  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.
