2018ApJ...857..118F

In cold dark-matter (CDM) cosmology, objects in the universe have grown under the effect of gravity of dark matter. The intracluster gas in a galaxy cluster was heated when the dark-matter halo formed through gravitational collapse. The potential energy of the gas was converted to thermal energy through this process. However, this process and the thermodynamic history of the gas have not been clearly characterized in connection with the formation and evolution of the internal structure of dark-matter halos. Here, we show that observational CLASH data of high-mass galaxy clusters lie on a plane in the three-dimensional logarithmic space of their characteristic radius r_s, mass M_s, and X-ray temperature T_X with a very small orthogonal scatter. The tight correlation indicates that the gas temperature was determined at a specific cluster formation time, which is encoded in r_s and M_s. The plane is tilted with respect to T_X ∝ M_s/r_s, which is the plane expected in the case of simplified virial equilibrium. We show that this tilt can be explained by a similarity solution, which indicates that clusters are not isolated but continuously growing through matter accretion from their outer environments. Numerical simulations reproduce the observed plane and its angle. This result holds independently of the gas physics implemented in the code, revealing the fundamental origin of this plane.