The options for segregating the luminous material from the bulk of the matter are very many. We wish to consider all of them, regardless of whether they produce a "desirable" result, such as allowing 0 1.0, or reconciling a particular clustering model with the observations. In Figure 1, I present a flow chart which summarizes the many choices of possible astrophysical processes. At the end points of different paths are presented summaries of possible observational and theoretical consequences of this set of choices, and a number, which is the probable maximum scale, in units of h-1 megaparsecs, over which these chosen processes may segregate light from mass.
Figure 1. Flow chart of the possible mechanisms for segregating from light. Numbers are maximum scale of segregation in, h-1 Mpc.
The most fundamental choice is whether or not the dark matter which dominates the mass density in the universe is composed of baryons, rather than some exotic particle. We will first take the left-hand branch, and consider non-baryonic material. The next choice is whether the baryons are closely coupled to the dark matter, and trace its distribution. If they are, then for the purpose of segregation the dark matter might as well be baryons, and we move to the right-hand branch of the diagram.
If the baryons do not trace the dark matter, we must provide a mechanism for segregating the two components. Again, there are two choices. We may separate them after recombination, using conventional astrophysical processes, or we may invoke new physics to separate them at, or soon after, the epoch at which the particles were formed. This latter process may be a natural consequence of the physics which produced the particles, or may require additional assumptions. If such a process does operate, it is likely that the largest scale on which segregation occurs is comparable to the largest scale on which baryon (i.e. galaxy) clustering occurs, namely, about 50 h-1 Mpc. Note, however, that if the baryons are more clumped than the dark matter at recombination, the CMB problem discussed above will be made worse, rather than better, unless the initial fluctuations were isothermal. If the baryons are less clumped than the dark matter, they will soon fall into the dark matter clumps, erasing the segregation.
(One conventional process, operating before recombination, can probably be ruled out. In the expanding universe, the mass contained within the event horizon grows with time. As density fluctuations corresponding to systems of a given size come within the horizon, any relativistic particles contributing to the mass density will be free to stream out of the density fluctuation. If, like photons at recombination, they are partially coupled to the baryons, they will damp out the baryon fluctuation (Silk 1974). If, however, they are very weakly coupled, the baryon fluctuation will remain, producing a universe in which the dark matter is more smoothly distributed than the baryons. Unfortunately, since the smooth dark matter dominates the mass density, baryons clumps cannot grow to form galaxies or clusters (see e.g. Bludman and Hoffman, 1986].)
Because of the many uncertainties associated with early segregation, one might choose the alternative, and assume that the baryons and dark matter had the same distribution at recombination, and any segregation occurred later. Since post-recombination physics is well understood, our options are more limited. The only widely-discussed model which might produce a large scale segregation after recombination is the explosive galaxy formation model of Ostriker and Cowie (1981), in which blast waves from the formation of the first generation of galaxies may drive gas across large distances, separating it from the dark mater (Ostriker 1988). In the flow chart in Fig. 1, I have labeled this option "speculative astrophysics", since our knowledge of the process of galaxy formation is too incomplete to tell whether this idea is viable. Therefore, a choice must be based on taste. If one chooses this option, the maximum scale of segregation is, again, similar to that of galaxy clustering, perhaps 50 h-1 Mpc.
The conservative astrophysicist, who dislikes the speculative nature of the previous mechanisms, is left with only two options. One is dissipation. Gas clouds can radiate energy, and collapse to smaller volumes; dark matter cannot. One expects, therefore, a natural segregation between the two on those scales over which radiative cooling can work in less than a Hubble time. White and Rees (1978) have argued that the maximum scale on which this can occur is that of a large galaxy. This process provides an explanation for the segregation of light and mass within galaxies, but not on scales larger than an individual galaxy halo, which, as I shall show later, seems to be about 100 h-1 kpc.
If dissipation can concentrate the baryons into relatively dense lumps, one may also invoke the process of relaxation. West and Richstone (1988) have presented a model for the collapse of a cluster of galaxies from an initial configuration in which the baryons are in tight bumps (i.e. galaxies) distributed through a uniform sea of dark matter. During the phase of violent collapse, the galaxies loose energy to the dark matter. When the cluster reaches equilibrium, the process stops, but by then the galaxies are much more concentrated toward the cluster center than the dark matter. There are two conditions for such a process to work. Firstly, it can only operate in an dynamical system in which the crossing time is less than the Hubble time. The largest such systems in the universe today are clusters of galaxies, with scales of about 1 h-1 Mpc. Secondly, it probably requires that the dark matter be distributed smoothly, rather than attached to individual galaxies. If it is initially attached to galaxies, in halos of, at most, 100 h-1 kpc in size, it is not clear whether it will be stripped from the galaxies, and deposited in a smooth component through which the galaxies can move, rapidly enough for relaxation to work before the cluster reaches equilibrium.
The conclusion to which one comes, by following this branch of our flow diagram, is that, if one is willing to invoke speculative physics or astrophysics, one can segregate baryons and dark matter on very large scales. If one sticks to known physical processes, the two components can only be separated on scales as large as galaxies or (possibly) clusters of galaxies.
If baryons are the dark matter, or if we wish to segregate mass from light on larger scales than we have yet achieved, we must take the right branch of our flow diagram. With this path, the distribution of galaxies and mass can only be changed by varying the efficiency with which baryons are turned into observable galaxies. For purposes of clarity, I shall refer to these, and only these, processes as biased galaxy formation. The first question, therefore, is whether the efficiency of galaxy formation is uniformly high throughout the universe. Most models of biased galaxy formation assume that it is not. This implies that there are substantial amounts of remnant gas, never incorporated into galaxies, in all regions where the ratio of mass to light is higher than its minimum value.
If, on the other hand, the efficiency of galaxy formation is uniformly high, only one option remains. Almost all surveys of galaxies use samples which are limited by the apparent brightness or apparent size of the objects. Intrinsically faint or small galaxies will only appear in such a sample if they are very near, while large, luminous galaxies will be included even if very far away. Thus, studies of the distribution of galaxies are very much weighted towards large, bright objects. If one varies the luminosity function of galaxies, putting varying fractions of the baryons into faint, unobserved galaxies, the observed distribution of galaxies may differ significantly from the distribution of baryons.
The latter option has clear, and easily observable consequences. The galaxy luminosity function will vary with environment, and the galaxy correlation function will vary with luminosity. The same is likely to be true of most models in which the efficiency of galaxy formation varies, since that efficiency is unlikely to be independent of the mass, density, or depth of the potential well of a protogalaxy. One example is the application of Kaiser's mechanism to a cold dark matter clustering model which White et al. (1987) have made. Since massive galaxies come from larger, rarer density fluctuations than do low mass galaxies, their distribution is more biased. White et al. find that the autocorrelation function of galaxies with circular velocities, vc > 250 km s-1 is higher than that of all galaxies with vc > 100 km s-1 by a factor of about 2 to 3. The largest scale on which any of these processes of biased galaxy formation are likely to work is, again, the largest scale of galaxy clustering, about 50 h-1 Mpc.