Entropy of gas and dark matter in galaxy clusters
  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. The quantity K_g = T_g \rho_g^{-2/3} provides a measure for the entropy of the intra-cluster gas. By analogy with the thermodynamic variables of the gas the velocity dispersion of the DM is associated with a formal temperature and thereby K_DM = \sigma_DM^2 \rho_DM^{-2/3} is defined. This DM entropy is related to the DM phase space density by K_DM \propto Q_DM^{-2/3}. In accord with other studies the DM phase space density follows a power law behaviour, Q_DM \propto r^{-1.82}, which corresponds to K_DM \propto r^{1.21}. The simulated intra-cluster gas has a flat entropy core within (0.8 \pm 0.4) R_s, where R_s is the NFW scale radius. The outer profile follows the DM behaviour, K_g \propto 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 \pm 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 > 0.8 R_s. The constant ratio of the gas thermal entropy to that of the DM implies that observations of the intra-cluster gas can provide an almost direct probe of the DM. 
A. Faltenbacher (1), Y. Hoffman (2), S. Gottloeber (3), G. Yepes (4)   ((1) UC Santa Cruz, (2) HU Jerusalem, (3) AIP Potsdam...