The X-Ray Fundamental Plane and LX-T Relation of Clusters of Galaxies

We analyze the relations among the central gas density, the core radius, and the temperature of X-ray clusters by plotting the observational data in the three-dimensional (log ρ0, log R, log T)-space and find 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 have a correlation and form a band on the plane. The observed relation LX ∝ T3 turns out to be the cross section of the band perpendicular to the major axis, while the major axis is found to describe the virial density. We discuss the implications of this two-parameter family nature of X-ray clusters.