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Observational determinations of the correlation between the characteristicdensity delta_c and the virial mass M_vir of dark halos constitute a criticaltest for models of hierarchical structure formation. Using the dynamicalproperties of dark halos reconstructed from the galaxy distributions in massivesystems (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 rangefrom 10**10 to 10**15 solar masses, which is in gross consistency with theprediction 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-rayemitting gas and the hydrostatic equilibrium hypothesis, which claimed ashallower scale-free spectrum of n=-1 for initial density fluctuations, maysuffer from nongravitational heating influence especially in low-mass systems.Comment: 5 pages, 1 figure, accepted for publication in A&

Observational tests of the $\delta_{\mathsf{c}}{-}$ $\vec M$ $_{\mathsf{vir}}$ relation in hierarchical clustering models