Annu. Rev. Astron. Astrophys. 1991. 29: 499-541 Copyright © 1991 by Annual Reviews. 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 / (H₀ )]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.