraviolet, it should be fading. A heated-void signal at redshift four would point to something other than blazars, and an absence at redshift two at the predicted level would rule out the original strong version.

The heating also has dynamical effects. Gas in voids that is suddenly hotter has more pressure, so it resists falling into the dwarf galaxies forming there; the smallest galaxies in voids would form later and with less gas than in a universe without the heating. Simulations that include it find the dwarf galaxy population at low mass reduced, by an amount that is again at the edge of what surveys can detect.

What the plasma physics has said since #

The decisive question is not astronomical but plasma-physical: do the instabilities really drain the beam, and how much of its energy goes into heat rather than into scattering?

Since 2012 the answer has moved towards “partly”. Miniati and Elyiv argued in 2013 that nonlinear damping of the plasma waves — the waves scattering off the plasma’s own thermal particles — would stop their growth well before they drained the beam. Particle-in-cell simulations, which follow individual charged particles in a scaled-down version of the beam and plasma, found that the beam’s energy is not efficiently converted to heat: the instability broadens the beam’s spread of directions and saturates, having transferred only a modest fraction of the energy, after which inverse-Compton scattering resumes. The inhomogeneity of real intergalactic gas, with its density gradients along the beam’s path, detunes the resonance the instability needs and suppresses it further.

The current view is therefore that the heating, if it happens at all, is weaker than originally proposed — perhaps a tenth of the beam’s energy rather than most of it — and that the cascades are only partly suppressed. That reopens both sides. A partly suppressed cascade still produces some halo, and the absence of halos then implies a field, perhaps somewhat weaker than the bound drawn from the three lengths:

The two explanations are not exclusive. A field near the bound and a modest heating could both be present, and the measurements that would detect each — the delayed gigaelectronvolt echo of a bright teraelectronvolt flare for the field, the forest’s temperature at low density for the heating — are independent. That independence is what makes the problem tractable: the missing halos are one observation with two candidate causes, and each cause has a second prediction that the other does not share.

The measurements coming #

Two kinds of data will sharpen the test in the next few years. Spectroscopic surveys are measuring the forest towards hundreds of thousands of quasars, enough to measure the flux distribution’s bright end statistically even where each spectrum is noisy, and enough to divide the data finely by redshift so that the heating’s rise and fall can be followed. And high-resolution spectra of the brightest quasars, from the largest telescopes, resolve the narrowest lines and measure the temperature directly at densities closer to the mean. Neither alone reaches the emptiest gas, but together they constrain the slope across the range where an inversion would begin.

The intergalactic gas also records its temperature in a quite different place. Before the first stars it was colder than the microwave background and absorbed at 21 centimetres; after reionisation the 21-centimetre signal comes only from neutral hydrogen in galaxies. That signal does not see the heated voids, which are ionised, but the radio surveys that map it also constrain the ultraviolet background that sets the photoheating floor the blazars would be added to, and so the size of the inversion any given heating would produce.

What a void is, for a beam #

The heating’s distinctive prediction depends on how empty the voids are and how uniformly the beams cross them. Voids are emptier and expanding faster than the universe around them, occupying most of the volume at densities of a tenth to a third of the mean, and they are not empty of structure — they hold dwarf halos in nearly the numbers the cosmic mean would predict, most too small to have kept their gas. The pair beams from blazars travel tens to hundreds of megaparsecs before their energy is lost, longer than a typical void is wide, so every void is crossed by beams from many blazars at once, and the heating within it is smooth. That uniformity is what makes the per-particle heating scale as one over the density, and it is what distinguishes blazar heating from any heating by the galaxies at the voids’ edges, which falls off into their interiors.

What the scaling leaves out #

The temperature–density relation is drawn as a sum of a photoheating power law and a heating term that goes as one over density. Real gas is not at one density for long: it falls into filaments or empties out of voids, and its temperature history depends on its path. The heating is taken as uniform per volume, where real beams are concentrated near blazars and attenuated with distance by the pair production itself, so voids far from any blazar receive less. The forest transmission uses photoionisation equilibrium and a fixed normalisation of the optical depth, which is itself fitted to the forest and would be refitted if the heating were included. Each changes the numbers; none changes the qualitative prediction that heating per volume inverts the relation at low density and that the inversion follows the blazars’ history.

Still open: whether the plasma takes the beam’s energy #

The heated-void hypothesis lives or dies on plasma physics that cannot be tested in a laboratory and is only partly captured by simulations that have to scale the beam’s parameters by orders of magnitude to be computable. Its astronomical tests are subtle — a modest change in the bright end of the forest’s flux distribution, a slight suppression of dwarf galaxies in voids — and each is at the edge of current data. The more direct route is through the field: if the gigaelectronvolt echo of a bright flare is seen, with the delay a weak field predicts, the cascades are not being drained and the voids are not being heated. If no echo is seen down to the weakest fields the bound allows, the heating becomes the leading explanation by elimination, and the oldest field in the universe will have been an inference from light that a plasma absorbed.