Halo Concentrations and the Fundamental Plane of Galaxy Clusters
  According to the standard cold dark matter (CDM) cosmology, the structure of
dark halos including those of galaxy clusters reflects their mass accretion
history. Older clusters tend to be more concentrated than younger clusters.
Their structure, represented by the characteristic radius $r_s$ and mass $M_s$
of the Navarro--Frenk--White (NFW) density profile, is related to their
formation time. In~this study, we showed that $r_s$, $M_s$, and the X-ray
temperature of the intracluster medium (ICM), $T_X$, form a thin plane in the
space of $(\log r_s, \log M_s, \log T_X)$. This tight correlation indicates
that the ICM temperature is also determined by the formation time of individual
clusters. Numerical simulations showed that clusters move along the fundamental
plane as they evolve. The plane and the cluster evolution within the plane
could be explained by a similarity solution of structure formation of the
universe. The angle of the plane shows that clusters have not achieved "virial
equilibrium" in the sense that mass/size growth and pressure at the boundaries
cannot be ignored. The distribution of clusters on the plane was related to the
intrinsic scatter in the halo concentration--mass relation, which originated
from the variety of cluster ages. The well-known mass--temperature relation of
clusters ($M_\Delta\propto T_X^{3/2}$) can be explained by the fundamental
plane and the mass dependence of the halo concentration without the assumption
of virial equilibrium. The fundamental plane could also be used for calibration
of cluster masses.
