2007MNRAS.376.1327F

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 K_g= 3k_BT_gρ^–2/3_g/(µm_p) = σ²_gρ^–2/3_gas measure for the entropy of the intracluster gas. By analogy the DM entropy is defined as K_DM = σ²_DMρ^–2/3_DM(σ²_DMis the 3D velocity dispersion of the DM). The DM entropy is related to the DM phase-space density by K_DM∝ Q^–2/3_DM. In accord with other studies, the radial DM phase-space density profile follows a power-law behaviour, Q_DM ∝ r^–1.82, which corresponds to K_DM∝ r^1.21. The simulated intracluster gas has a flat entropy core within (0.8 ±0.4)R_s, where R_sis the Navarro-Frenk-White scale radius. The outer profile follows the DM behaviour, K_g∝ 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 K_g/K_DM= 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 ≳ 0.8R_s. 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.