The equilibria of the intracluster plasma (ICP) and of the gravitationally dominant dark matter (DM) are governed by the hydrostatic and the Jeans equation, respectively. Jeans, with the DM “entropy” set to K∝rα and α~1.25–1.3 applying from groups to rich clusters, yields our radial α-profiles for DM density and gravitational potential. In the ICP the entropy run k(r) is mainly shaped by shocks, as steadily set by supersonic accretion of gas at the cluster boundary, and intermittently driven from the center by merging events or by AGNs; the resulting equilibrium is described by the exact yet simple formalism constituting the ICP “Supermodel”. With a few parameters, this accurately represents the runs of density n(r) and temperature T(r) as required by recent X-ray data on surface brightness and spectroscopy for both cool core (CC) and non cool core (NCC) clusters; the former are marked by a middle temperature peak, whose location is predicted from rich clusters to groups. The Supermodel inversely links the inner runs of n(r) and T(r), and highlights their central scaling with entropy nc∝kc−1 and Tc∝kc0.35, to yield radiative cooling times tc≈0.3 (kc/15keV cm2)1.2Gy. We discuss the stability of the central values so focused both in CC and NCC clusters. From the Supermodel we derive as limiting cases the classic polytropic β-models, and the “mirror” model with T(r)∝σ2(r) suitable for NCC and CC clusters, respectively; these highlight how the ICP temperature T(r) tends to mirror the DM velocity dispersion σ2(r) away from entropy injections. Finally, we discuss how the Supermodel connects information derived from X-ray and gravitational lensing observations.
