Yp. Jing et G. Borner, THE VELOCITY DISPERSION PROFILES OF CLUSTERS OF GALAXIES - A COSMOLOGICAL TEST AND THE SAMPLING EFFECT, Monthly Notices of the Royal Astronomical Society, 278(1), 1996, pp. 321-325
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.