This article on the “baryon catastrophe” comes from my book Companion to the Cosmos, published nearly 20 years ago, before the discovery of the “accelerating Universe”, which implies the existence of dark energy, aka the cosmological constant. I just thought I’d like to make it clear that cosmologists (at least, some cosmologists) were not surprised by that discovery, which neatly fitted a gap in their description of the cosmos. It came as a surprise to the discoverers, because they were not cosmologists! (And clearly had not read my book.)
The baryon catastrophe is the puzzle that studies of the amount of hot gas in clusters of galaxies suggests that the proportion of baryons to dark matter in the Universe is too great to allow the possibility of there being exactly the right amount of all kinds of matter put together to match the predictions of the simplest versions of inflation and make spacetime flat.
It has become firmly established that most of the matter of the Universe is in some invisible form. But while theorists delight in playing with mathematical models that include such exotica as Cold Dark Matter, Hot Dark Matter, WIMPs and Mixed Dark Matter, the observers have slowly been uncovering an unpalatable truth. Although there is definitely some dark matter in the Universe, there may be less to the Universe than some of these favoured models imply.
The standard model of the hot Big Bang (incorporating the idea of inflation, which invokes a phase of extremely rapid expansion during the first split-second of the existence of the Universe) says that the Universe should contain close to the “critical” amount of matter needed to make spacetime flat and to just prevent it expanding forever. But the theory of how light elements formed in the early Universe (see nucleosynthesis) limits the density of ordinary baryonic matter (protons, neutrons, and the like) to be about one twentieth of this. The residue, the vast majority of the Universe, consists (on the standard picture) of some kind of exotic particle such as axions. These particles have never been seen directly, although their existence is predicted by the standard theories of particle physics. In the favoured cold dark matter (CDM) model of the Universe, the gravitational influence of the dark particles on the bright stuff gives rise to structures first on small scales, then on successively larger ones as the Universe evolves.
The evidence for dark matter comes from observations on a range of scales. Within our own Galaxy, the Milky Way, there is at least as much unseen matter as that in visible stars. But observations of gravitational lensing of stars in the Magellanic Clouds suggest that this particular component of the dark matter may be baryonic, either large planets or faint, low mass stars known as brown dwarfs. There is also evidence from the speed at which stars and gas clouds orbit the outer parts of disk galaxies for more extensive halos of dark matter, but once again these could be baryonic. As far as individual galaxies are concerned, there is actually no need to invoke CDM at all.
There is no reason to suppose, however, that the contents of galaxies are representative of the Universe as a whole. When a protogalaxy first collapsed it would have contained the universal mix of baryonic matter (in the form of a hot, ionised gas) plus dark matter. The dark matter is “cold” in the sense that individual particles move slowly compared with the speed of light, but like the baryonic stuff they have enough energy to produce a pressure which keeps them spread out over a large volume of space. The baryons lose energy by radiating it away electromagnetically, so they cool very quickly; the baryon component of the cloud loses its thermal support and will sink into the centre of the protogalactic halo to form the galaxy that we see today. This leaves the dark matter, which cannot cool (because it does not radiate electromagnetically) spread out over a much larger volume.
To find a more typical mixture of material we must therefore look at larger, more recently formed structures, in which cooling is less efficient. These are clusters of galaxies. A typical rich cluster may contain a thousand galaxies. These are supported against the attractive force of gravity by their random speeds which can be more than a thousand kilometres per second, and are measured from the Doppler effect produced by their motion, which shifts features in their spectra either towards the blue or towards the red (this is independent of the redshift produced by the expansion of the Universe, which has to be subtracted out from these measurements). By balancing the kinetic energy of the galaxies against their gravitational potential energy it is possible to estimate the total mass of the cluster. This was first done by Fritz Zwicky in the 1930s, and led to the then surprising conclusion that the galaxies comprise only a small fraction of the total mass. This was so surprising that for several decades many astronomers simply ignored Zwicky’s findings.
Without the experimental background in particle physics, or the cosmological models which are available today, it would have been natural for those astronomers who did take the observations seriously to identify this missing matter as hot gas. However this was not done, perhaps because the physical condition of the gas would render it undetectable by any means available at the time. The gas particles are moving at similar speeds to the galaxies, which is equivalent to a gas temperature of about one hundred million degrees this is sufficient to strip all but the most tightly bound electrons from atomic nuclei, leaving behind positively charged ions. Such an ionised gas emits mainly at Xray energies, which are absorbed by the Earth’s atmosphere. It was onlywith the launch of Xray satellite observatories in the 1970s that clusters were found to be very bright Xray sources and it was finally realised that the hot gas, or intracluster medium (ICM), cannot be neglected (see Xray astronomy).
The ICM has turned out to be a very important component of clusters of galaxies. Not only does it contain more matter than is present in the galaxies, but its temperature and spatial distribution can be used to trace the gravitational potential and hence the total mass of the cluster in a much more accurate way than from the galaxies alone. To obtain the total mass of gas one looks at the radiation rate. This radiation is produced in collisions between oppositely charged particles (ions and electrons) and so depends upon the square of the gas density. We observe only the projected emissions, as if the cluster were squashed on the plane of the sky, but assuming spherical symmetry it is relatively easy to invert this to find the variation of density with distance from the centre of the cluster. The gas is found to be much more extended than the galaxies and can in some cases be traced out to several million light years from the cluster centre. Whereas the galaxies dominate in the core of the cluster there is at least three times as much, and probably a lot more, gas in the cluster as a whole as there is matter in the form of galaxies (it is not the mass of gas which is uncertain but the mass of the galaxies). But even the combined mass of gas and galaxies is less than the total cluster mass, showing that a large amount of dark matter is also present. The hot gas is supported against gravitational collapse in the cluster by its pressure gradient. To uniquely derive this from the observations we would have to know the variation of temperature with distance from the cluster centre. Unfortunately this is not yet possible with present Xray telescopes (although it is beginning to be so with the Japanese ASCA satellite) and so some simplifying assumptions have to be made. It is usually supposed that the gas is isothermal the same temperature right across the cluster. This is consistent with both observations and numerical simulations which show little variation of either random galaxy speeds or gas temperature across the cluster. It is possible that the gas temperature may fall in the outer parts of clusters this would tend to lower the overall mass estimates.
A study by David White and Andy Fabian of the Institute of Astronomy in Cambridge, published in 1995, examined data from the Einstein satellite for 19 bright clusters of galaxies. They compared the mass of gas with the total cluster mass and concluded that it comprises between 10 and 22 percent, with an average value of about 15 percent. These fractions would increase by between 1 and 5 percent (of the total mass) if the mass of galaxies was included. So the total baryon content of clusters is much greater than the 5 per cent predicted by the standard CDM model for a flat Universe. You still need some dark matter (to the relief of the particle physicists), but only five times as much as there is baryonic matter, not 20 times as much. Since the Big Bang models still say that only 5 per cent of the critical density can be in theform of baryons, this means that if the distribution of matter in clusters of galaxies is typical of the Universe at large, overall there can only be about 30 per cent of the critical density, even including the dark stuff. If you want to keep the high overall value of the density parameter, you have to allow much more than 5 per cent of the total mass of the Universe to be in the form of baryons, but this is forbidden by the rules of primordial nucleosynthesis.
What is the resolution of this problem? There are various uncertainties in the models (for example the gas may be clumped or may not be isothermal) but these are unlikely to alter the conclusions greatly. One major uncertainty, however, is the distance to the clusters, which is in turn determined by the rate at which the Universe has expanded from the Big Bang to its present size. There is a lively debate among astronomers about the exact value of the parameter which measures the expansion rate, the so-called Hubble constant. So far, we have assumed a Hubble constant of 50 kilometres per second per Megaparsec, which is at the lower end of the accepted range and corresponds to a large, old universe. Thus means that a galaxy one Megaparsec away (a million parsecs, or about 3.26 million light years from us) is receding at a rate of 50 km/sec as a result of the expansion of the Universe, and so on.
In the cosmological models, as the Hubble constant is lowered, the calculated baryon fraction increases. But the predicted baryon fraction from primordial nucleosynthesis increases even faster and so the discrepancy between the two is reduced. By making the Hubble constant low enough one could reconcile the two, but long before this happens the baryon fraction becomes equal to unity. Since there cannot be more than 100 per cent of the mass of the Universe in the form of baryons, this argument can be reversed to place an absolute lower bound on the Hubble constant of about 14, in the usual units. Very few astronomers would countenance going to such extremes. But it is worth mentioning that a new technique for estimating the Hubble constant (based on the Sunyaev-Zel’dovich effect) uses measurements of the influence of the hot cluster gas on the background radiation passing through it to determine how fast the Universe is expanding. This technique is in its infancy, but early results from it do suggest a low value of the Hubble constant, perhaps even less than 50.
It would seem, therefore, that one of the cherished foundations of the standard model must be relinquished. Perhaps the least fundamental of these is that the dark matter must be ‘cold’. Hot dark matter, made of particles (such as neutrinos) which emerge from the Big Bang with speeds close to that of light, is unable to cluster efficiently due to the large random motions of its particles. At first sight, you might guess that it could fill the space between clusters of galaxies with huge amounts of matter, so that even the clusters are not representative of the stuff of the Universe. However, hot dark matter cannot comprise more than about one third of the total amount of dark matter because interactions between the hot stuff and ordinary baryonic matter would slow the development of structures such as galaxies and clusters, delaying their formation until later times; this conflicts with the observed number of distant, old radio galaxies and quasars.
There is certainly no way that the baryonic material found so far will go away, and there could be even more of it than we have estimated. If the same analysis is carried out for larger volumes around the clusters, it tends to show an even larger proportion of mass in gas, because the galaxies themselves congregate in the centres of the clusters. In some cases, as much as half the mass of the cluster is in the form of hot gas. In general, heating of the gas will tend to expel it from clusters and exacerbate the baryon discrepancy still further if there is cold baryonic material outside clusters, then there is even more ordinary stuff than the observations suggest. It has been suggested that clusters may contain a surplus of baryons because they have been formed by the aggregation of gas swept up at the edges of large voids produced by huge cosmic explosions. But unfortunately such models seem to have been ruled out because they would produce excessive distortions in the cosmic microwave background.
People have toyed with the idea of nonstandard nucleosynthesis, for example allowing the baryon abundance to vary from place to place. This allows some relaxation of the upper bound on the baryon fraction but the models are rather contrived and anyway the models do not work as well as the standard one.
We are left with the simplest explanation, and yet the one which most cosmologists would least like to accept, that the mass density of the Universe is much less than the critical density. If”what you see is what you get”, the Universe could contain as much as 25 per cent baryonic material, with overall about 30 per cent of the critical density, with the baryons themselves mostly in the form of about a third hot cluster gas and about two thirds in the form of galaxies. The other 75 per cent of the stuff of the Universe would be mainly cold dark matter, perhaps with a smattering of hot dark matter The Hubble constant could then be rather higher than 50, as some recent observations seem to suggest.
If cosmologists then wish to preserve the idea of a spatially flat Universe, as predicated by theories of cosmic inflation, then they may have to reintroduce the idea of a cosmological constant.