In galaxy clusters 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 ; in either case gravity is withstood by the corresponding , entropy-modulated pressure .
Jeans , with the DM ‘ entropy ’ set to K \propto r ^ { \alpha } and \alpha \approx 1.25 - 1.3 applying from groups to rich clusters , yields our radial \alpha - profiles ; these , compared to the empirical NFW 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 a few 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 } \propto k _ { c } ^ { -1 } and T _ { c } \propto k _ { c } ^ { 0.35 } , to yield radiative cooling times t _ { c } \approx 0.3 ( k _ { c } / 15 \mathrm { keV~ { } cm } ^ { 2 } ) ^ { 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 derive as limiting cases the classic polytropic \beta -models , and the ‘ mirror ’ model with T ( r ) \propto \sigma ^ { 2 } ( 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 \sigma ^ { 2 } ( r ) away from energy and entropy injections .
Finally , we discuss how the Supermodel connects information derived from X-ray and gravitational lensing observations .