Gas entropy in a representative sample of nearby X-ray galaxy clusters (REXCESS): relationship to gas mass fraction

We examine the radial entropy distribution and its scaling using 31 nearby galaxy clusters from the representative XMM-Newton cluster structure survey (REXCESS), a sample in the temperature range 2-9 keV selected in X-ray luminosity only, with no bias toward any particular morphological type. The entropy profiles are robustly measured at least out to R-1000 in all systems and out to R-500 in thirteen systems. Compared to theoretical expectations from non-radiative cosmological simulations, the observed distributions show a radial and mass-dependent excess entropy, such that the excess is greater and extends to larger radii in lower mass systems. At R-500, the mass dependence and entropy excess are both negligible within the large observational and theoretical uncertainties. Mirroring this behaviour, the scaling of gas entropy is shallower than self-similar in the inner regions, but steepens with radius, becoming consistent with self-similar at R-500. There is a large dispersion in scaled entropy in the inner regions, apparently linked to the presence of cool cores and dynamical activity; at larger radii the dispersion decreases by approximately a factor of two to 30 per cent, and the dichotomy between subsamples disappears. There are two peaks in the distribution of both inner slope and, after parameterising the profiles with a power law plus constant model, in central entropy K-0. However, we are unable to distinguish between a bimodal or a left-skewed distribution of K-0 with the present data. The distribution of outer slopes is unimodal with a median value of 0.98, and there is a clear correlation of outer slope with temperature. Renormalising the dimensionless entropy profiles by the gas mass fraction profile f(gas)(