Correlation between the halo concentration c and the virial mass M-vir determined from X-ray clusters

Numerical simulations of structure formation have suggested that there exis ts a good correlation between the halo concentration c (or the characterist ic density delta(c)) and the virial mass M-vir for any virialized dark halo described by the Navarro, Frenk, & White density profile. In this Letter, we present an observational determination of the c-M-vir (or delta(c)-M-vir ) relation in the mass range of similar to 10(14) M. < M-vir <similar to 10 (16) M. using a sample of 63 X-ray luminous clusters. The best-fit power-la w relation, which is roughly independent of the values of Omega(M) and Omeg a(Lambda), is c proportional to M-vir(-0.5) or delta(c) proportional to M-v ir(-1.2), indicating n approximate to -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.