Edmund Bertschinger

Dark matter is mass that does not emit or reflect detectable electromagnetic radiation, yet is detectable by its gravitational effect on other, luminous, matter. Perhaps 90% or more of all the matter in the universe is dark. Dark matter has been inferred to exist in galaxies and on larger scales in the universe, but not in the solar system. The nature and total amount of dark matter are unknown, although there are constraints from astronomical observations and particle physics experiments. The abundance, distribution, and nature of dark matter are outstanding questions in modern cosmology.

The total abundance of dark matter has important implications for the evolution of the universe. If the mean density is large enough, dark matter can close the universe, causing the universal Hubble expansion eventually to halt and reverse. For cosmological purposes, the most convenient way to express the abundance of some type of mass labeled i is by the ratio of the mean mass density rhoi of that substance to the mean mass density rhocrit, required to close the universe:

Omegai ident rhoi / rhocrit = 8piGrhoi / 3H02; rhocrit = 1.9 x 10-29 h2 g cm-3

The critical density depends on the gravitational constant G and the Hubble constant H0 = 100 h km s-1 Mpc-1. The Hubble constant is poorly known, but nearly all modern estimates give 0.5 < h < 1.0. If the total density parameter Omega from all types of matter exceeds 1, the universe is closed and will eventually collapse. If Omega < 1, the universe will continue expanding forever. The inflationary universe model of Big Bang cosmology predicts that Omega = 1 to high precision, but this idea has not been confirmed by observations. Observational estimates yield a total Omega approx 0.1-1, with some preference for smaller values (Omega approx 0.2).

To place the abundance question in perspective, it is useful to compare the mean density of dark matter with that of luminous matter-stars and gas in galaxies and galaxy clusters - Omegalum approx 0.01h-1. It is plausible that most of the ordinary, baryonic matter (with atomic nuclei made of baryons, i.e., protons and neutrons) in the universe does not emit radiation detectable using present technology. For example, planets, brown dwarfs, cold white dwarfs, neutron stars, and intergalactic gas are difficult to detect at large distances, although they are not dark in principle. Baryonic matter in these forms could increase the total baryonic density parameter to Omegab approx 0.05-0.10. Support for this possibility comes from the theory of primordial nucleosynthesis, which predicts the abundance of the light isotopes of hydrogen, helium, and lithium produced during the first three minutes after the Big Bang. Excellent agreement with measurements is obtained for Omegab = (0.02 ± 0.01)h-2.


The first measurement of dark matter in the Galaxy was made by Jan Oort in 1932, who concluded that visible stars near the sun could account for only about half the mass implied by the velocities of stars perpendicular to the disk of our Galaxy. In 1933, Fritz Zwicky applied a similar dynamical argument to clusters of galaxies, noting that observed galaxies accounted for 10% or less of the mass needed to gravitationally bind clusters, given the large velocities of galaxies in a cluster. For a self-gravitating system in equilibrium, the mass is M approx RV2 / G, where R is the characteristic size of the system and V is the characteristic velocity of stars or other test bodies in the system.

The most straightforward and extensive mass measurements have been made for spiral galaxies, for which V is the circular rotation speed at radius R and M is the mass interior to R. The rotation curve V (R) has been measured for hundreds of spirals, using the Doppler shift of the optical Halpha line or the radio 21-cm line of hydrogen. In almost all cases, V (R) is nearly constant outside of the galactic nucleus, indicating a mass increasing linearly with radius or a density decreasing with the inverse square of the radius. Since the luminosity density typically decreases exponentially with radius, the mass-to-light ratio becomes large in the outer parts, implying that spiral galaxies are embedded in halos of dark matter. For our own Galavy, with V approx 220 km s-1, M could be as large as 1012 solar masses if the halo extends to 100 kpc. Adopting a mean separation of 5h-1 Mpc, Omega in bright spirals alone is ~ 0.03.

Gravitational mass measurements have also been performed for elliptical galaxies, small groups, and rich clusters of galaxies. These measurements are less certain than those for spirals, largely because of the uncertainty of the distribution of stellar or galactic orbits in the systems analyzed. X-ray emission from hot gas in hydrostatic equilibrium in clusters should allow more precise determinations once accurate gas temperature measurements become available. The mass measurements of ellipticals, groups, and clusters confirm the existence of dark matter and increase the estimated total Omega in galaxies and clusters to ~ 0.1-0.2. Similar results follow from the cosmic virial theorem, a statistical method based on the relative velocities of all close pairs of galaxies.

Because galaxies and clusters occupy a small fraction of the volume of the universe, measurements on larger length scales are needed to obtain the total mean density in dark matter. Unfortunately, equilibrium structures larger than galaxy clusters do not exist, so that large-scale gravitational mass density measurements cannot be based on the simple formula M approx RV2 / G. Instead, cosmologists apply the linear theory of gravitational instability in an expanding universe, supposing that the mass density fluctuations have small amplitude on large scales. The mass density is written rho = rhobar + deltarho, where rhobar is the mean density and deltarho / rhobar is the spatially varying relative density fluctuation. When smoothed on the scale of superclusters of galaxies, deltarho / rhobar should be, according to theory, related to the ``peculiar'' velocity field - the velocity remaining after the Hubble velocity of uniform cosmological expansion is subtracted - with a constant of proportionality depending on Omega. Measurements of Omega based on this relation have yielded values in the range 0.2 to 1, with a preference for small values. However, this technique suffers from a major problem. The net density contrast deltarho / rhobar must be known, but the density on large scales is dominated by the unseen dark matter. In practice the assumption is usually made that on large scales dark and luminous matter are distributed similarly, so that deltarho2 / rhobar = delta ng / nbarg, where nbarg + delta ng is the smoothed galaxy density. However, there is no empirical evidence supporting this assumption, and there are sound theoretical arguments suggesting that the galaxy distribution should be biased with respect to the dark matter distribution. In the simplest theoretical model, the galaxy distribution has a density contrast larger by a factor b, called the bias parameter, than the matter distribution: deltang / nbarg = b(deltarho / rhobar). If b = 2.5, then the apparent Omega could be ~ 0.2, whereas the true Omega = 1. This possibility is favored by theorists who advocate the inflationary-universe model, but presently is a conjecture neither confirmed nor refuted by observations.

It is possible to measure Omega on still larger scales, by computing the rate of deceleration of the Hubble expansion using observations of cosmologically distant objects. There are a variety of methods for accomplishing this, but all those employed to date suffer from large uncertainties of the structure and cosmological evolution of the objects studied.


Many important theoretical questions are raised by the existence of dark matter. Perhaps the most obvious are: What is it? Is it baryonic? This possibility is marginally allowed if Omega approx 0.1, being consistent with primordial nucleosynthesis for h = 0.5 and with most dynamical determinations. However, the isotropy of the cosmic microwave background radiation imposes theoretical constraints on baryonic dark matter models that are difficult to satisfy.

If the dark matter is nonbaryonic, it probably consists of elementary particles without electromagnetic or strong interactions; for otherwise it should have been detected by now. There is no shortage of possible candidates proposed by particle physicists, although none except the neutrino are known to exist. Most of these dark matter candidates undergo weak nuclear interactions, so it should be possible to detect them in laboratory experiments of sufficient sensitivity. A key implication of the dark matter hypothesis is that these particles should be abundant in every laboratory on the Earth, with a flux ~ 102 cm-2 s-1 if the particle has mass comparable to a proton. Many experiments are underway to try to detect these particles.

From an astrophysical point of view, most of the properties of The dark matter are irrelevant. The one significant detail is the temperature of the dark matter distribution. Cold dark matter (CDM) particles have negligible random velocities before the epoch of galaxy formation, while hot dark matter (HDM) is hot enough to evaporate (erase by free streaming) galaxy-scale primordial density perturbations. Cosmological scenarios with hot and cold dark matter differ in that, in the former, galaxy formation occurs only after the fragmentation of cluster-or supercluster-sized sheets of collapsed matter (``pancakes''), whereas in the CDM model, galaxy formation and clustering proceeds hierarchically, with small objects merging to form larger ones. The latter scenario appears to be more consistent with the relative ages of galaxies and superclusters, but no model is entirely successful. Another problem with HDM is that it cannot cluster enough to provide the dark matter in dwarf galaxies. The best-known HDM candidate is a neutrino with mass ~ 20h-2 eV c-2, for example, the tau neutrino, whose experimental mass limit allows this possibility. The most widely discussed CDM candidates are axions, invoked to solve problems in the theory of quantum chromodynamics, and the lightest supersymmetric particle, which is predicted to be stable. Theories of unstable dark matter or of two or more types of dark matter have been advanced occasionally but they are not as appealing as the simple models with one stable dark matter particle.

Additional Reading
  1. Faber, S.M. and Gallagher, J.S. (1979). Mass and mass-to-light ratios of galaxies Ann. Rev. Astron. Ap. 17 135.
  2. Krauss, L.M. (1986). Dark matter in the universe. Scientific American 255 (No. 6) 58.
  3. Peebles, P.J.E. (1986). The mean mass density of the Universe. Nature 321 27.
  4. Rubin, V.C. (1983). Dark matter in spiral galaxies. Scientific American 248 (No. 6) 96.
  5. Trimble, V. (1987). Existence and nature of dark matter in the Universe. Ann. Rev. Astron. Ap. 25 425.
  6. Tucker, W. and Tucker, K. (1988). The Dark Matter. William Morrow and Co., New York.
  7. See also Cosmology, Galaxy Formation; Cosmology, Theories.