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

438 The High-Redshift Universe

density but their luminosities change with time. An independent test of this kind of analysis is a orded by the N–z or M–z relationship for the same galaxies. If pure luminosity evolution explains the excess counts, then one expects a significant number of the faint objects to be at very high redshifts. This actually seems not to be the case: the majority of these sources are at redshifts z < 0.5. One ought to admit, however, that the redshift distribution at very faint magnitudes is not well known. This issue is still quite controversial, but it may be that one is seeing a population of dwarf galaxies undergoing some kind of burst of starformation activity at intermediate redshifts. This is some evidence that galaxies may be forming a significant part of their stars at low redshift, but the sources observed may be localised star formation within a much bigger object. Perhaps the apparent starburst could be induced in a similar way to that usually considered likely for the true ‘starburst’ galaxies mentioned in Chapter 4; they are somehow induced by mergers.

Number-counts in the infrared K-band appear to be quite di erent to that of the blue counts shown in Chapter 4. In particular there is an apparent deficit of galaxies at faint magnitudes, compared with a straightforward extrapolation of the bright counts. An examination of the colours (B–K) of the galaxies suggests that the same population of galaxies is being sampled here as in the blue counts, but that the colours are evolving strongly with redshift.

One possible reconciliation of the blue and infrared counts is that mergers of galaxies have been important in the recent past. Perhaps the faint blue dwarfs merge into massive galaxies by the present epoch. The amount of merging required to achieve this is rather large, but perhaps compatible with that expected in hierarchical models of structure formation. At any rate it seems clear that at least a subset of galaxies have enjoyed a period of star formation, perhaps associated with the formation of a disc. Since the amount of metals produced by the known blue luminosity is comparable with that found in spiral discs, it may be that these objects are somehow related to the damped Lyman-α systems discussed above. Perhaps massive protodiscs, which do not undergo a burst of star formation at such low redshifts and thus appear in the blue population, survive to the present epoch as large galaxies with an extremely low surface brightness. Examples of such systems have been found, but would generally not be included in the normal galaxy surveys. These considerations might reconcile the apparent excess of high-column-density Lyman-α systems at z 2 compared with the number of normal spiral discs at the present epoch.

20.6 Star and Galaxy Formation

The partial and incomplete data we have about galaxies and the IGM at high redshift obviously make it di cult to say for certain at what redshift galaxy formation can have occurred. Obviously, it is unlikely that there is a definite redshift, zg, at which galaxy formation occurred, particularly in hierarchical theories where structure forms on di erent scales continuously over a relatively long interval of time.

In fact, there is also considerable confusion about what galaxy formation actually is, and how one should define its epoch. Since galaxies are observed mainly by the starlight they emit, one might define their formation to be when most of the stellar population of the galaxy is formed. Alternatively, since galaxies are assumed to be formed by gravitational instability, one might define formation to have occurred when most of the mass of a galaxy has been organised into a bound object. There is no necessary connection between these two definitions. A galaxy may well have formed as a gas-rich system very early in the Universe, but su ered an intense period of star formation very recently. We shall therefore consider star formation and mass-concentration epochs separately and try to interpret various observations in terms of the epochs at which these can have happened.

Since we know most about the bright central parts of galaxies, say the part within rc 10h−1 kpc, it makes sense to define the epoch of galaxy formation in the second sense as the redshift by which, say, the mass within this radius reached half of its present value. This will be di erent for di erent galaxies, so one picks as a representative epoch the median redshift, zg, at which this occurs. Spiral galaxies have prominent discs, so one could also usefully define zd to be the median redshift at which half the mass of a present-day disc had been accumulated. According to most cosmogonical theories, the spiral disc is not the dominant mass within rc, and the formation of a disc may well take place over an extended period of time. Studies of the dynamics of galaxies suggest that stars contribute a significant fraction of the mass within rc. Accordingly we define z to be the median redshift at which half the stellar content (in long-lived stars of relatively low mass) of a bright galaxy has formed within rc. We may similarly define zm to be the redshift at which half the present content of metals, i.e. elements heavier than helium, was formed. In the standard picture, the initial gas content of a protogalaxy would have a chemical composition close to the primordial abundances and therefore a negligible fraction of metals. These would have to be made in stars as the galaxy evolves. Because most stars within rc are relatively metal rich and most metals are in stars, it seems likely that zm > z .

As we have already explained, we cannot give firm model-dependent values for any of the characteristic redshifts zg, zd, z or zm. But can we at least place constraints on them, put them in some kind of order or, better still, obtain approximate values? This is what we shall try to do in this section. Although there has been a rapid growth of pertinent observational data, we will find that conclusions are not particularly strong. Notice also that zg is the epoch which is in principle most closely related to the theoretical models of structure formation by gravitational instability. Unfortunately, it is also probably the furthest removed from observations. Nevertheless, we shall begin with some constraints on zg.

The most obvious constraint comes from the fact that galaxies, once fully developed, have a relatively well-defined physical size. Galaxies, as we know them, could therefore only have formed after the time at which the volume they now fill occupied all of space. Depending on how one counts them, bright galaxies (which we shall restrict all these considerations to) have a mean separation of 4h−1 Mpc. The diameter of the bright central parts is 2rc 20h−1 kpc. This suggests an

440 The High-Redshift Universe

upper limit on zg of order 200, but this is decreased by the factor C by which a protogalaxy collapses. We therefore have

It is also the case that galaxies could not have existed when the mean cosmological density was greater than the density inside the galaxy. Suppose a galaxy has circular velocity vc at the present epoch. An estimate of the mean density of its progenitor at maximum expansion is then

According to the spherical collapse model (Section 15.1), this should be given by

where we have taken zg to be approximately the turnaround redshift. If vc 250 km s−1, then

which is consistent with Equation (20.6.1).

The problem with these estimates is that we do not really know how to estimate the collapse factor C accurately. The simple theory in Section 14.1 suggests C = 2, corresponding to dissipationless collapse, but as we already discussed in Section 15.7, this is probably not accurate. If galaxies formed hierarchically, the continuity of clustering properties has led some to argue against a large collapse factor, so that C < 3 or so. On the other hand, if our discussion of the origin of angular momentum in Section 15.9 is taken seriously, one seems to require a relatively large collapse factor for spiral galaxies to generate a large enough value of the dimensionless angular momentum parameter λ, while the appropriate factor for ellipticals should be of order unity. In ‘top-down’ scenarios or in the explosion picture the factor is di cult to constrain.

Now let us turn to z . The most obvious constraint on this comes from the fact that the evolutionary timescale for reasonably massive stars is of order 107– 108 years. Since heavy elements need several generations of massive stars, a reasonably conservative bound on tm, the time when ρ = ρm, is

and, according to the argument given above, we can also conclude that z < zm. At very high redshifts, z > 103 or so, the temperature is enough to ionise hydrogen and radiation drag ensures that clouds of plasma expand with the radiation

background. Although this drag e ect decreases after z 103 when recombination occurs, any material ionised by stars will still su er from it; this will prevent any further star formation. After z 102 this can no longer occur. This suggests an upper limit of z 102 on z and probably also on zg, since star formation is presumably required to halt collapse.

As we mentioned in Section 14.7, the behaviour of a gas cloud is determined by the rate of radiative cooling if Compton scattering o the CMB radiation is negligible, i.e. when z < 10. If galaxy formation proceeds hierarchically, the lower mass end of the distribution will cool slowly since the material in such objects will have a relatively low temperature. Higher-mass objects, corresponding to temperatures around 104 K and above, will cool rapidly and collisional ionisation will be important; star formation presumably ensues. The mass scale when this becomes important is easily calculated to be around 1010–1012M , in good accord with the typical mass scale of bright galaxies. This agreement would not exist if Compton cooling were important during galaxy formation and this therefore provides a certain amount of motivation for the requirement that zg and z are both less than 10.

These theoretical comments on z are disappointingly vague because our understanding of star formation is poor, even for nearby objects. However, once again observations have led the way and a clutch of di erent programmes have resulted in estimates of star-formation rates from observed colours and synthetic stellar populations; a prominent example of this kind of study is described in Madau et al. (1996) using observations of the Hubble Deep Field shown in Figure 4.10. The plot shown as Figure 20.2 is generically known as a ‘Madau Plot’. It appears that these observations favour a scenario in which star formation peaks at moderate redshift. The theoretical curve shown in Figure 20.2 also shows that, in a broad-brush sense, this behaviour can be accounted for in hierarchical clustering models (Baugh et al. 1998). It is also noteworthy that the integrated star formation that these observations imply is not observed. The infrared background measurements mentioned above perhaps explain why: about half the optical starlight ever produced in the Universe has probably been absorbed by dust and re-radiated in the infrared part of the spectrum.

Although the vaguer arguments we gave above admit the possibility that galaxy formation could occur relatively early, at redshifts up to around 10, in hierarchical models galaxies are expected to form at redshifts much lower than this: zg 1. The reason for this is that the clustering pattern of galaxies, as measured by the two-point correlation function, evolves very rapidly with time in models based on the Einstein–de Sitter universe. If galaxies formed at redshifts zg 10, one would expect drastic steepening of the correlation function between z = 10 and z = 0, which is incompatible with the observed slope. This problem, though rather di cult to quantify, does seem compelling in dark-matter models where light traces mass.

Various other kinds of observations are capable of probing the Universe up to the redshift of quasar formation, so it is interesting to see if these can yield any clues about zg or z .

442 The High-Redshift Universe

t (Gyr)

Figure 20.2 The star-formation history of the Universe. Estimates of the star-formation rate as a function of redshift, along with the predictions of a semi-analytic model of galaxy formation described in Chapter 14. Picture courtesy of Carlton Baugh (Baugh et al. 1998).

First there is the question of whether some galaxies may have formed at z < 1. The number-counts, discussed in Section 20.5, certainly show evidence of strong evolution in galaxy properties at these redshifts. How the faint blue galaxies fit into this picture is still an open question: are they connected with the epoch of galaxy formation, or are they merely a sideshow? There is also the problem posed by the population of starburst galaxies, which, though usually dwarf galaxies, are forming stars at a prodigious rate at the present epoch. It has yet to be established, however, if these sources are really young in the semi-quantitative sense defined above. They could merely have evolved more slowly, as a consequence of their cooling properties. If they are young, however, then they certainly suggest the possibility that larger galaxies may also have formed recently. A more direct argument is based on the relative age of the disc and central spheroid of the Milky Way, as estimated by stellar evolution arguments. If the disc turns out to be half the age of the spheroid, one has zd < 1 regardless of the value of zg. It appears that there are disc stars as old as 12 Gyr, which might therefore be a reasonable estimate of td. In an Ω0 = 1 Universe we therefore have

so that zd 2 if t0 15 Gyr.

At redshifts of order unity and above, galaxies are still reasonably observable and one can attempt therefore to study their stellar populations to see how much evolution there has been between z 1 and the present. There are some notable di erences between galaxies then and now: in the past, galaxies were luminous and had younger-looking stellar populations, they were richer in gas and there was also more merging. These di erences are, however, not extreme. The giant radio galaxies mentioned in Section 20.2 do seem brighter than would be expected without evolution, but they are only about one magnitude brighter at z 1 than at redshifts much lower than this. This is consistent with relatively slow evolution from a much higher redshift of formation. Many features of ‘normal’ galaxies at z 1 seem to be characteristic of relatively old stellar populations and there is little evidence for significant evolution in the (comoving) number density of such objects with time. This suggests that both zg and z are rather greater than unity.

The redshift at which galaxies can be observed in large numbers was pushed back further by Steidel et al. (1996), who implemented a novel technique for targetting galaxies at high redshift. By choosing appropriate filters they were able to select objects using colours in such a way that preferentially picked out objects in which the ionisation limit of the Lyman series (in the UV part of the spectrum of a galaxy in its rest frame) is redshifted into an optical band. This allows the observer to pick a small subset of galaxies with extreme colours for follow-up spectroscopy. The galaxies thus found tend to have redshifts z 3. This has been a remarkably successful approach, but the most interesting thing is that the galaxies found seem to have roughly the same number-density as present-day bright spirals and have similar clustering properties.

Observations at higher redshift are much more di cult and have only become feasible in the last five years or so. We have discussed some of these observations already in Sections 20.2–20.4, so let us now discuss them in the context of structure formation.

First, the damped Lyman-α absorbers discussed in Section 20.2 are usually interpreted as the progenitors of galactic discs. Certainly the mean mass density seems to be of the correct order, but they do seem to be more abundant than one would expect by extrapolating the properties of present-day discs back to redshifts of order 3. If they are not protodiscs, then presumably zd is relatively low, which again poses problems.

Secondly, as discussed in Section 20.2, there have been a number of indications of relatively old-looking galaxies at high redshifts, z > 3. The stellar ages of these objects are di cult to determine because of the redshifting of the optical and UV spectra into the infrared region. None of the objects so far claimed to have been seen has been unambiguously identified as a fully formed galaxy, but if one such object is ever found it will place very important constraints on z .

The highest-redshift objects known to observational astronomy are the quasars. Again the evolution of the number density of these objects with time is di -

444 The High-Redshift Universe

cult to quantify, but it seems relatively constant (at least for the brightest ones) from z 2 up to z 4. This suggests that zg > 4, if quasars are housed in galaxies.

Finally, the highest-redshift quasars show that the IGM (Section 20.3) was ionised by z 4. The consequences of this for zg or z are also unclear. One might be led to conclude that zg > 4 on the grounds that galactic stars must have ionised the IGM. On the other hand, a separate population of very massive stars might have formed before galaxies and caused this ionisation.

These arguments are clearly all compatible with z 4 and zg > 4 but do not rule out more recent epochs. We shall have to wait for further observational breakthroughs before anything more concrete can be said. This is indeed an area where a tremendous observational e ort is being directed, and one can expect much to be learned in the next few years.

20.7 Concluding Remarks

In this chapter we have discussed the evolution of the Universe between trec and the present epoch. Clearly, many questions remain unanswered but we hope we have conveyed to the reader some idea of the intense activity and progress which is taking place in this field. This chapter and the previous three have been aimed at a somewhat more detailed level than the earlier chapters in order to provide a ‘bridge’ between the fundamentals, covered in Parts 1–3, and some of the areas of particular current research interest. These chapters should make it clear that we still have a long way to go before we can claim to have a complete understanding of the origin and evolution of cosmic structures, but we are making considerable progress both theoretically and observationally. The basic idea that structures form by gravitational instability from small-initial-density perturbations seems to account, at least qualitatively, for most of the observational data we have. Whether this will still be the case when more data are acquired remains to be seen. There is a very good chance that the cosmological parameters H0 and Ω will be pinned down in the next few years or so. This will also make it easier to construct rigorous tests of these theories. In any event, one thing we can be sure of is that the question of the origin of galaxies and the large-scale structure of the Universe will remain the central problem in cosmology for many years to come.

Bibliographic Notes on Chapter 20

Peebles (1993) contains excellent accounts of the astrophysics of the intergalactic medium. A good review of the properties of Lyman-α absorption systems is given in Wolfe (1993); for some theoretical ideas see Rees (1986). The cosmic X-ray background was reviewed by Boldt (1987). For detailed discussion of the infrared background see Bond et al. (1986) and Carr (1994); see also Signore and Dupraz

(1992). The problem of the faint blue galaxies is discussed by Ellis (1993); interpretation of the faint counts in hierarchical models is attempted by Kau mann et al. (1994). Some of this chapter is based on an entertaining discussion described in Frenk et al. (1989).

Problems

1.A population of sources in a flat matter-dominated (Einstein–de Sitter) universe

has a number-density n0 at the present epoch and a monochromatic luminosity P(ν) ν−α at frequency ν. Show that the flux density S(ν0) observed at the present epoch from a source at redshift z satisfies

S(ν0) = P(ν0)(1 + z)1−αDL−2,

where DL is the luminosity distance.

2.Following on from Question 1, if sources are neither created nor destroyed as the universe expands, show that the number of sources observed per steradian with

redshift < z is

3.Following on from Question 2, show that the integrated background light intensity at frequency ν0 from this population of sources is

21

A Forward Look

21.1 Introduction

From our vantage point at the beginning of the 21st century, we can look back on a hundred years of truly amazing progress in the development of astronomical techniques and technology. Ground-based optical observatories, such as the Keck telescopes and the VLT, o er collecting areas many times larger than their predecessors at Mt Wilson and Mt Palomar, and are equipped with much more sophisticated instrumentation. Perhaps the most important developments, however, have been in the introduction to astronomy of entirely new wavelength regimes. Radio astronomy only came into being after World War II, and X-ray astronomy only in the 1960s with the development of space missions. Some regions of the spectrum, such as the submillimetre region, are still relatively unexplored, but here too progress has been dramatic over the past decade or so.

There are also potentially important phenomena that have not yet emerged as practical possibilities for observation. A prominent example related to cosmology is neutrino astronomy; direct detection of the low-energy neutrino background discussed in Chapter 8 would furnish an important test of the Big Bang. This is as yet a remote possibility. More likely to be feasible in the very near future is the detection of gravitational waves, which we discuss briefly in Section 21.10.

Faced with this continuing revolution driven largely by advances in instrumentation and manufacturing techniques, it seems almost to be inviting ridicule to suggest that the future might be anything like as exciting as the past. But a glance at some of the planned projects and space missions to come over the next two decades suggests that this is indeed very likely to be the case. What is di erent about the future is that, in contrast to the dawn of the 20th century, we now have a robust theoretical framework within which we can interpret observations and plan future strategies. The bulk of this book has been devoted to this framework.

We are not saying that the emerging consensus model of the Universe is exact in every detail, nor that we are anywhere near a complete understanding of the