  We investigate the origin of the variation of the gas mass fraction in the
core of galaxy clusters, which was indicated by our work on the X-ray
fundamental plane. The adopted model supposes that the gas distribution
characterized by the slope parameter is related to the preheated temperature.
Comparison with observations of relatively hot (~> 3 keV) and low redshift
clusters suggests that the preheated temperature is about 0.5-2 keV, which is
higher than expected from the conventional galactic wind model and possibly
suggests the need for additional heating such as quasars or gravitational
heating on the largest scales at high redshift. The dispersion of the preheated
temperature may be attributed to the gravitational heating in subclusters. We
calculate the central gas fraction of a cluster from the gas distribution,
assuming that the global gas mass fraction is constant within a virial radius
at the time of the cluster collapse. We find that the central gas density thus
calculated is in good agreement with the observed one, which suggests that the
variation of gas mass fraction in cluster cores appears to be explained by
breaking the self-similarity in clusters due to preheated gas. We also find
that this model does not change major conclusions on the fundamental plane and
its cosmological implications obtained in previous papers, which strongly
suggests that not only for the dark halo but also for the intracluster gas the
core structure preserves information about the cluster formation.
