THE VELOCITY DISPERSION PROFILES OF CLUSTERS OF GALAXIES - A COSMOLOGICAL TEST AND THE SAMPLING EFFECT

In this paper we investigate the velocity dispersion profiles of clust ers of galaxies for seven cosmological models. One model is the SCDM m odel, and the others are six low-density models with the density param eter Omega = 0.1, 0.2 or 0.3 and with or without a cosmological consta nt Lambda = 1-Omega. We find that the velocity dispersion profiles dep end both on Omega and on Lambda. For Lambda = 0, the profiles are stee per in a lower-Omega model than in a higher-Omega one. The cosmologica l constant significantly weakens the dependence on Omega: the differen ce in the profile distributions between two flat models is much smalle r than that between the two corresponding open models with the same Om ega. These results in principle can be used to constrain the cosmologi cal parameters when a large sample of velocity dispersion profiles is available. Motivated by the practical situation that a sample of simil ar to 100 clusters with similar to 100 measured redshifts per cluster is still the best sample available for the foreseeable future, we exam ine carefully to what degree the cosmological parameters can be constr ained by the velocity dispersion profiles of such a sample of clusters . The limited sampling around clusters and the limited number of clust ers seriously degrade the discriminative power of the velocity dispers ion profiles among cosmological models. We find that the five models w ith Omega greater than or equal to 0.2 cannot be distinguished by this type of observation. Owing to the limited sampling, one should be ver y cautious in extracting information about the density profile and/or the dynamics around single clusters from the diluted velocity dispersi on profiles.