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

**5.2 The Distribution of Dark Matter**

One of the greatest puzzles of modern cosmology is the apparent
discrepancy between the amount of visible matter and that inferred from
gravitational studies, in particular the increasing discrepancy with
increasing scale within bound systems. Mass-to-blue light ratios on the
order of 5-20 *h* are measured in the case of single galaxies, from their
internal velocity fields; they double or triple in the case of binaries
(Schweizer 1987),
reach values several times larger in the case of groups
(Tully 1987),
and reach a few 100 *h* in rich clusters. The
fast-growing data base of well-sampled clusters yields increasingly
consistent values of mass-to-light ratios. For the dozen or so
well-defined clusters with the highest numbers of members with known
redshift, mass-to-light ratios are in the range *M / L*_{B}
~ 340-600 *h*, in
solar units. If the matter distribution traces that of the luminous
matter, then the interesting implication of the mass density in the
universe is that ~ 0.2.

Fueled by the inflationary prediction that = 1, the focus on mapping
the large-scale distribution of luminous matter has rapidly been
complemented by that of mapping the large-scale distribution of mass.
While we have limited this review to redshift surveys and the
determination of galaxy distances by the simple application of Hubble's
law, a less space-limited review of our understanding of the universe
would also encompass the derivation of galaxy distances by means other
than the redshift: including the developing applications of the
luminosity-velocity relations at both optical and radio wavelengths,
through refinements of the original Tully-Fisher and Faber-Jackson
relations. The determination of redshift-independent distances (a much
more laborious effort than that of obtaining redshifts alone) is
currently limited to galaxies within about 10,000 km s^{-1}, as the
accuracy of individual distance determinations has not been reduced
below 15%. The technique seeks to measure peculiar motions, i.e. the
difference between the measured redshift and the redshift-independent
distance expressed in km s^{-1}. Such deviations from pure
expansion can be
related to structure in the gravitational potential field caused by
perturbations ( / ) in the density field. A
density perturbation will
produce a peculiar gravity **g** which, in the growing mode and in the
linear regime, will produce a peculiar velocity **v**_{p} =
(2/3) [*f* / (*H*_{0} )]**g**,
where *f* ~ ^{0.6}
(Peebles 1980,
p. 65). In this mode, the peculiar velocity
grows as *t*^{1/3}. Redshift-independent distances rely on
measurements of the
combination of velocity widths of galaxy spectra and high quality
photometry at optical or infrared bands. This work has produced
surprising and as yet controversial results, suggesting that the
perturbation dynamics of the local universe (within 5000 km s^{-1}) is
regulated by few large mass condensations, which do not appear to
linearly scale with the large-scale distribution of light. The motions
produced by these perturbations would be large, perhaps in excess of 500
km s^{-1}, and they might explain the dipole in the cosmic microwave
background radiation field
(Smoot et al 1991
and refs. therein).
Uncertainties derive primarily front the sparse sampling of peculiar
motion yardsticks and from galactic extinction.
Burstein (1990) has
recently reviewed this field, which, together with that of high redshift
surveys, promises to be among the most active in the next decade.

The existence of structure on large scales and sizeable bulk motions
would imply significant inhomogeneity in the local mass distribution.
Against this unruly backdrop, we might recall that the cosmic microwave
background provides a reference of sobering smoothness, as temperature
fluctuations *T / T* over
angular scales of up to a few degrees are unlikely to exceed 10^{-4}.