A New Interpretation of the Mass-Temperature Relation and Mass
  Calibration of Galaxy Clusters Based on the Fundamental Plane
  Observations and numerical simulations have shown that the relation between
the mass scaled with the critical density of the universe and the X-ray
temperature of galaxy clusters is approximately represented by $M_\Delta
\propto T_X^{3/2}$ (e.g. $\Delta=500$). This relation is often interpreted as
evidence that clusters are in virial equilibrium. However, the recently
discovered fundamental plane (FP) of clusters indicates that the temperature of
clusters primarily depends on a combination of the characteristic mass $M_s$
and radius $r_s$ of the Navarro-Frenk-White profile rather than $M_\Delta$.
Moreover, the angle of the FP revealed that clusters are not in virial
equilibrium because of continuous mass accretion from the surrounding matter.
By considering both the FP and the mass dependence of the cluster concentration
parameter, we show that this paradox can be solved and the relation $M_\Delta
\propto T_X^{3/2}$ actually reflects the central structure of clusters. We also
find that the intrinsic scatter in the halo concentration-mass relation can
largely account for the spread of clusters on the FP. We also show that X-ray
data alone form the FP and the angle and the position are consistent with those
of the FP constructed from gravitational lensing data. We demonstrate that a
possible shift between the two FPs can be used to calibrate cluster masses
obtained via X-ray observations.
