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2.1 Missing Mass in Galaxies

This story begins, as do many in extragalactic astronomy , with Fritz Zwicky. Until quite recently, it was universally assumed that stars were the repository of most mass in the universe. If that were so, light would naturally trace the mass, and the ratio of mass to light could be calculated from knowledge of the stellar population. In the early 1930's Zwicky (1933, 1937) applied the virial theorem to observations of the internal motions of the Virgo and Coma Clusters and deduced masses much larger than could be accounted for by the known stellar populations of the galaxies. These remarkable papers (which also discussed dark matter in clusters, tidal interactions between galaxies, and the use of gravitational lenses to measure galaxy masses) were, like many of Zwicky's, ignored for twenty years. However, by the late 1950's, the slow accumulation of additional observations had produced a body of data, on what came to be called, rather misleadingly, the "missing mass problem", which could no longer be ignored. The revival of interest in the problem led to a conference on the subject in 1961 (Neyman, Page, and Scott 1961), centered on the bizarre idea that the missing mass problem was the result of cluster explosions.

The problem remained, as a major puzzle, until the early 1970's. More and better observations only hardened the contrast between the derived masses of clusters and those of individual galaxies. The failure of conventional explanations encouraged the proliferation of exotic ones, such as those invoking non-gravitational redshifts. The breakthrough came not, as I and many others expected, from a closer examination of clusters, but rather from the discovery of large amounts of mass in the outer parts of galaxies. The most important new data were - and still remain - 21 cm observations of the outer rotation curves of spiral galaxies, which showed, unambiguously, that the mass distributions in spirals were much more extended than the light. The paper of Ostriker, Peebles, and Yahil (1974) was an important contribution, which synthesized the new results into a coherent picture of the distribution of mass in galaxies. From observations of the kinematics of galaxies and groups of galaxies, they concluded that the mass distributions about galaxies were very extended isothermal spheres, as much as 1 megaparsec in radius. The ratio of mass to light interior to a given radius appeared to increase monotonically with radius, rising from values of order unity on scales of a few kpc, to values of order 100 on scales of a megaparsec. (For an useful overview of this subject, the reader is referred to the review by Trimble, 1987 and to IAU Symposium 117 Dark Matter in the Universe, Kormendy and Knapp, 1987).

2.2 The Cosmological Context

Fifteen years after the paper of Ostriker, Peebles, and Yahil, it is still true that the most reliable and unambiguous determinations of dark matter only refer to the distribution of mass within the potential wells centered on individual galaxies. The progress in our understanding which they have provided is in knowing that the total masses of galaxies are greater than previously imagined: perhaps sufficiently greater to resolve the problem of missing mass raised by Zwicky. It is, of course, of great astrophysical importance to understand the nature of that dark mass, and the reason that it is distributed differently than are the visible stars. Nevertheless, the direct impact of this on the cosmological problem of the large scale structure of the universe is minimal. However, coincident with this discovery there occurred two developments in theoretical physics and astrophysics which suggested to many people that one might extend the idea of a segregation of mass and light to much larger scales.

2.3 Theoretical Difficulties

In theoretical cosmology, several decades of work on understanding the formation of structure in the universe has produced mixed results. It has proved quite easy to reproduce the qualitative distribution of galaxies, starting with a wide variety of initial conditions at the epoch of recombination, and growing structure by several processes, of which the most popular has been gravitational instability. However quantitative agreement has been almost impossible to achieve. The problems are varied. Most clustering models contain some free parameters including the shape and amplitude of the initial density fluctuation spectrum, and the value of Omega0. The most important observational constraints are the present value of the galaxy autocorrelation function and upper limits on the temperature fluctuations within the matter at recombination, as seen in the cosmic microwave background (CMB). In no model has a combination of parameters been found which would satisfy these constraints and also produce a universe which looks like the observed one.

Voids are one problem. Even one void the size of that in Bootes (Kirshner et al. 1987) is very improbable in the volume of the universe which has been studied. In most conventional models, the probability of detecting the Bootes void with existing surveys is less than 10-3. Also, voids are very large negative density fluctuations. If they have grown by gravitational instability, as most models require, their amplitudes at recombination should have been sufficiently large to perturb the CMB by much more than is observed. Even without large voids, the density fluctuations at recombination needed to produce the clustering seen today would have produced fluctuations in the CMB which are perilously close to the present upper limits.

The geometry of the clustering is another problem. It is clear that the large scale distribution of galaxies contains sheets and filaments as well as roughly spherical lumps (vid. deLapparant, Geller, and Huchra 1986). It is also rather clear that the only gravitational clustering models which can produce such features in any abundance are those in which structure formed by the fragmentation of initially smooth, very large structures, commonly called pancakes (Melott, Weinberg, and Gott 1988). Unfortunately, such models push the epoch of galaxy formation to embarrassingly recent epochs (z = 1, Centrella and Melott 1983) and may be inconsistent with other properties of the galaxy distribution (West, Oemler, and Dekel, 1988). There are many other quantitative difficulties with specific models. For example, the cold dark matter model cannot simultaneously reproduce the observed peculiar velocities and the two and three point correlation functions of galaxies (Davis et al. 1985). Hot dark matter models, which produce pancake structures, have too large a correlation length at the present epoch (White et al. 1983).

The conflicts between theories and observations of clustering are discouraging, but no more than that. Both the theory and the observations have a short history, and are still incomplete. Much work remains to explore a wide variety of initial conditions and possible mechanisms for growing structure. Observations of the distribution of galaxies have yet to survey a large enough volume to fairly sample the universe. It is, therefore, probably premature to conclude that conventional astrophysics is unable to account for the observed structure of the universe.

The problem of the cosmic density parameter, Omega0, is a much more severe embarrassment. There is a very strong presumption, among cosmological theorists, that Omega0 must be exactly unity. Part of the motivation is esthetic: Omega0 = 1.0 is the only special value, and the only stable value; any other value requires fine tuning because Omega0 diverges rapidly from unity as the universe expands. For Omega0 to within a factor of 10 of unity, as it clearly is, but not exactly unity, seems too much of a coincidence. The theory of inflation, an outgrowth of new ideas in particle physics (Guth 1986), also provides a physical mechanism to force Omega0 extremely close to unity, whatever its original value.

Unfortunately, the observations stubbornly refuse to confirm this very plausible argument. The abundances of the light elements produced by primordial nucleosynthesis are only consistent with a baryon density equivalent to values of Omega0 no greater than 0.2 (Boesgaard and Steigman 1985, Deliyannis et al. 1988). And, as I shall describe in some detail later, a variety of dynamical observations consistently give values of Omega0 appeq 0.2. Whatever may be the random and systematic uncertainties of individual estimates, the uniformly low results of a number of determinations makes a value of Omega0 = 1.0 very unlikely.

2.4 A Way Out

Simultaneous with the appearance of these frustrations in astrophysics, there occurred significant developments in theoretical physics. Much effort has been directed to unifying the three non-gravitational forces by means of a grand unified theory (GUT). A consequence of many attempts at such a theory is the existence of new types of particles, some of which are stable, of non-zero mass, and interact very weakly with ordinary baryonic matter (see, e.g. Turner 1987, Kraus 1988 for discussions of the possibilities).

A few years ago it occurred almost simultaneously to a number of people that all of the problems in theoretical cosmology enumerated above could be avoided if the universe were dominated by one of these hypothesized new forms of non-baryonic matter, distributed in a different way than the galaxies. Among the happy consequences of such a model are the following: 1. The total cosmic density can give Omega0 = 1.0 without violating the constraints on baryon density set by primordial nucleosynthesis. 2. The difficulties of growing the present structure from a universe as smooth as that seen in the CMB is removed, since the CMB is only sensitive to the baryons, which could have been more smoothly distributed than the dominant form of matter at recombination. 3. If the matter is more smoothly distributed than are the galaxies today, all dynamical estimates of mass densities and mass-to-light ratios will be systematically low. Low estimates of Omega0 based on these quantities would, therefore, be incorrect. 4. The conflicts between clustering theories and observations could be removed, since the former predict the matter distribution, while the latter describe the galaxy distribution. 5. Since non-gravitational interactions of the baryonic and non-baryonic forms of matter are, at best, extremely weak, is should be possible to segregate them in order to form such features as the dark halos of galaxies.

Such a wonderful fix for so many theoretical problems is, obviously, too good to resist. All that is needed to make it work is (besides, of course, the actual existence of these totally speculative particles) a way of separating mass from light. Since such a separation clearly occurs in the dark halos of galaxies, the feeling has been that this is not a difficult problem. A number of mechanisms have been proposed. On small scales, such as galaxy halos, dissipation in the gas will do it. On large scales, most rely on a variable efficiency of galaxy formation to vary the ratio of mass to light. Such processes have come to be called biased galaxy formation, since the result is that galaxies are a biased indicator of the distribution of mass.

One of the first, and most straightforward, mechanisms of biased galaxy formation was proposed by Kaiser (1986). Suppose, as is true in many scenarios, that galaxies grow from initially small-amplitude gaussian density fluctuations, superimposed on lower amplitude, but much larger scale fluctuations. If the formation of luminous galaxies is a rare process, only occurring in nsigma peaks, where sigma is the standard deviation of the density fluctuations on the scale of galaxies and n >> 1, then galaxy formation will be enhanced in regions where the large scale fluctuations have maxima, and will be suppressed in large-scale minima. The result is a distribution of galaxies more strongly clustered than that of the underlying mass. This is only one possibility. Given our almost total ignorance of the process of galaxy formation, it is easy to imagine many other ways to produce a distribution of galaxies which is either more or less clustered than the matter. A good discussion of the possibilities has been presented by Dekel and Rees (1987).

Because the range of possible processes to separate mass from light is so large, it is very difficult to discuss, much less to test, each individually. In the remainder of this paper, I shall attempt a generic analysis, looking for properties characteristic of all, or many mechanisms. I shall try to demonstrate that, even without knowledge of the details of any particular mechanism, one can make general predictions of the observable consequences of biased galaxy formation, consequences which can, in many cases, be tested with existing observations. I shall then try to sift through observations of the properties of the galaxy population, distinguishing those which are relevant to biased galaxy formation from those which are irrelevant, and reach at least a preliminary conclusion about the viability of this idea.

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