  We investigate core structures of X-ray emitting intracluster gas based on
the so-called beta-model, which is an isothermal hydrostatic model often used
in observational studies. We reconsider the beta-model and find that the virial
temperature T_vir of a cluster may be represented better by beta T_X than T_X,
where beta is the parameter obtained from the X-ray surface brightness and T_X
is the emission-weighted mean temperature of the gas. We investigate 121
clusters observed by ROSAT and ASCA and find that the luminosity-temperature
relation L_X - beta T_X is less steep than L_X - T_X. We classify the clusters
into two core-size groups in order to investigate their properties in detail.
While in the larger core group the core radius is marginally proportional to
the virial radius, no significant relation is found for the smaller core group.
This may suggest that the smaller cores reflect the presence of cD galaxies,
effect of radiative cooling or asymmetry in the surface brightness. We examine
such possibilities, and find that the clusters of smaller cores have shorter
cooling time than the Hubble time, while no significant correlation is found
with cD or asymmetry. We carry out hydrodynamical calculations to simulate the
beta-model, intending to see the behavior of the isothermal gas under the
gravitational potential including the dark matter and galaxies with or without
a central cD galaxy. Calculations show r_c \propto r_vir and T_vir \simeq beta
T consistently with our consideration to the beta-model. Also is found from
calculations that the presence of a large cD galaxy may form a gas core \sim 40
kpc, which seems too small to account for the range of the core sizes, 40--80
kpc, of the smaller core group.
