4.2 Groups and Clusters
The traditional way to demonstrate the presence of dark matter has been to collect radial velocity data from the individual members of a group and cluster, from optical and/or radio data, and to apply some form of the virial theorem. This has been pioneered by Zwicky (1933), and became popular in the 70s and 80s. Data for many groups and clusters indicate high mass-to-light ratios, of order 100-500, which is much higher than expected for the mass-to-light ratios of individual galaxies which are of order 5-10 if they do not contain much dark matter.
Another way to study dark matter comes from X-ray data, assuming hydrostatic equilibrium. The enclosed mass within a given radius depends on the temperature of the hot gas giving rise to the X-ray emission, its radial gradient, and the gradient of the gas density. Mapping the latter using X-ray imaging is rather straightforward, but the determination of the temperature gradient is rather more difficult. In the 80s, data of the Einstein satellite were used to determine estimates of the dark matter content of several clusters of galaxies. Further improvement of the data came from the Rosat and ASCA satellites, and soon high quality data will come from the AXAF and XMM facilities.
A third way to determine masses of clusters is using gravitational lensing, using arcs and arclets. This has grown from the first demonstration of that arcs are due to lensing (Soucail et al. 1988) to an impressive field in its own right, in particular with imaging data from the Hubble Space Telescope, and the development of reliable estimates of the mass of the lensing object from the distorted shapes of more distant galaxies.
An interesting study comparing all three methods for a number of distant clusters is the one by Smail et al. (1997). They find reasonable agreement between the results from the X-ray and lensing data, but the optical data do not correspond that well, presumably due to the influence of both substructure and interlopers in the samples of galaxies used to determine the cluster velocity dispersion. In any case, they confirm the high mass-to-light ratios found previously, and give an upper bound to of ~ 0.4.
Compact groups of galaxies are a somewhat special case of ordinary groups, but their properties are quite interesting (see Hickson 1997 for a review). If there is little dark matter in a common halo around such groups, numerical simulations show that the galaxies should merge quite fast into one object. However, inclusion of a large extended common halo, such a the one found for HCG 62 from X-ray data, will retard the merging timescale to longer than a Hubble time (cf. Athanassoula, Makino & Bosma 1997). X-ray observations of sparser groups also indicate high mass-to-light ratios, and thus the presence of dark matter in them.