Half the ordinary matter was missing, and a millisecond found it

The ordinary matter in the universe is the part everything else in this collection is made of, and its total is one of the best-measured numbers in the subject. Deuterium read off a quasar spectrum gives it; the relative heights of the first two acoustic peaks give it; the two agree to four parts in a thousand. There are $\Omega_{\rm b} = 0.049$ of the critical density in baryons and no serious doubt about it.

Where they are is a separate question, and it is answered by adding up surveys rather than by any single measurement. Do that carefully and the total comes out about half.

That gap is not a small discrepancy in a hard measurement. It is a statement that the majority of the matter that people are made of had never been observed, by any instrument, in any band.

Counting what there is #

The census is a sum over reservoirs and each entry is a different subject with its own systematics.

Stars are the smallest and the easiest. Integrating the luminosity function over all galaxies and multiplying by a mass-to-light ratio gives the stellar mass density, and it comes to about seven per cent of the baryons. That number is worth pausing on: the fraction of the universe made of anything that has ever shone is a fourteenth of five per cent, which is a third of one per cent of everything.

Cold gas in galaxies — atomic hydrogen seen in the twenty-one centimetre line, molecular gas inferred from carbon monoxide — is smaller still, under two per cent of the baryons.

Hot gas in clusters is the one reservoir that is easy to see, because it is at $10^{7}$ kelvin and radiates X-rays in proportion to the square of its density. It holds about four per cent of the baryons, and clusters are where the baryon fraction is closest to the cosmic value, which is itself an important check.

The Lyman-α forest is the largest entry in the early census. Every quasar spectrum shows hundreds of absorption lines from diffuse hydrogen clouds along the sight line, and the total column implied is large — about thirty per cent of the baryons at low redshift.

Add those and the answer is a little over forty per cent. At redshift two or three the same accounting closes almost completely, because at those epochs nearly all the baryons are in the forest and the forest is easy to measure. The deficit is a low-redshift problem: something happened to the gas between then and now that made it harder to see.

Why the gas became invisible #

What happened is that the universe got hotter in the places where most of the gas is.

Structure formation is violent. As matter falls into the filaments of the cosmic web it shocks, and shocking converts orbital energy into heat. The characteristic temperature of gas falling into a filament is set by the depth of the potential well, and for a filament rather than a cluster that comes out at $10^{5}$ to $10^{7}$ kelvin.

That range is the worst possible one for detection, and it is worth being precise about why.

Below $10^{4}$ kelvin hydrogen is neutral and absorbs Lyman-α, which is how the forest is seen. Above $10^{7}$ it is hot and dense enough to radiate X-ray bremsstrahlung, which is how cluster gas is seen. Between those, the gas is fully ionised — so it has almost no neutral hydrogen to absorb with — and far too diffuse to radiate detectably. It emits and absorbs almost nothing.

The phase has a name, the warm–hot intergalactic medium, and it was predicted by simulations in the late 1990s before there was any way to observe it. The simulations said that by the present day something like forty per cent of the baryons should have been shock-heated into it. That is almost exactly the size of the deficit, which was suggestive and was not evidence.

What was tried, and why it took twenty years #

Three routes were attempted and each returned a partial answer.

Absorption by highly ionised oxygen. Gas at a million kelvin retains a trace of five- and six-times-ionised oxygen, whose resonance lines fall in the far ultraviolet and the soft X-ray. Looking for those lines against bright background quasars is the direct approach, and it works — the ultraviolet lines are detected routinely and account for a further ten to twenty per cent of the baryons. The X-ray lines, which probe the hotter part of the phase, sat at the edge of detectability for two decades, with claimed detections that did not reproduce.

Stacking the Sunyaev–Zel’dovich signal. Hot electrons scatter microwave background photons and shift their energies, and the resulting decrement does not fade with distance. Stacking the signal around large numbers of galaxy pairs reveals gas in the filaments between them, at a level consistent with a substantial baryon reservoir. It measures a pressure rather than a density, so converting it needs a temperature.

X-ray emission from stacked filaments, which suffers from the same problem in reverse: the emission goes as the square of the density, so it is dominated by the densest and least representative parts.

All three are statistical detections of a diffuse medium against a bright background, and all three required assumptions about the gas’s temperature or clumping to turn into a baryon fraction. None of them was decisive on its own.

A delay that counts electrons #

The measurement that settled it uses a phenomenon nobody had connected to the problem, because the phenomenon was not known to exist.

A radio pulse travelling through ionised gas is slowed, and it is slowed more at lower frequencies. The delay between two frequencies is proportional to the dispersion measure — the integral of the electron density along the path — and it is a standard tool in pulsar astronomy, where it gives distances within the Galaxy.

Fast radio bursts are millisecond pulses of extragalactic origin, dispersed the way a pulsar’s signal is by the interstellar medium, discovered in 2007. Their dispersion measures are enormous, far above anything the Galaxy can supply, and the excess is the intergalactic column. A burst whose host galaxy can be identified has a redshift as well, and the pair of numbers is a point on the relation in the first figure.

The relation itself involves no astrophysics at all. The mean electron density at any redshift follows from the baryon density, the fraction of baryons in diffuse ionised gas, and the number of electrons per baryon — which is 0.875, because hydrogen contributes one electron per nucleon and helium two per four. The path length follows from the expansion history. So:

$$\langle \mathrm{DM}\rangle(z) = \frac{3cH_0\Omega_{\rm b}f_{\rm IGM}\chi_e}{8\pi G m_p}\int_0^z \frac{(1+z')\,dz'}{E(z')}$$

and $f_{\rm IGM}$ is the only unknown.

The measurement is decisive because the thing that causes the delay is free electrons, and the gas is missing precisely because it is fully ionised. Every other technique was defeated by the ionisation; this one requires it.

The first well-localised bursts, published in 2020, gave a fraction consistent with all of the baryons being accounted for, with an uncertainty of a few tens of per cent. The census closed.

What a burst has to be, for it to count #

The chain from a detected pulse to a point on the relation has one step that was the bottleneck for a decade, and it is worth being explicit about because it explains the shape of the field.

A burst is detected as a dispersed sweep across a radio band, lasting a few milliseconds. A single-dish telescope records it with a beam a fraction of a degree across, which contains thousands of galaxies — so the burst has a dispersion measure and no host. Without a host there is no redshift, and without a redshift the point has no abscissa.

Localisation is therefore the measurement, and it requires an interferometer: an array whose baselines resolve the position to an arcsecond or better, operating with enough bandwidth and enough time resolution to catch a millisecond event, and buffering its raw data so that a detection can be reconstructed after the fact. That combination did not exist when the first bursts were found, and building it is what the last decade of the subject has been.

The payoff is that each localised burst supplies a complete data point with no model in it beyond the ionisation fraction of helium. A handful of them constrain the baryon fraction to a few tens of per cent, because the relation is a straight line through the origin whose slope is the answer.

There is a further step that would sharpen it, and it is now being taken. A burst from a repeating source can be localised at leisure and its host studied in detail, which pins down the host’s own contribution to the dispersion — the one term that cannot be measured for a single event. Repeaters are a minority of sources and it is not settled whether they are a distinct population or the same objects seen more often.

The cluster check, and what it was used for first #

There is an older and completely independent use of the baryon census, and it was one of the first strong arguments that the matter density is low.

A cluster of galaxies is deep enough that nothing escapes it. Gas heated by any process inside it is still bound, so a cluster’s ratio of baryons to total mass should be the universal one — and both quantities are measurable, the gas from its X-ray emission and the total from the gas’s own temperature, which is a cluster weighed by the motions inside it or from the lensing of galaxies behind it.

The observed ratio is about 0.15. Set that equal to $\Omega_{\rm b}/\Omega_{\rm m}$, put in the nucleosynthesis baryon density, and $\Omega_{\rm m}$ comes out near 0.3.

That argument was made in the early 1990s, when the expected answer was 1, and it was resisted on the grounds that clusters might be unrepresentative. It was right. It is also the reason the cluster entry in the census is the one with the fewest doubts attached: the measurement is a ratio within a single object, and most of the systematics in a mass and a gas mass cancel between them.

What the argument cannot do is close the cosmic census, because clusters contain only a few per cent of the matter in the universe. A representative sample and a well-measured one are different things, and in this subject they are usually in tension.

What the scatter says, and it is the next measurement #

The relation in the figures is a mean. Any individual sight line crosses a particular arrangement of filaments, voids and galaxy haloes, so its dispersion measure scatters about the mean by a large amount — tens of per cent at low redshift, falling as the path lengthens and averages over more structure.

That scatter is usually treated as noise on the baryon measurement. It is also a measurement in its own right, and a more interesting one.

How much a sight line’s column varies depends on how the gas is distributed: a universe where the baryons sit in dense clumps produces a skewed distribution with a long tail, and one where they are spread smoothly produces a narrow symmetric one. The shape of the distribution of dispersion measures at fixed redshift is therefore a direct probe of how galaxy feedback has redistributed gas — how far winds have pushed baryons out of haloes and into the intergalactic medium.

That is the same question the small-scale power spectrum is limited by, arrived at from a completely different direction, and it is the reason surveys expecting thousands of localised bursts are being built.

The halo that keeps most of what a galaxy was given #

The census closes cosmically and it does so partly by locating gas that a galaxy once had and no longer contains, which is worth a section because it is where the physics is.

Ultraviolet absorption spectroscopy against background quasars whose sight lines pass near foreground galaxies shows that those galaxies are surrounded by enormous reservoirs of gas — hundreds of kiloparsecs across, at $10^{4}$ to $10^{6}$ kelvin, detected in the lines of ionised silicon, carbon and oxygen. The mass implied is comparable with, and often larger than, everything in the galaxy’s disc.

That material is the circumgalactic medium, and its existence changes what a galaxy is. A spiral galaxy is not a disc of stars and gas in a halo of dark matter; it is a disc inside a far larger atmosphere of warm gas, most of which is not doing anything and some of which is falling in.

How it got there is the unresolved part. Some of it never fell in — gas accreting onto a halo shocks at the virial radius and can sit there for a long time. Some was expelled: supernovae and the winds of massive stars drive material out of a disc at hundreds of kilometres a second, and an active nucleus can drive it out at thousands.

The distinction matters because the two make different predictions about composition. Gas that never entered the galaxy should be near-primordial; gas that was expelled carries the metals that stars made. Absorption-line measurements find metals throughout the circumgalactic medium out to large radii, which says that a substantial fraction of the material a galaxy was born with has been through it at least once and is now outside it.

A galaxy’s baryons are largely not in the galaxy, and that is the same statement as the cosmic one at a scale where it can be attributed to a mechanism.

Where the argument stops #

The fraction is not the whole census. What the dispersion measure counts is free electrons along a sight line, which includes the diffuse intergalactic gas, the circumgalactic gas around any galaxy the line passes near, and the host galaxy’s own contribution. Separating those requires either a model of the halo gas or a large sample in which the near-halo contribution can be averaged.

The host’s contribution is the dominant uncertainty for a single burst. A burst in a dense star-forming region of its host may carry hundreds of dispersion units from its immediate surroundings, and there is no way to measure that for an individual event. The statistical approach — fitting the population with a distribution of host contributions — is what the constraint actually rests on.

And the relation assumes the gas is ionised all the way back. That is safe below redshift six and not above it: before reionisation the intergalactic medium is neutral and contributes almost nothing to the dispersion. A burst from beyond that epoch would carry a column that stops growing, which is a measurement of when reionisation happened — and is a different subject from this one.

The shape of the argument #

Three features of this episode are worth extracting, because each recurs.

A total known independently of its parts is what makes a deficit meaningful. Nucleosynthesis and the acoustic peaks fix the number of baryons without locating a single one, so the census has something to fall short of. Without that, forty-two per cent would just have been the answer.

A phase of matter can be invisible without being exotic. The missing baryons were ordinary hydrogen and helium at an unremarkable density. What hid them was a temperature that sat between two detection windows, and that is a property of the instruments as much as of the gas.

And the measurement that worked used the property that caused the problem. The gas was undetectable because it was ionised; the technique that found it counts free electrons. That inversion — the obstacle becoming the observable — is worth looking for whenever a search has failed on the same grounds for a long time.

Still open: the same accounting inside a galaxy #

The cosmic census now closes. The one for an individual galaxy does not.

A galaxy’s halo should contain baryons in the cosmic proportion — about a sixth of its total mass. Counting the stars and the cold gas in a galaxy like the Milky Way gives a fraction well under half of that, and the deficit grows for smaller galaxies, reaching a factor of a hundred for dwarfs.

Some of the missing material is in the hot circumgalactic medium, detected in absorption against background quasars and in emission at the very lowest surface brightnesses. How much is there, how far out it extends, and how much has been expelled from the halo entirely are all unsettled, and the answers matter: they are the difference between feedback that redistributes gas within a halo and feedback that removes it.

That question is now the one the dispersion-measure scatter is aimed at, and it is the same measurement as the cosmic one with the averaging removed. What made the cosmic answer easy — that a long sight line crosses everything — is exactly what makes the galactic one hard.