Annu. Rev. Astron. Astrophys. 1991. 29:
499-541
Copyright © 1991 by Annual Reviews Inc. All rights reserved |

A common experience to those who analyze the properties of redshift
samples has been that of verifying that the largest traceable
inhomogeneities in the galaxian distribution escape through the
boundaries of the sampled region, raising the question of what is a fair
sample of the universe. To some degree, the measure of fairness for a
sample depends on the statistical tools that are to be applied to
determine its properties. While the scale length of the galaxy-galaxy
correlation function
*(r)* is about the same in any sample (hovering near
*r*_{0} = 5 *h*^{-1} Mpc), the sizes of the
largest structures in 2- and 3-D
surveys, be they voids, or connected high density regions, are
nonetheless comparable to those of the sampled volumes, typically 20
*h*^{-1}
to 60 *h*^{-1} Mpc. How much power is there at the large
scales, or up to
what scale is there any measurable power? A useful analogy to illustrate
the ambiguities associated with these measurements might be the
determination of the size of oceans on Earth: Although a single body of
water can be continuously traced around the planet's surface, we
characterize the oceanic structure by a scale length related to the mean
separation of continents. Thus, the definition of structure and the
measurement of the ocean's size are strongly linked to topology.
Topological decriptions of the galaxian distribution have evolved from
the visual, highly subjective appreciation of morphologies in poorly
sampled data (see
Peebles' (1984)
criticism], to more objective
numerical approaches applied to progressively richer samples. Panoramic
surveys have played an important role in forming our views of the cosmic
fabric, as in establishing the prejudices that permeate the numerical
approaches that strive for its objective description.

The concept of ``supercluster'' gained acceptance during the late 1970s.
The early studies of the Coma
(Chincarini & Rood
1975,
Gregory & Thompson
1978),
Hercules
(Tarenghi et al 1980),
and Perseus regions
(Gregory et al 1981,
Einasto et al 1980)
identified features that extend
well beyond the boundaries of clusters (see the review by
Oort 1983).
Kirshner et al (1981)
and Davis et al (1982)
brought attention to the
existence of large, underdense volumes with typical sizes of tens of Mpc
that the first CfA slice suggested
(de Lapparent et al
1986),
might be outlined by a bubblelike galaxian distribution. The Arecibo
Pisces-Perseus supercluster survey, on the other hand, revealed the
existence of very extensive, linear, filamentlike structures
(Haynes & Giovanelli
1986).
Topology-discriminating algorithms have been developed
(e.g. Gott et al 1987,
Ryden et al 1989)
and applied to a variety of redshift catalogs
(Gott et al 1989):
they indicate that, when the
galaxian distribution is smoothed to scales as large as the correlation
length (*r*_{0}), the topology appears spongelike in all
samples, an
appearance consistent with the standard model in which today's structure
has grown from small, random noise fluctuations in the early universe.
However, when the galaxian distribution is smoothed to lengths smaller
than *r*_{0}, the character of the topology shifts towards
a meatball rather
than a bubble character (i.e. one where volumes are dominated by voids
surrounding the enhancements in the galaxian distribution, rather than
one where voids are surrounded by closed surfaces of enhanced galaxian
density). Reservations on the adequacy of this type of analysis have
been expressed by
Geller & Huchra (1988).

The ability of a survey to trace a structure from one end of the
volume sampled to the other does not exclude that the volume has
approximated a fair sample. In a cellular network, for example,
connected structures that stretch across the sampled region would be
seen, no matter how large the sampled volume is, yet a fair sample will
be approximated once the volume spans a few cells. Has such a point been
reached with nearby, wide-area redshift surveys, or have we not yet run
the gamut of large-scale inhomogeneities? The open-ended aspect of the
Pisces-Perseus supercluster as surveyed over nearly two radians, and the
galaxian distribution on a 360° display that led to the popularization
of the feature dubbed ``the Great Wall''
(Geller and Huchra
1989)
suggests that the answer to that question might be negative. Even more
impressively, the finding of
Broadhurst et al (1990)
of a strong clustering feature with a characteristic scale of 128
*h*^{-1} Mpc indicates
that structure may exist on scales much larger than could have been
found by wide-area surveys.
Karachentsev (1984)
pointed out a similar
feature in the clustering spectrum, with a periodicity of about 70
*h*^{-1}
Mpc, although his result, based on only 92 redshifts, was less
convincing than that of Broadhurst et al. Given the Karachentsev finding
and the pencil-beam nature and huge redshift coverage of the Broadhurst
et al survey, the specific value of the periodicity remains
statistically weak.
Kaiser & Peacock
(1990)
warn that in pencil-beam
surveys, apparent clustering on large scales might result from aliasing
of 3-D clustering on small scales, a form of clustering noise. In
addition, one should maintain clear perspective that, over volumes of
size comparable with those discussed here, several aspects of the
galaxian distribution suggest that mean properties have been measured:
e.g. the identity of slopes of galaxy counts log *N (m)* in all
directions,
known already from the work of Hubble, pose a strong case in favor of
fairness over sizes on the order of 100 *h*^{-1}
Mpc. Nonetheless, the
perspective that the large-scale structure of the galaxian distribution
might be dominated by a network of structures with characteristic scale
on the order of 100 *h*^{-1} Mpc is most tantalizing, and
it remains to be
established whether the diminishing amplitude of density perturbations
with the increasing size of inhomogeneities (found and suggested) can be
accommodated with constant slope of the galaxy counts. Much debate will
also be focused on the issue of the adequacy of previously favored
theoretical and modeling schemes, in the description of the largest
scale clustering features.
Weinberg & Gunn
(1990)
have examined the
structures expected to be seen when varying magnitude limits are imposed
on the numerical results of biased cold dark matter simulations. They
propose that wide angle surveys to limiting magnitudes fainter than 16.5
should reveal an even greater wealth of structure. They also underscore
the resilience of current theoretical schemes to the threats of, at
first sight, hostile observational results: ``. . . the existence of
50-150 *h*^{-1} Mpc structures is not in itself an argument
against gravitational instability, Gaussian fluctuations, and cold dark
matter''.