X-ray gas density profile of clusters of galaxies from the universal dark matter halo

The X-ray cluster gas density distribution in hydrostatic equilibrium is computed from the universal density profile of the dark matter halo recently proposed by Navarro, Frenk and White (1996, 1997). If one assumes the isothermality, the resulting distribution is well approximated by the conventional $\beta$-model. We predict the core radius $r_{c}$, the $\beta$-parameter, and the X-ray luminosity of clusters as a function of the temperature $T_{X}$ of clusters in some representative cosmological models, and compare them with observations and results of numerical simulations. The predicted size of $r_{c}$ is a factor of ($3 \sim 10$) smaller than the average of observed values. If both the universal density profile and the hydrostatic equilibrium are reasonable approximation to the truth, then this suggests either that the previous X-ray observations systematically overestimate the core radius of gas densities in clusters of galaxies, or that some important physical mechanisms, which significantly increase the core radius, is still missing.