Galaxy Clusters, a Novel Look at Diffuse Baryons Withstanding Dark
  Matter Gravity
  [abridged] The equilibria of the intracluster plasma (ICP) and of the
gravitationally dominant dark matter (DM) are governed by the hydrostatic and
the Jeans equation. Jeans, with the DM `entropy' set to K ~ r^\alpha and \alpha
~ 1.25 - 1.3 applying from groups to rich clusters, yields our radial
\alpha-profiles. 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 our 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 n_c ~ k_c^-1 and T_c ~ k_c^0.35, to yield radiative
cooling times t_c ~ 0.3 (k_c/15 keV cm^2)^1.2 Gyr. We discuss the stability of
the central values so focused either in CC and NCC clusters. From the
Supermodel we derive as limiting cases the classic polytropic \beta-models, and
the `mirror' model with T(r) ~ \sigma^2(r) suitable for NCC and CC clusters,
respectively; these highlight how the ICP temperature T(r) tends to mirror the
DM velocity dispersion \sigma^2(r) away from entropy injections. Finally, we
discuss how the Supermodel connects information derived from X-ray and
gravitational lensing observations.
