Cosmology. The Origin and Evolution of Cosmic Structure - Coles P., Lucchin F

428 The High-Redshift Universe

between activity, such as jets, and star formation in galaxies. One popular idea for the peculiar optical morphology of these objects and the alignment between their radio jets and optical emission is that a radio jet may have triggered star formation in the parent galaxy. The fact that these objects have considerable optical emission allows one to study their stellar populations to figure out possible ages. This is di cult because of the high redshift, which means that interesting features of the optical spectrum are shifted into the infrared K-band, which is notoriously problematic to work in. It has been claimed that these objects have relatively old stellar populations: if true, this would be a significant problem for some theories. At the moment, however, it is best to keep an open mind about these claims; we shall mention these objects again in Section 20.6.

20.3 The Intergalactic Medium (IGM)

We now turn our attention to various constraints, not on objects themselves, but on the medium between them: the IGM.

20.3.1 Quasar spectra

Observations of quasar spectra allow one to probe a line of sight from our Galaxy to the quasar. Absorption or scattering of light during its journey to us can, in principle, be detected by its e ect upon the spectrum of the quasar. This, in turn, can be used to constrain the number and properties of absorbers or scatterers, which, whatever they are, must be associated with the baryonic content of the IGM. Before we describe the possibilities, it is therefore useful to write down the mean number density of baryons as a function of redshift:

This is an important reference quantity for the following considerations.

20.3.2 The Gunn–Peterson test

Neutral hydrogen has a resonant scattering feature associated with the Lyman-α atomic transition. This resonance is so strong that it is possible for a relatively low neutral-hydrogen column density (i.e. number-density per unit area of atoms, integrated along the line of sight) to cause a significant apparent absorption at the appropriate wavelength for the transition. Let us suppose that light travels towards us through a uniform background of neutral hydrogen. The optical depth for scattering is

where σ(λ) is the cross-section at resonance and nI is the proper density of neutral hydrogen atoms at the redshift corresponding to this resonance. (The usual convention is that HI refers to neutral and HII to ionised hydrogen.) We have assumed in (20.3.2) that the Universe is matter dominated. The integral is taken over the width of the resonance line (which is very narrow and can therefore be approximated by a delta function) and yields a result for τ at some observed wavelength λ0. It therefore follows that

where Λ = 6.25 × 108 s−1 is the rate of spontaneous decays from the 2p to the 1s level of hydrogen (the Lyman-α emission transition); λα is the wavelength corresponding to this transition, i.e. 1216 Å. Equation (20.3.3) can be inverted to yield

This corresponds to the optical depth τ at z = (λ0/λα) − 1, when observed at a wavelength λ0.

The Gunn–Peterson test (Gunn and Peterson 1965) takes note of the fact that there is no apparent drop between the long-wavelength side of the Lyman-α emission line in quasar spectra and the short-wavelength side, where extinction by scattering might be expected. Observations suggest a (conservative) upper limit on τ of order 0.1, which translates into a very tight bound on nI:

Comparing this with Equation (20.3.1) with Ωb = 1 yields a constraint on the contribution to the critical density due to neutral hydrogen:

There is no alternative but to assume that, by the epoch one can probe directly with quasar spectra (which corresponds to z 4), the density of any uniform neutral component of the IGM was very small indeed.

One can translate this result for the neutral hydrogen into a constraint on the plasma density at high temperatures by considering the balance between collisional ionisation reactions,

and recombination reactions of the form

The physics of this balance is complicated by the fact that the cross-sections for these reactions are functions of temperature. It turns out that the ratio of neutral

430 The High-Redshift Universe

hydrogen to ionised hydrogen, nI/nII, has a minimum at a temperature around 106 K, and at this temperature the equilibrium ratio is

Since this is the minimum possible value, the upper limit on nI therefore gives an upper limit on the total density in the IGM, which we can assume to be made entirely of hydrogen:

If the temperature is much lower than 106 K, the dominant mechanism for ionisation could be electromagnetic radiation. In this case one must consider the equilibrium between radiative ionisation and recombination, which is more complex and requires some assumptions about the ionising flux. There are probably enough high-energy photons from quasars at around z 3 to ionise most of the baryons if the value of Ωb is not near unity, and there is also the possibility that early star formation in protogalaxies could also contribute substantially. Another complication is that the spatial distribution of the IGM might be clumpy, which alters the average rate of recombination reactions but not the mean rate of ionisations. One can show that, for temperatures around 104 K, the constraint emerges that

if the medium is not clumpy and the ionising flux, I21, is measured in units of 10−21 erg cm−2 s−1 Hz−1 ster−1. The limit (20.3.10) is reduced if there is a significant clumping of the gas.

These results suggest that the total IGM density cannot have been more than ΩIGM 0.03 at z 3, whatever the temperature of the plasma. This limit is compatible with the nucleosynthesis bounds given in Section 8.6.

20.3.3 Absorption line systems

Although quasar spectra do not exhibit any general absorption consistent with a smoothly distributed hydrogen component, there are many absorption lines in such spectra which are interpreted as being due to clouds intervening between the quasar and the observer and absorbing at the Lyman-α resonance. An example spectrum is shown in Figure 20.1.

The clouds are grouped into three categories depending on their column density, which can be obtained from the strength of the absorption line. The strongest absorbers have column densities Σ 1020 atoms cm−2 or more, which are comparable with the column densities of interstellar gas in a present-day spiral galaxy. This is enough to produce a very wide absorption trough at the Lyman-α wavelength and these systems are usually called damped Lyman-α systems. These are

wavelength (Å)

Figure 20.1 An example of a quasar spectrum showing evidence of absorption lines at redshifts lower than the Lyman-α emission of the quasar. Picture courtesy of Sandhya Rao.

relatively rare, and are usually interpreted as being the progenitors of spiral discs. They occur at redshifts up to around 3 (Wolfe et al. 1993).

A more abundant type of object is the Lyman limit system. These have Σ 1017 atoms cm−2 and are dense enough to block radiation at wavelengths near the photoionisation edge of the Lyman series of lines. Smaller features, with Σ 1014 atoms cm−2 appear as sharp absorption lines at the Lyman-α wavelength. These are very common, and reveal themselves as a ‘forest’ of lines in the spectra of quasars, hence the term Lyman-α forest. The importance of the Lyman limit is that, at this column density, the material at the centre of the cloud will be shielded from ionising radiation by the material at its edge. At lower densities this cannot happen.

As we have already mentioned, the damped Lyman-α systems have surface densities similar to spiral discs. It is natural therefore to interpret them as protogalactic discs. The only problem with this interpretation is that there are about ten times as many such systems at z 3 than one would expect by extrapolating backwards the present number of spiral galaxies. This may mean that, at high redshift, these galaxies are surrounded by gas clouds or very large neutral hydrogen discs which get destroyed as the galaxies evolve. It may also be that many of these objects end up as low-surface-brightness galaxies at the present epoch, which do not form stars very e ciently (e.g. Davies et al. 1988): in such a case the present number of bright spirals is an underestimate of the number of damped Lyman-α systems that survive to the present epoch. It is also pertinent to mention that these systems have also been detected in CaII, MgII or CIV lines and that they do seem to have significant abundances of elements heavier than helium. There is some evidence that the fraction of heavy elements decreases at high redshifts.

The Lyman-α forest clouds have a number of interesting properties. For a start they provide evidence that quasars are capable of ionising the IGM. The number densities of systems observed along lines of sight towards di erent quasars are similar, which strengthens the impression that they are intervening objects and not connected with the quasar. At redshifts near that of the quasar the num-

432 The High-Redshift Universe

ber density decreases markedly, an e ect known as the proximity e ect. The idea here is that radiation from the quasar substantially reduces the neutral hydrogen fraction in the clouds by ionisation, thus inhibiting absorption at the Lyman-α resonance. Secondly, the total mass in the clouds appears to be close to that in the damped systems or that seen in present-day galaxies. This would be surprising if the forest clouds were part of an evolving clustering hierarchy, but if they almost fill space then one might not see any strong correlations in any case. Thirdly, the comoving number density of such systems is changing strongly with redshift, indicating, perhaps, that the clouds are undergoing dissipation. Finally, and most interestingly from the point of view of structure formation, the absorption systems seem to be only weakly clustered, in contrast to the distribution of galaxies. How these smaller Lyman-α systems fit into a picture of galaxy formation is not absolutely certain, but it appears that they correspond to lines of sight passing through gas confined in the small-scale ‘cosmic web’ of filaments and voids that corresponds to an earlier stage of the clustering hierarchy than is visible in the local galaxy distribution.

20.3.4 X-ray gas in clusters

We should mention here that there is direct evidence from X-ray observations of hot gas at T 108 K in the IGM in rich clusters of galaxies. We mentioned in Chapter 17 that this gas could cause an observable Sunyaev–Zel’dovich distortion of the CMB temperature in the line of sight of the cluster. Direct observations of the gas show that it also has quite high metal abundances and its total mass is of order that contained in the cluster galaxies. Since the cooling time of the gas at these temperatures is comparable with the Hubble time, one expects to see cooling flows as the gas dissipates and falls into the potential well of the cluster (a cooling flow occurs whenever the rate of radiative cooling is quicker than the cosmological expansion rate, H). It seems likely, however, that much of the cluster gas is actually stripped from the cluster galaxies, so these observations say nothing about the properties of the primordial IGM.

We discuss the properties of the di use extragalactic X-ray background and its implications in Section 20.4.

20.3.5Spectral distortions of the CMB

The Sunyaev–Zel’dovich e ect also allows one to place constraints on the properties of the intergalactic medium. If the hot gas is smoothly distributed, then one would not expect to see any angular variation in the temperature of the CMB radiation as a result of this phenomenon. However, the Sunyaev–Zel’dovich e ect is frequency dependent: the dip associated with clusters appears in the Rayleigh– Jeans region of the CMB spectrum. If one measures this spectrum one would expect a smooth gas distribution to produce a distortion of the black-body shape due to scattering as the CMB photons traverse the IGM. The same will happen if

gas is distributed in objects at high redshift which are too distant to be resolved. We mentioned this e ect in Section 9.5 and defined the relevant parameter, the so-called y-parameter, in Equation (9.5.5). The importance of this e ect has been emphasised by the CMB spectrum observed by the FIRAS experiment on COBE, which has imposed the constraint y < 3 × 10−5.

From Equation (9.5.5) the contribution to y from a plasma with mean pressure nekBTe at a redshift z is

where the su x e refers to the electrons. Various kinds of object containing hot gas could, in principle, contribute significantly to y. If Lyman-α clouds are in pressure balance at z 3, then they will contribute only a small fraction of the observational limit on y, so these clouds are unlikely to have an e ect on the CMB spectrum. Similarly, if galaxies form at high redshifts with circular velocities v, then one can write

if v 100 km s−1 and Ωg is the fractional contribution of hot gas to the critical density. The contribution from rich clusters is similarly small, because the gas in these objects only contributes around Ωg 0.003. On the other hand, a smooth hot IGM can have a significant e ect on y, as we shall see shortly.

20.3.6 The X-ray background

It has been known for some time that there exists a smooth background of X- ray emission. This background actually furnishes an additional argument for the large-scale homogeneity of the Universe because the flux is isotropic on the sky to a level around 10−3 in the wavelength region from 2 to 20 keV.

It has been a mystery for some time precisely what is responsible for this background but many classes of object can, in principle, contribute. Clusters of galaxies, quasars and active galaxies at high redshift and even starburst galaxies at relatively low redshift could be significant contributors to it. Disentangling these components is di cult because it may be di cult to locate any counterpart of an X-ray-emitting source in any other waveband. Recently, however, using the sensitive instruments on Chandra, Mushotzky et al. (2000) have resolved about three-quarters of the hard X-ray background into sources. The mean X-ray spectrum of these sources is in good agreement with that of the background. The X-ray emission from the majority of the detected sources is unambiguously associated with either the nuclei of otherwise normal bright galaxies or optically faint sources, which could either be active nuclei of dust-enshrouded galaxies or the first quasars at very high redshifts.

434 The High-Redshift Universe

The spectrum and anisotropy may well provide strong constraints on models for the origin of quasars and other high-redshift objects. We shall concentrate on the constraints this background imposes on the IGM. A hot plasma produces radiation through thermal bremsstrahlung. The luminosity density at a frequency ν produced by this process for a pure hydrogen plasma is given approximately by

where the integral is taken over a line of sight through the medium. If the emission takes place predominantly at a redshift z, then

at energies around 3 keV. Suppose a fraction f of this is produced by a hot IGM with temperature T 108(1 + z) K; in this case,

If the plasma is hot and dense enough to contribute a significant part of the X-ray background, then it would violate the constraints on y.

20.4 The Infrared Background and Dust

We have already discussed the importance of the CMB radiation as a probe of cosmological models. Two other backgrounds of extragalactic radiation are important for the clues they provide about the evolution of gas and structure after recombination.

It has been suggested that various kinds of cosmological sources might also generate a significant background in the infrared (IR) or submillimetre parts of the spectrum, near CMB frequencies. A cosmological IR background is very di - cult to detect even in principle because of the many local sources of radiation at

these frequencies. Nevertheless, the current upper limits on flux in various wavelength regions can place strong constraints on possible populations of pregalactic objects. For simplicity one can characterise these sources by the contribution their radiation would make towards the critical density:

where I(ν) is the flux density per unit frequency. The CMB has a peak energy density at λmax = 1400 m, corresponding to ΩCMB 1.8 × 10−5h−2. The lack of distortions of the CMB spectrum reported by the FIRAS experiment on COBE suggests that an excess background with 500 m < λ < 5000 m can have a density less than 0.03% of the peak CMB value:

One obvious potential source of IR background radiation is galaxies. To estimate this contribution is rather di cult and requires complicated modelling. The nearIR background would be generated by redshifted optical emission from normal galaxies. One therefore needs to start with the spectrum of emission as a function of time for a single galaxy, which requires knowledge of the initial mass function of stars, the star-formation rate and the laws of stellar evolution. To get the total background one needs to integrate over a population of di erent types of galaxies as a function of redshift, taking into account the e ect of the density parameter upon the expansion rate. If galaxies are extremely dusty, then radiation from them will appear in the far-IR region. Such radiation can emanate from dusty discs, clouds (perhaps associated with the ‘starburst’ phenomenon), active galaxies and quasars. The evolution of these phenomena is very complex and poorly understood at present.

More interesting are the possible pregalactic sources of IR radiation. Most of these sources produce an approximate black-body spectrum, because the low density of neutral hydrogen in the IGM is insu cient to absorb photons with wavelengths shorter than the Lyman cut-o . For example, the cooling of gas clouds at a redshift z after they have collapsed and virialised would produce

where v is the RMS velocity of gas in the clouds. In principle, this could therefore place a constraint upon theories of galaxy formation, but the number of objects forming as a function of redshift is di cult to compute in all but the simplest

436 The High-Redshift Universe

hierarchical clustering scenarios. Pregalactic explosions, often suggested as an alternative to the standard theories of galaxy formation, would produce a much larger background. COBE limits on the spectral distortions (20.4.2) appear to rule out this model quite comfortably. Constraints can also be placed on the numbers of galactic halo black holes, halo brown dwarfs and upon the possibility of a decaying particle ionising the background radiation.

The constraints obtained from this type of study only apply if the radiation from the source propagates freely without absorption or scattering to the observer. Many sources of radiation observed at the present epoch in the IR or submillimetre regions are, however, initially produced in the optical or ultraviolet and redshifted by the cosmological expansion. The radiation may therefore have been reprocessed if there was any dust in the vicinity of the source. Dust grains are generally associated with star formation and may consequently be confined to galaxies or, if there was a cosmological population of pregalactic stars, could be smoothly distributed throughout space. The cross-section for spherical dust grains to absorb photons of wavelength λ is of the form

πr2

σd = + d , (20.4.5) 1 (λ/rd)α

where rd is the grain radius and α 1 is a suitable parameter; the cross-section is simply geometrical for small λ but falls as a power law for λ rd. If radiation is absorbed by dust (whether galactic or pregalactic), then thermal balance implies that the dust temperature Td obeys the relation

If the radiation density parameter is less than the critical quantity

then the dust temperature will be the same as the CMB temperature at redshift z. On the other hand, if ΩR > Ω , the dust will be hotter than the CMB and one will expect a far-IR or submillimetre radiation background with a spectrum that peaks at

Notice the very weak dependence on the various parameters, indicating that the peak wavelength is a very robust prediction of these models. This was interesting a few years ago because a rocket experiment by the Nagoya–Berkeley collaboration had claimed a detection of an excess in the CMB spectrum in this wavelength region. Unfortunately, we now know this claim was incorrect and that the experiment had detected hot exhaust fumes from the parent rocket.

Note that if ΩR > Ω , the total spectrum has three parts: the CMB itself, which peaks at 1400 m; the dust component, peaking at λmax; and a residual component from the sources. If ΩR < Ω , the dust and CMB parts peak at the same wavelength, so there are only two components. Nevertheless, the dust component is not a pure black body, so there is some distortion of the CMB spectrum in this case.

We should also mention that a dust background would also be expected to be anisotropic on the sky if it were produced by galaxies or a clumpy distribution of pregalactic dust. One can study the predicted anisotropy in this situation by allowing the dust to cluster like galaxies, for example, and computing the resulting statistical fluctuations. Various experiments have been devised, along the lines of the CMB anisotropy experiments, to detect such fluctuations, with success finally resulting from an analysis of data from the DIRBE measurement on COBE (Wright and Reese 2000). We shall return to this background, and its theoretical importance, shortly.

20.5 Number-counts Revisited

We discussed in Section 1.8 how the number–magnitude and the number–redshift relationships, in the past thought to be good ways to probe the geometry of the Universe, are complicated by the fact that galaxies appear to be evolving on a timescale which is less than or of order the Hubble time; an example is Figure 4.11. While evolution makes it very di cult to obtain the deceleration parameter q0 from these counts, there is at least the possibility that they can tell us something about how galaxy formation, or at least star formation in galaxies, changes at relatively low redshifts. This, in turn, can yield useful constraints on theories of the origin of structures.

Again, this is an area in which considerable observational advances have been made in recent years. The possibility of obtaining images of extremely faint galaxies using CCD detectors has made it possible to accumulate number-counts of galaxies in a systematic way down to the 28th magnitude in blue light (so-called B-magnitudes). In parallel with this, developments in infrared technology have allowed observers to obtain similar counts of galaxies in other regions of the spectrum, particularly in the K-band. Since these di erent wavelength regions are sensitive to di erent types of stellar emission, one can gain important clues from them about how the stellar populations have evolved with redshift. Blue number-counts tend to pick up massive young stars and therefore are sensitive to star formation; longer wavelengths are more sensitive to older stars.

The blue number-counts display a feature at faint magnitudes corresponding to an excess of low-luminosity blue objects compared with what one would expect from straightforward extrapolation of the counts of brighter galaxies. The game is to try to fit these counts using models for the evolution of the stellar content and (comoving) number density of galaxies, as well as the deceleration parameter. The best-fitting model appears to be a low-density-universe model with significant luminosity evolution, i.e. the sources maintain a fixed comoving number