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The X-ray Fundamental Plane of Clusters of Galaxies
Yutaka Fujita
National Astronomical Observatory, Japan
We analyze the relations among central gas density, core radius,
and temperature of X-ray clusters by plotting the observational
data in the three-dimensional (log  gas;0 , log r c , and log T gas )
space and nd that the data lie on a 'fundamental plane'. Its
existence implies that the clusters form a two-parameter family.
The data on the plane still has a correlation and form a band on
the plane. The observed relation LX / T 3
gas turns out to be the
cross section of the band perpendicular to the major axis. The
two parameters describing the plane are formation redshift and
temperature of clusters. Based on the two-parameter family na-
ture of X-ray clusters of galaxies, we discuss the formation history
of clusters and cosmological parameters of the universe. Utilizing
the spherical collapse model of cluster formation, we nd that the
observed relations among the density, radius, and temperature of
clusters imply that cluster formation occurs in a wide range of
redshift. The observed relations favor the low-density universe.
We also nd that the preheating of the intracluster medium aect
the form of the fundamental plane. The observed form indicates
that the preheated temperature is about 0.5-2 keV and strongly
suggests that not only for the dark halo but also for the intraclus-
ter gas the core structure preserves information about the cluster
formation.
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