Entropy of gas and dark matter in galaxy clusters

Abstract

On the basis of a large-scale 'adiabatic', namely non-radiative and non-dissipative, cosmological smooth particle hydrodynamic simulation we compare the entropy profiles of the gas and the dark matter (DM) in galaxy clusters. We employ the quantity Kg = 3kBTgρ g-2/3/(μmp) = σg2ρg-2/3 as measure for the entropy of the intracluster gas. By analogy the DM entropy is defined as KDM = σDM2ρDM-2/3 (σDM2 is the 3D velocity dispersion of the DM). The DM entropy is related to the DM phase-space density by KDM ∝ QDM-2/3. In accord with other studies, the radial DM phase-space density profile follows a power-law behaviour, QDM ∝ r-1.82, which corresponds to KDM ∝ r1.21. The simulated intracluster gas has a flat entropy core within (0.8 ± 0.4)Rs, where Rs is the Navarro-Frenk-White scale radius. The outer profile follows the DM behaviour, Kg ∝ r 1.21, in close agreement with X-ray observations. Upon scaling the DM and gas densities by their mean cosmological values, we find that outside the entropy core a constant ratio of Kg/KDM = 0.71 ± 0.18 prevails. By extending the definition of the gas temperature to include also the bulk kinetic energy the ratio of the DM and gas extended entropy is found to be unity for r ≳ 0.8Rs. The constant ratio of the gas thermal entropy to that of the DM implies that observations of the intracluster gas can provide an almost direct probe of the DM. © 2007 RAS.