Galaxy Clusters: A Novel Look at Diffuse Baryons Withstanding Dark Matter Gravity

In galaxy clusters, the equilibria of the intracluster plasma (ICP) and of the gravitationally dominant dark matter (DM) are governed by the hydrostatic equation and by the Jeans equation, respectively; in either case gravity is withstood by the corresponding, entropy-modulated pressure. Jeans, with the DM "entropy" set to K vprop r ^α and α ≈ 1.25-1.3 applying from groups to rich clusters, yields our radial α-profiles these, compared to the empirical Navarro-Frenk-White distribution, are flatter at the center and steeper in the outskirts as required by recent gravitational lensing data. In the ICP, on the other hand, 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 active galactic nuclei (AGNs); the resulting equilibrium is described by the exact yet simple formalism constituting our ICP Supermodel. With two parameters, this accurately represents the runs of density n(r) and temperature T(r) as required by up-to-date 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 vprop k ^-1 _c and T_c vprop k ^0.35 _c , to yield radiative cooling times t_c ≈ 0.3(k_c /15 keV cm²)^1.2 Gyr. We discuss the stability of the central values so focused: against radiative erosion of k_c in the cool dense conditions of CC clusters, that triggers recurrent AGN activities resetting it back; or against energy inputs from AGNs and mergers whose effects are saturated by the hot central conditions of NCC clusters. From the Supermodel, we also derive as limiting cases the classic polytropic β-models, and the "mirror" model with T(r) vprop σ²(r) suitable for NCC and CC clusters, respectively; these limiting cases highlight how the ICP temperature T(r) strives to mirror the DM velocity dispersion σ²(r) away from energy and entropy injections. Finally, we discuss how the Supermodel connects information derived from X-ray and gravitational lensing observations.