Although the intensity of the CMBR is extremely uniform in all directions, with fluctuations measured at only 1 part in 105, the local distribution of galaxies is extremely irregular, with fluctuations in the density of galaxies per volume of space being well in excess of 100 percent. Maps of the distribution of galaxies in space reveal a remarkable pattern of thin, filamentary structures connecting small and large central concentrations of galaxies, punctuated by large, quasi-spherical voids. The example of the map shown in Figure 2 is the result of several years of painstaking spectroscopic observations with modest-size optical telescopes. The far-flung distribution of galaxies in the universe, the complex assemblage of clusters, filaments, and voids, is referred to as large-scale structure.
It is not surprising that galaxies are clustered. As explained above, the early universe contained small density irregularities, as measured by fluctuations in the CMBR, and the amplitude of these small bumps grew via their self-gravity to make the structure seen today. This condition of gravitational instability can amplify the initial density fluctuations of seeds on all scales. Galaxies and large-scale structure are all part of the same process; both are relics of the Big Bang.
Finding clumps of galaxies was thus expected, but their huge extent caught astronomers by surprise. Typical voids are 200 million light-years across, and one enormous curtain-like structure-the Great Wall-is draped across the universe in a span half a billion light-years across. Even this large size, however, is less than a tenth the scale measured by the COBE satellite discussed above. Altogether, the distances involved in the study of large-scale structure range over a factor of a million, from the size of galaxies to the CMBR anisotropy measured by the COBE satellite. This combination of observations gives us a powerful probe of Big Bang density fluctuations over a wide range of scales. The extent of early density fluctuations on different size scales and their subsequent growth under gravity are critical clues to the nature and amount of dark matter in the universe, as explained below.
Making maps of galaxies in three dimensions requires knowing how far away each galaxy is from Earth. One way to get this distance is to use Hubble's law for the expansion of the universe. Hubble discovered that the velocity at which two galaxies recede from each other is proportional to the distance between them. Inverting this relation yields an estimate of distance from observed velocity. The velocity with which a galaxy is receding from us is obtained by measuring the shift to redder colors of spectral features in its spectrum, a "redshift" analogous to the familiar Doppler shift in the frequency of sound waves from a receding source. The greater the redshift, the larger the velocity, and, by Hubble's law, the larger the distance.
We are truly living in the age of mapping the universe. The last decade has seen a revolution in the technology of light detectors that has made it possible to measure redshifts rapidly, even with modest-size telescopes. In 1976, there were only 2,700 galaxies with measured redshifts-now there are 100,000. By the year 2000 astronomers expect 1 million! This field of astronomy is still on a steep discovery curve.
The first step in making a redshift survey is compiling a catalog of galaxy positions and brightnesses on the sky. Traditionally such catalogs have been based on photographic surveys taken in visible light. We are learning, though, that even small biases in the list of target galaxies may have a big effect on the final maps. Hence there is strong interest in new and better ways of finding galaxies. Three basic avenues are being explored. Deeper surveys of the whole sky in visible light are being conducted using highly sensitive detectors (called charge-coupled devices; CCDs) that can detect intrinsically faint galaxies, galaxies of low surface brightness, and distant galaxies. Near-infrared surveys of the sky at 2-micron wavelength will make it possible for the first time to observe the dip down near the plane of our galaxy, whose dust clouds obscure 35 percent of the sky in visible light. Finally, x-ray satellite surveys provide yet another means of mapping clusters of galaxies.
A fundamental question is whether one large section of the universe looks like another. In other words, how large do sections have to be before they begin to appear statistically uniform? Unfortunately, a single ground-based observatory sees only a portion of the sky. To achieve the high degree of uniformity needed over the whole sky requires careful surveys. There are three requirements: First, individual surveys must cover as much of the celestial sphere as possible. Second, surveys must be closely coordinated and well standardized so that they can be knitted together. Finally, homogeneous all-sky surveys need to be conducted by satellites above Earth, such as the Infrared Astronomy Satellite (IRAS), a joint mission of the United States, the United Kingdom, and The Netherlands that was flown in 1983.
A major goal for the next generation of surveys is to increase their range out to 3 billion light-years, roughly 20 percent of the radius of the visible universe. On such scales cosmologists would be probing structures that are the same size as the smallest structures in the COBE microwave map. The clustering behavior of galaxies over an extremely wide range of scales could be measured and compared directly to the CMBR anisotropy with no extrapolation. This would tell us how the density fluctuations have evolved from the epoch of CMBR emission (the epoch of photon decoupling) to the present. This information would yield essential clues to the amount and nature of dark matter in the universe.
Statistical description and theoretical modeling of the observed galaxy distribution have been extremely productive over the past decade. Much of this modeling has been done with large computer simulations on the largest available supercomputers. This is a problem in the "grand challenge" class, with the goal of understanding in detail the formation of structure on both small and large scales. The models typically follow the evolution of a large patch of the universe. Calculations start with random initial fluctuations as statistically predicted for different cosmological parameters and different types of dark matter. The equations governing the gravitational coupling, as well as other physical processes, are then solved numerically by the computer. Starting from small amplitudes, the fluctuations become increasingly larger, as expected from the gravitational instability picture. The computational results can then be compared to the observed properties of large-scale structure in the universe. With careful analysis, such comparisons can set constraints on the amount and nature of dark matter. Some proposed dark-matter candidates have already been ruled out in this way. Figure 3 is a recent example of a numerical simulation, processed with similar selection criteria as for observational redshift surveys. The similarity in the voids and filaments shown in Figures 2 and 3 is striking.
Clusters of galaxies, with size on the order of 3 million light-years
and mass of 1015 Suns, are central to our understanding
of structure. Astronomers have recently discovered that galactic
cores are dense enough to act as gravitational lenses (discussed
in section IV in "Gravitational Lenses"), that most
of the baryonic (ordinary) matter within them is in the form of
hot gas, not galaxies, that dark matter constitutes approximately
80 percent of their total mass, and that they show a considerable
amount of substructure when examined at high spatial resolution.
The abundance of clusters and their detailed internal structure
are predicted by models to be sensitive to assumptions about properties
of the dark matter and the total amount of matter in the universe.
Only the most powerful parallel supercomputers can adequately
represent the gravitational and gas dynamical processes at sufficient
resolution to model clusters.
| Figure 3. A simulated galaxy redshift survey based on a cosmological model dominated by cold dark matter and a nonzero cosmological constant. The observer is at the center of the circle, and the outer radius is at a distance of 600 million light-years. Compare to Figure 2. (Courtesy of Renyue Cen, Princeton University Observatory.) |
An even more challenging problem is the question of how galaxies formed. For decades these fundamental building blocks of the universe were taken for granted, but now cosmologists realize that galaxy formation represents the smallest scale of the overall process of structure formation. Galaxy formation is fearsomely complicated because it involves the detailed physics of gas clouds, not just the simple pull of gravity. For example, in order to fall into a forming galaxy, gas has to cool first, which involves the emission of radiation. The cold gas then forms into stars. (Astronomers are not sure just how or how fast.) Dying stars in turn eject energy and gas back into the gas reservoir of the galaxy via supernova explosions. All the while, gas clouds are colliding and pushing one another around via shock waves and gas pressure. A galaxy is a complex system.
In the past few years computer advances have made possible the first attempts to calculate galaxy formation starting from expanding universe models and including the effects of gas. The results are encouraging, but much more computer power is needed to obtain accurate results. Fortunately, with the continuing development of ever-more-powerful computers and sophisticated gas-modeling techniques, one can reasonably hope that progress in this field will be rapid.
Galaxy maps of the universe by themselves are unreliable tracers of the true density of matter because astronomers do not know precisely how or where galaxies formed. Perhaps matter did not "light up" equally in all places to make visible galaxies. Matter that did not form into galaxies may exist today but be invisible. Astronomers sum up this question by asking: Do galaxies fairly trace mass? This cannot be told from redshift maps alone.
Cosmic flows offer a way to answer this question because they
are generated by the gravity of all matter, whether luminous or
not. These flows are the irregularities in the Hubble expansion
that are created (according to gravitational instability) as galaxies
stream out of voids and fall onto clusters and superclusters.
A map of cosmic flows can be used to generate a map of the mass
density distribution that caused them, including any dark matter
between the galaxies. Such a map is shown in the upper panel of
Figure 4, along with a map of the directly
observed galaxy distribution of the same region in the lower panel.
The two roughly agree, suggesting that galaxies do trace mass,
at least approximately. This result is important evidence that
the gravitational instability picture is basically correct.
| Figure 4. The density distribution of mass inferred from studies of large-scale flow using the POTENT method (upper panel) is compared with the density distribution of galaxies derived from the Infra-Red Astronomy Satellite (IRAS) redshift survey (lower panel). The two distributions have been smoothed and are shown in the supergalactic plane. The height in the plot is proportional to the density fluctuation about the mean density of the universe. The Local Group of galaxies is at the center, the Great Attractor (GA) on the left, the Perseus-Pisces (PP) supercluster on the right, and the Sculptor void in between. The similarity between the two density fields indicates that galaxies tend to trace mass and that the cosmological parameter is of order unity. (Courtesy of Yair Sigad, Avishai Dekel, Michael A. Strauss, and Amos Yahil, submitted to the Astrophysical Journal in 1997, and Avishai Dekel, private communication.) |
Because cosmic flows can measure the clustering of matter on even very large scales, they are the best indicator of the absolute level of density fluctuations in the universe today. This indicator of density fluctuations can be compared to the strength of CMBR fluctuations on larger scales at earlier times. Close to Earth, within 250 million light-years where flows are well measured, flow velocities have approximately the magnitude predicted if standard dark-matter theories employ the COBE measurements. This local agreement suggests that our basic model for structure formation, spanning many decades of length scale and depending on details of the nature of dark matter, is approximately correct.
By measuring the size of the flow motions around particular clumps of galaxies, astronomers can estimate the total amount of matter in each one. If galaxies trace the distribution of matter, or even if not, as long as their distribution is biased in a consistent and predictable way, astronomers can generalize from the galaxy masses to estimate the total matter density in the universe. In short, astronomers can "weigh the universe" and measure the elusive parameter the ratio of the mean mass density to that required to close the universe and eventually stop its expansion.
Our present knowledge of galaxy formation and biasing is still poor. Nevertheless, cosmologists can draw two conclusions. First, measurements of cosmic flows on all scales are an important test of competing theories of structure formation. And second, the high values observed for cosmic velocity flows are the strongest indicator so far that might actually be 1, a value favored by theoretical considerations, as explained below in section V.
Since cosmic flow is a deviation from the Hubble-law motion of a galaxy, measuring it requires two types of observations: First, the observed redshift of the galaxy must be measured from its spectrum. Second, an independent estimate of the distance of the galaxy must be made, which is much more difficult. If a galaxy has no motion other than the Hubble flow, its redshift will correlate perfectly with its distance via Hubble's law. Any deviation outside of that due to errors in the estimated distance represents the cosmic flow.
Unfortunately, distances are hard to estimate, and errors can lead to spurious measurements of cosmic flows. The distance to galaxies is usually estimated by the Tully-Fisher relation, which states that big galaxies rotate faster than small ones. (Rotation speed can be measured from features in optical or radio spectra.) Rotation rate is thus a measure of true galaxy brightness, allowing one to deduce how far away a galaxy is based on its apparent brightness. The Tully-Fisher relation has an accuracy of about 15 percent. This translates to an error in flow motion of 600 km/s at a distance of 200 million light-years, and the error grows with distance. Even the largest cosmic motions are no bigger than this. By averaging together several galaxies in a group or cluster, the error can be reduced, but measuring flows is still only reliable out to about 400 million light-years using current methods.
Two conclusions follow. First, cosmic flow surveys are limited by distance errors to volumes that are much smaller than those sampled by redshift surveys. Second, distance measuring techniques with smaller errors are badly needed to increase the viable range of cosmic-flow surveys. At present, the catalog of flow motions contains about 3,000 galaxies out to a radius of 300 million light-years over the whole sky. This volume can be enlarged incrementally with current methods, but a major increase would require better measures of distance. More accurate distance measures would also allow us to study nearby motions more precisely, make better density maps, and derive a more precise measure of the mean mass density of the universe. An improvement in the accuracy of distance measurements by as little as 30 percent would be extremely important. Several approaches are under study, including improvements to the Tully-Fisher method as well as some entirely new methods.
Cosmic flow measurements and redshift maps go hand in hand, since the structures they reveal arise from the same cause. Combining these two tools has already had a big impact on our view of structure in the universe. When combined with the COBE measurement of CMBR fluctuations, flow measurements and maps have quantified the fluctuation amplitudes on virtually all scales of interest. Estimates of mass on the scales of galaxy clusters and on smaller scales appear to suggest that the density of the universe is low, a factor of 10 less than required for closure of the universe ( 0.1). This result has been known for two decades and has not changed with recent data. On the other hand, the newer data on large-scale flows, which measure mass on scales 30 times larger than the older work, seem to suggest that the universe may contain sufficient density for closure ( 0.5 to 1). This contradiction must be telling us something about the nature of the dark matter distribution. It appears as though the dark matter clusters only weakly with galaxies and groups of galaxies but clusters more strongly on the larger scales of superclusters. At present, it is not clear how these apparently contradictory observations can be reconciled. Whether any of the current models of large-scale structure can describe all the observations is an open question.
The field of large-scale structure is still growing rapidly from
the infusion of new data, and even more ambitious surveys are
now in the planning stages. Prospects also exist for improvement
in the accuracy of the distance indicators for galaxies. With
better data and theoretical tools, cosmologists have the prospect
of solving several key cosmic mysteries: What is the nature of
the dark matter and how dense is it? What is the average density
of matter in the universe? Is it near the closure density, W =
1, or is it much less than that, as some measurements seem to
indicate? Where and how were galaxies formed?