LARGE SCALE STRUCTURE
The first examinations of the large-scale distribution of galaxies were carried out in the 1930s independently by Edwin Hubble and Harlow Shapley. Hubble worked in numerous narrow selected fields. Shapley covered most of the sky using wide-angle photographs. He noted regions where the galaxy count was much higher than average and labeled these as "clouds" of galaxies. Many of his clouds are recognized today as superclusters.
Improved wide-angle photographic surveys, such as the classic National Geographic Society-Palomar Observatory Sky Survey, do reveal hundreds of thousands of galaxies, but give only a two-dimensional view of their distribution. To some extent, the third dimension (distance) can be gauged by the angular diameters of the galaxies. A nearby galaxy appears larger than a more distant one, although one may sometimes be misled by a small nearby galaxy mimicking the appearance of a larger distant galaxy. However, there would be little problem in deciding between nearby and distant clusters of galaxies. In this way, in the 1950s and 1960s, George Abell and Fritz Zwicky independently gauged the relative distances of clusters on the Palomar Sky Survey. Abell concentrated on rich clusters, whereas Zwicky's cluster boundaries lay far from the central condensations. Abell also noted that certain regions of the sky had a greater number of clusters than others. Thus, both suspected much larger entities. In a similar way, C.D. Shane, working from Lick photographs, described "superclusters" or (as he preferred to describe them, using Shapley's term) "clouds of galaxies."
The true recognition of superclusters required a three-dimensional view. When distances to relatively nearby galaxies were calibrated, Gerard de Vaucouleurs advocated the existence of a "supergalaxy," now recognized as our local supercluster.
At larger distances, the most effective way of obtaining galaxy distances is to measure redshifts. Due to the overall expansion of the universe, an observer in any galaxy would see its neighbors moving away from it. The velocity of recession increases with distance from the observer's galaxy according to Hubble's well known relation
where V is the velocity of recession, d is the distance, and H0 is the Hubble constant (in the range 50-100 km s-1 Mpc-1 or 15-30 km s-1 per million light-years). The velocity can be measured by the Doppler shift of spectral features (redshift): either absorption or emission lines in the optical spectra, or 21-cm neutral hydrogen emission in the radio region. knowing the velocity, the distance can be inferred.
Strictly speaking the observed velocity is not entirely cosmological but should be expressed as
where the velocity V0 is now corrected for our Sun's motion within the Galaxy and for the streaming motion of our galaxy, V0 is the streaming motion associated with the observed galaxy, and Vp is the observed galaxy's own individual motion over and above systematic streaming; Vp is significant (several hundred kilometers per second) in rich clusters. Because it is difficult to disentangle these velocities, and because of the uncertainty in the value of the Hubble constant, it is customary to plot data in "redshift space" (with dimensions shown as kilometers per second) rather than in conventional three-dimensional space. Gross structures are much the same in either space, but the peculiar velocities in rich clusters make the clusters appear stretched radially (the "Finger of God" effect) in redshift space (examples of this can be seen in Fig. 2).
In the past, obtaining the spectrum of a single galaxy called for a photographic exposure of some hours duration. The advent of electronic image intensifiers and the replacement of the photographic plate by charge-coupled devices (CCDs) and Reticon arrays has greatly accelerated the acquisition of redshifts. Around 1950 little more than 100 redshifts were known, by 1960, 1000 were known and twice that number had been collected by 10 years later. Yet, by 1980 the figure exceeded 10,000 and by 1990 it was around 40,000.
With greater numbers of redshifts available in the mid-1970s, Guido Chincarini pointed out that, even when clusters are avoided in a study, redshifts seem to favor certain values and to avoid others (for the region of sky involved). Thus superclustering was revealed in the third dimension, and three-dimensional mapping became possible. Much pioneering work was done in the region of the Coma cluster where a bridge to a neighboring cluster, Abell 1367, was discerned, with a void immediately in front of the structure.
In order to map completely the neighboring superclusters to our own "Virgo supercluster," one would need to work out to a redshift corresponding to several thousand kilometers per second. Within such a volume of space, there are hundreds of thousands of giant galaxies. Even with present technology, it is quite impossible to obtain all their redshifts (the number to be observed would be much greater because a vast number of background galaxies would have to be candidates). Thus, it is necessary to restrict observations to a "representative" sample. The most common approach is to observe all galaxies brighter than a selected limiting apparent luminosity (apparent magnitude). Such a choice is satisfactory for the capabilities of the telescopes involved, but nearer low-luminosity galaxies are included in the sample, whereas distant high-luminosity galaxies may be excluded. The data thin with distance, and low galactic latitudes (where light from distant objects is subject to extinction by matter in the MilKy Way) have to be avoided. Nevertheless, knowledge of the galaxy luminosity function (the relative numbers of galaxies versus luminosity) allows one to derive true number densities and other statistics. Difficulties could arise if the luminosity function varies with environment; such tendencies have been claimed in the literature. The alternative approach is to disregard a strict magnitude limit and to observe what appears to constitute a representative sample on the sky. This allows for initial mapping of superclusters (mainly because the intervening voids are almost completely empty), but cannot produce quantitative parameters. Whatever system of sampling is used, the outcome is plots revealing filamentary or sponge-like structures, reminiscent of aqueous media even though the data are in the form of discrete points.
Figure 1 gives an indication of neighboring superclusters. The nearest of these is the Hydra-Centaurus-Pavo supercluster. The names reflect the main constellations in which the structure is seen on the sky (although constellations are based on nearby stars in our galaxy, they conveniently represent general directions when looking far beyond those stars). Although the Hydra-Centaurus portion is seen on the sky on one side of the Milky Way and the Pavo portion on the other side, the agreement in redshift and general continuity of structure point to its being a single entity, with the main bulk lying in Centaurus or probably behind the foreground obscuration of the Milky Way. The Hydra condensation centers around the Hydra I cluster (redshift 3500 km s-1) and there is only a relatively weak bridge to the Centaurus concentration. The latter is dominated by the Centaurus cluster, which shows a composite structure in redshift space, with concentrations at both 3000 and 4500 km s-1. However, the weaker 4500 km s-1 concentration may be, to some extent, background galaxies because 4500 km s-1 is the dominant redshift for the bulk of the extended Centaurus superclustering. The same redshift (4500 km s-1) is picked up on the Pavo side, which contains a number of weaker clusters. All these clusters contain both elliptical and spiral galaxies, but the cores of both Hydra I and Centaurus have greater proportions of elliptical and SO galaxies. There seem to be some filamentary links between our own Virgo supercluster and the Centaurus concentration, almost as if our supercluster were something of an appendage. We are separated from the Hydra and Pavo concentrations by foam-like voids with only a sprinkling of galaxies around their perimeters.
The Coma supercluster, mentioned earlier, is separated from our own supercluster and Hydra-Centaurus by a number of voids. Its structure is centered on the Coma cluster, the nearest rich cluster of galaxies (composed almost entirely of elliptical and SO galaxies). From this central concentration, extensions run out more or less perpendicular to our line of sight. Although that running (west-wards) to the Abell 1367 cluster was the first discovered, present-day surveys (particularly the Harvard-Smithsonian "slices") show it extending both east, north, and southward, so much so that it has been referred to as the Great Wall, and its full extent is still being assessed.
Although the Virgo, Centaurus, and Coma superclusters dominate the northern galactic hemisphere, the other side of the obscuring band of the Milky Way is dominated by the Perseus-Pisces supercluster (which has been mapped extensively by the radio redshifts of Martha P. Haynes and Riccardo Giovanelli). Particularly interesting in this supercluster is a filamentary central condensation that is well marked by elliptical galaxies. It is some 4000 km s-1 long in redshift space and runs perpendicular to the line of sight. Toward one end lies the Perseus cluster. Voids again intervene between this supercluster and ours their peripheral galaxies provide tenuous interconnections. Toward the south the supercluster continues and connects to another heavy wall-like structure, in the Sculptor region, that runs at an angle to our line of sight.
It has been remarked that these surrounding structures give a sort of "tree ring," appearance to the distribution within distances from our galaxy that correspond to redshifts of several thousand kilometers per second. More redshifts still are needed to define the nature and extent of such larger patterns. What is relevant is that, whenever a volume of space is sampled, there always seems to be structure with a dimension comparable to that of the volume surveyed. This has led to considerations of fractal structures (identical forms repeated on ever-increasing scales) occurring in the universe. If this is correct, although one would gain a geometrical interpretation to the nature of the structures, it would make a physical explanation extremely difficult.
Beyond redshifts of several thousand kilometers per second, a number of further superclusters have been mapped tentatively. The volume is incompletely sampled, although it is unlikely that very conspicuous superclusters would have been overlooked. For example, in the north there is a pair of superclusters in Hercules (at redshifts around 10,000 km s-1), whereas in the south Shapley's cloud of galaxies in Horologium is resolved into two superclusters (at redshifts of 12,000 and 18,000 km s-1) seen along a common line of sight (see Fig. 2).
An alternative approach for reaching out to larger distances is to assume that Abell's clusters, which mark peak number densities, flag the high points of superclusters. Thus, distant superclusters can be recognized as groupings (in redshift space) of Abell clusters, and examinations of even larger volumes of space can be carried out. On this basis, ever larger conglomerations (to scales of 30,000 km s-1) have been claimed. The work recently has been extended to the southern skies.
The future holds exciting prospects. Just as human
eyes scanned the
galaxies on the wide-angle photographs, the finest-quality photographs
of the U.K. Schmidt telescope and the new Palomar sky surveys are now
being scrutinized by machine and millions of galaxies already have
been detected and cataloged. From these sky densities comes evidence
of possible larger superclusters. In parallel, the development of
fiber-optic spectrographs that can be used to observe many galaxies
simultaneously may lead to the mass determination of redshifts. We can
look forward to finding even more remarkable structures in the
superclustering of galaxies.
2. VOIDS
Definition
of the problem
In extragalactic astronomy, the basic unit is a galaxy with a
characteristic
length of 20 kpc that typically moves
within a group
or clusters with diameter 50 kpc to 5 Mpc which in turn is located in a supercluster
with diameter 50 Mpc or larger. Superclusters
and voids are often discussed together because they are identified and
studied
on a common data base and it is likely that they share a common origin
and represent
two complementary effects of related evolutionary processes.
The structure of superclusters, the material entities that make
up the contiguous
shell, was reviewed by Oort,
1983,
and the voids by Rood, 1988. Voids were not immediately
recognized
in the surface distribution of galaxies because they are superimposed
by
background and especially foreground galaxies.
Voids were
recognized only after Doppler velocities were measured for
statistically homogeneous
samples of galaxies in selected solid angles of the sky, which provided
direct information
on the three-dimensional distribution of galaxies.
In extragalactic
astronomy, the three-dimensional region that constitutes a void is
transparent
and empty or nearly empty of galaxies. It is often useful to think of a
void as
for a discrete entity - a region containing significantly fewer
galaxies than predicted
by the appropriate Poisson distribution. The occurrence of physical
groupings
of galaxies evidently requires the presence
Early surveys of
galaxies over large solid angles of the sky indicated a superclustering
of galaxies, i.e. predominant occurrence of galaxies, groups, and
clusters within
larger structures now called superclusters
(Lundmark, Holmberg, Shapley,
Oort, de Vaucoleurs,
Shane & Wirtanen, Abell).
To discriminate
between these models, we need to know the three-dimensional
distribution of galaxies
in large homogeneous samples.
The testing of theories of structure formation using observations of the large-scale structure of the distribution of galaxies requires a statistical approach. Theoretical studies of the problem of structure formation generally consist of performing numerical N-body simulations on powerful computers. Such simulations show how galaxies would form and cluster according to some well-defined assumptions about the form of primordial density fluctuations, the nature of any dark matter and the parameters of an underlying cosmological model, such as the density parameter and Hubble constant. The simulated Universe is then compared with observations, and this requires a statistical approach: the idea is to derive a number (a `statistic') which encapsulates the nature of the spatial distribution in some objective way. If the model matches the observations, the statistic should have the same numerical value for both model and reality. It should always be borne in mind, however, that no single statistic can measure every possible aspect of a complicated thing like the distribution of galaxies in space. So a model may well pass some statistical tests, but fail on others which might be more sensitive to particular aspects of the spatial pattern. Statistics therefore can be used to reject models, but not to prove that a particular model is correct.
One of the simplest (and most commonly used)
statistical methods
appropriate for the analysis of galaxy clustering observations is the
correlation function or, more accurately, the two-point
correlation
function. This measures the statistical tendency for galaxies to
occur
in pairs rather than individually. The correlation function, usually
denoted by 
(r),
measures the number of pairs of galaxies found at a separation r
compared with how many such pairs would be found if
galaxies were distributed at random throughout space. More formally,
the probability of finding two galaxies in small volumes
dV1 and dV2
separated by a distance r is defined to be be
dP = n2 (1 + (r)) dV1 dV2
where n is the average density of galaxies
per unit volume. A positive
value of (r)
thus indicates that there are more pairs of galaxies with a separation
r than would occur at random; galaxies are then said
to be clustered on the scale r. A negative value indicates that
galaxies tend to avoid each other; they are then said to be
anticlustered. A completely random distribution, usually called
a
Poisson distribution, has (r) = 0 for all values of r.
Estimates of the correlation function of galaxies
indicate that
(r)
is a power-law function of r:
(r) 
(r/r0)-1.8
where the constant r0 is usually
called the
correlation length. The value of r0 depends
slightly on the type of galaxy
chosen, but is around 5 Mpc for bright galaxies. This behaviour
indicates that these
galaxies are highly clustered on scales of up to several tens of
millions of light years in a roughly fractal pattern. On larger
scales, however,
(r) becomes negative, indicating the presence of
large voids (see large-scale structure). The correlation function
(r)
is mathematically related to the power spectrum P(k) by
a Fourier
transformation; the function P(k) is also used as a descriptor
of
clustering on large scales.
Compiled by G.T.Petrov, 2004