2018ApJ...863...37F

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_Δ∝T_X^3/2 (e.g., Δ=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_Δ. 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_Δ∝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.