A shadow cast on the microwave background

Everything known about the end of reionisation comes from light that the neutral hydrogen took away. A quasar’s spectrum loses everything blueward of Lyman-α once the neutral fraction exceeds about one part in ten thousand, which makes the method exquisitely sensitive at the very end of reionisation and blind to the rest of it: by the time the gas is a few per cent neutral, the trough is saturated and says nothing more. The patchy end of the process, when the ionised bubbles met, was reconstructed that way. The half-billion years before it, when the first stars and galaxies formed in a universe of neutral gas, is invisible to it.

There is one kind of light that the neutral gas makes rather than removes. A hydrogen atom in its ground state has two hyperfine levels, with the electron’s and proton’s spins parallel or opposed, and a transition between them emits or absorbs a photon of 21 centimetres wavelength. Neutral hydrogen between the galaxies, at redshifts of 6 to 30, shifts that line to between 45 and 200 megahertz — the band of FM radio and television — and in principle every neutral atom in the early universe contributes to it. The difficulty is that the signal is not emission in the ordinary sense. It is a difference from the microwave background, and its sign depends on a temperature that the first stars controlled.

A line predicted before it was seen #

The line itself has a history that makes it the natural tool. Van de Hulst predicted in 1944 that the hyperfine transition of hydrogen should be observable from interstellar gas, despite a spontaneous lifetime of about eleven million years per atom, because there is so much hydrogen along any line of sight that even so slow a transition adds up. Ewen and Purcell detected it from the Milky Way in 1951, and within a few years it had mapped the Galaxy’s spiral arms and the rotation of galaxies far beyond their visible stars — the first strong evidence for their dark haloes. It is the one spectral line that neutral hydrogen, the most abundant substance in the universe, emits in its ground state, at a wavelength long enough to pass through dust and gas unaffected.

The same slowness that made the line hard to predict makes it useful in the early universe. A transition that rare never becomes optically thick in the intergalactic gas: the neutral hydrogen between redshift 6 and 30 is transparent in its own 21-centimetre line, so every atom along the line of sight contributes to the signal and none hides the ones behind it, unlike the Lyman-α troughs, which saturate at a neutral fraction of one in ten thousand.

A temperature that sets a sign #

The 21-centimetre line is seen against a background — the microwave background, which fills the same sky at every radio frequency. Whether the hydrogen adds to that background or subtracts from it depends on the ratio of the two hyperfine levels’ populations, and that ratio is described by a temperature: the spin temperature $T_S$. If the spin temperature is higher than the background’s, the gas emits more 21-cm photons than it absorbs and appears bright; if lower, it absorbs, and appears as a shadow. The brightness temperature relative to the background is

$$\delta T_b \approx 27\,x_{\rm HI}\left(1 - \frac{T_{\rm CMB}}{T_S}\right)\sqrt{\frac{1+z}{10}}\ \ {\rm mK},$$

with small factors for the cosmological densities, where $x_{\rm HI}$ is the fraction of hydrogen still neutral. The prefactor is the whole signal available — tens of millikelvin — and the bracket decides its sign and size.

What sets the spin temperature is a competition. The microwave background itself drives the transition, pulling the spin temperature towards its own. Collisions between atoms pull it towards the gas’s kinetic temperature, but in the diffuse gas between galaxies after redshift thirty or so collisions are too rare to matter. That leaves the spin temperature equal to the background’s and the signal zero — unless something else couples it to the gas.

A thermometer read against the one temperature that is known #

That something is starlight. When the first stars formed, their ultraviolet photons at the Lyman-α wavelength scattered repeatedly off the neutral hydrogen, and each scattering can flip the hyperfine state. The repeated scattering drives the spin temperature towards the colour temperature of the Lyman-α radiation, which in turn is driven towards the gas’s kinetic temperature. The process is called the Wouthuysen–Field effect, and it means that the moment the first stars switched on, the 21-centimetre line began to report the temperature of the gas.

The gas was cold. After the universe became transparent at recombination — the surface the background actually is — the leftover free electrons kept the gas in thermal contact with the microwave background by Compton scattering, until about redshift 150, when the expansion had diluted them too far. From then on the gas expanded adiabatically. A monatomic gas expanding adiabatically cools as its density to the two-thirds power, which in an expanding universe is as $(1+z)^2$, while the background cools only as $1+z$. By redshift 20 the gas is at about 8 kelvin and the background at 57.

So when the Lyman-α coupling switched on, it pulled the spin temperature below the background’s, and the hydrogen appeared in absorption: a shadow of the neutral gas on the microwave background. Later, the X-rays from the first black holes and binary stars heated the gas above the background, and the signal turned to emission. And then reionisation ionised the gas and the signal vanished. The sky-averaged signal against frequency — the “global signal” — records all three events in order: a trough when the first stars coupled the spin, a rise when X-rays heated the gas, a fall when the neutral gas was used up.

The timing of each is unknown, and the model drawn here puts them at plausible redshifts rather than fitted ones. What is known exactly is the reference: the microwave background is the most perfect blackbody ever measured, so its temperature at every redshift is known without any model at all. A signal measured against it is an absolute thermometer for gas that has never been seen by any other light.

The deepest shadow cooling allows #

The depth of the absorption has a floor, and the floor is set by physics that is not in doubt. The deepest absorption occurs if the spin temperature is fully coupled to the gas, the gas is entirely neutral, and the gas has not been heated at all since it decoupled from the background. Then $T_S$ is the adiabatic temperature and the bracket is as negative as it can be.

At redshift 17 the floor is about −265 millikelvin. Any real model is shallower, because the coupling is never complete when the gas is coldest and some heating has always begun. The model drawn in the first figure reaches −171.

In 2018 an experiment in the Western Australian desert — a single, carefully calibrated antenna measuring the sky’s total radio brightness between 50 and 100 megahertz — reported an absorption trough centred at 78 megahertz, with a depth of 500 millikelvin, flat-bottomed and with sharp sides. The frequency was about where models had put the cosmic dawn. The depth was about twice the floor.

A trough deeper than the floor cannot be made by any adjustment of the first stars or the heating. It needs one of two things. Either the gas was colder than adiabatic cooling allows — about 3 kelvin rather than 6 at that redshift — which requires something to have extracted heat from it; the proposal most discussed was that a small fraction of dark matter carries a tiny electric charge and scattered off the gas, cooling it, since dark matter was colder still. Or the radio background behind the gas was brighter than the microwave background alone — about 88 kelvin at that redshift rather than 50 — which requires an unknown population of early radio sources, and the excess radio background measured at lower frequencies by a balloon experiment has been cited in support. Every explanation offered falls into one of those two classes, because the bracket has only two temperatures in it.

A foreground ten thousand times brighter #

The other possibility is that the trough is not in the sky.

At these frequencies the sky is dominated by synchrotron emission from cosmic-ray electrons spiralling in the Milky Way’s magnetic field, with a spectrum that is a steep power law. Its brightness temperature at 78 megahertz is well over a thousand kelvin at the quietest parts of the sky. The signal sought is a tenth of a kelvin. Measuring one part in ten thousand of a bright background is possible only because the two differ in shape: the foreground is smooth in frequency, a power law with slight curvature, while the signal has a trough tens of megahertz wide. The analysis fits a smooth function to the measured spectrum, subtracts it, and treats the residual as the signal.

That procedure is only as good as the smoothness of everything between the sky and the numbers. The antenna’s response to the sky changes with frequency — its beam widens and narrows, its reflections interfere — and the foreground, multiplied by any ripple in that response, produces structure in the spectrum. A ripple of one part in ten thousand is as large as the signal. The claimed trough’s flat bottom and sharp sides are unlike any model of the cosmic dawn and not unlike what an unmodelled instrumental systematic can produce, and a series of re-analyses showed that the published data can be fitted about as well by a smooth foreground plus a sinusoidal ripple as by a foreground plus a trough.

In 2022 a second experiment, with a different antenna design, floating on lakes in southern India so that the water beneath it was a uniform, well-understood reflector, reported no trough of that depth at that frequency, excluding the claimed profile at high confidence. That does not settle whether the 21-centimetre global signal has been detected; it settles that the one claimed detection has not been confirmed, and that the discovery about dark matter it implied is not required.

Where the signal ends #

The late part of the global signal is fainter and in some ways cleaner. Once X-rays have heated the gas well above the microwave background, the bracket approaches one and stops depending on the temperature at all; the signal is then simply proportional to the fraction of hydrogen that is still neutral.

The emission, about 25 millikelvin, falls away as reionisation proceeds, and the frequency at which it falls dates the middle of the process: 161 megahertz for reionisation half complete at redshift 7.7, 142 for 9, 184 for 6.5. The width of the fall is the duration of reionisation. Those two numbers are exactly what the other probes constrain from different directions — the quasar troughs bound the end, the microwave background’s polarisation bounds the column of free electrons along the line of sight — and an early radio experiment ruled out reionisation histories that were too rapid, by failing to see the step that a sudden reionisation would have made.

The late signal is a step, not a trough, which makes it harder to separate from the foreground: a smooth function can absorb part of a gentle step, and the residual depends on how the smooth function was chosen. It is also lower in amplitude than the early trough. Its advantage is that it depends only on the neutral fraction, not on the uncertain temperature of the gas, so a detection would be a direct measurement of the reionisation history with no astrophysical model in between.

What the global signal leaves out #

The sky average discards most of the information. The 21-centimetre brightness varies from place to place, because the neutral gas is clumpy, the first sources were clustered, and reionisation proceeded through expanding bubbles; mapping those fluctuations — rather than averaging them away — is the goal of large interferometers built for the purpose, which measure the power spectrum of the fluctuations at a range of scales and frequencies. Their foregrounds are the same, but they are separated in a different way, by the fact that foregrounds are smooth in frequency while the signal fluctuates along the line of sight. They have produced upper limits, steadily lowering, but not yet a detection.

The model drawn here also compresses the physics into three smooth steps with chosen centres. Real models follow the formation of the first stars in dark matter haloes of a million solar masses, their ultraviolet and X-ray output, the absorption of X-rays by the gas and the escape of ionising photons from galaxies, and they predict troughs from −50 to −250 millikelvin at frequencies from 50 to 110 megahertz depending on those choices. The first figure’s trough is one plausible member of that family. The floor is not a model; it is the one number every member respects.

The first light, measured by its shadow #

The first stars are expected to have been unlike any seen today. Formed from gas with no elements heavier than helium, which cools inefficiently, they are thought to have been massive — tens to hundreds of solar masses — and therefore brilliant in the ultraviolet and short-lived, exploding within a few million years and seeding the gas around them with the first metals. Whether their mass function was as top-heavy as that argument suggests is not known from any observation, and the timing and depth of the 21-centimetre trough would constrain it: a population of massive stars couples the spin temperature quickly and heats the gas soon after through the X-rays of their remnants.

The claimed detection, whatever its fate, showed what the measurement would mean. If the trough is found at the depth models predict, its frequency dates the formation of the first stars that were bright enough to couple the spin temperature, its width says how quickly they appeared, and its depth measures the temperature of the gas — and hence how much X-ray heating had already happened — at redshifts twenty or more, a third of a billion years after the Big Bang. No telescope can image those first stars individually; the most sensitive infrared telescopes reach galaxies at redshift ten to fourteen. The 21-centimetre signal would push the record back by half the universe’s age at the time, using the combined shadow of all the gas the first stars lit.

The same measurement tests fundamental physics in a way almost nothing else does. The floor assumes only that the gas cooled adiabatically and that the background behind it is the microwave background; a trough deeper than the floor, if it were real and astrophysical, would require either a new way for gas to lose heat or a new source of radio photons, both in an epoch no other observation reaches. That the one claimed trough appears to have been instrumental does not remove the test. It shows how hard it is to apply.

Still open: the trough nobody has confirmed #

The global 21-centimetre signal has not been detected. What exists is one claim at a depth physics does not allow, one independent measurement that does not see it, and a family of models that predict a trough between a fifth and a half of the claimed depth, somewhere between 50 and 110 megahertz. The experiments under way differ from each other deliberately — in antenna design, in site, in how they calibrate their frequency response — because the only defence against a systematic that mimics the signal is a second instrument with different systematics. When two of them agree on a trough, its frequency will date the first starlight and its depth will be the temperature of the dark ages, measured against the one temperature in cosmology that is known exactly. Until then the shadow of the first stars on the microwave background is a prediction with a floor under it, and a claimed measurement twice as deep as the floor.