Observational tests of the δc Mvir relation in hierarchical clustering models

Observational determinations of the correlation between the characteristic density delta (c) and the virial mass M-vir of dark halos constitute a critical test for models of hierarchical structure formation. Using the dynamical properties of dark halos reconstructed from the galaxy distributions in massive systems (groups/clusters) and the rotation curves in less massive systems (dwarf, low surface brightness and spiral galaxies) drawn from the literature, we confirm the existence of the delta (c)-M-vir relation over a broad mass range from 10(10) M-circle dot to 10(15) M-circle dot, which is in gross consistency with the prediction of a at cosmological model with Omega (M) = 0.3 and Omega (A) = 0.7. It is pointed out that previous analyses based on the measurements of X-ray emitting gas and the hydrostatic equilibrium hypothesis, which claimed a shallower scale-free spectrum of n approximate to -1 for initial density fluctuations, may suffer from nongravitational heating influence especially in low-mass systems.