Observational tests of the delta_c-M_vir 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 to 10**15 solar masses, which is in gross consistency with the prediction of a flat cosmological model with Omega_M=0.3 and Omega_Lambda=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=-1 for initial density fluctuations, may suffer from nongravitational heating influence especially in low-mass systems.