Correlation between the Halo Concentration [CLC][ITAL]c[/ITAL][/CLC] and the Virial Mass [ITAL]M[/ITAL][TINF][CLC]vir[/CLC][/TINF] Determined from X-Ray Clusters

Numerical simulations of structure formation have suggested that there exists a good correlation between the halo concentration c (or the characteristic density deltac) and the virial mass Mvir for any virialized dark halo described by the Navarro, Frenk, & White density profile. In this Letter, we present an observational determination of the c-Mvir (or deltac-Mvir) relation in the mass range of approximately 1014 M middle dot in circle<Mvir< approximately 1016 M middle dot in circle using a sample of 63 X-ray luminous clusters. The best-fit power-law relation, which is roughly independent of the values of OmegaM and OmegaLambda, is c~M-0.5vir or deltac~M-1.2vir, indicating n approximately -0.7 for a scale-free power spectrum of the primordial density fluctuations. We discuss the possible reasons for the conflict with the predictions by typical cold dark matter models.