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)(<R), leads to a remarkable reduction in the scatter, implying that gas mass fraction variations with radius and mass are the cause of the observed entropy structural and scaling properties. The results are consistent with the picture of a cluster population in which entropy modification is centrally concentrated and extends to larger radii at lower mass, leading to both a radial and a mass-dependence in the gas mass fraction, but which is increasingly self-similar at large radius. The observed normalisation, however, would suggest entropy modification at least up to R-1000, and even beyond, in all but the most massive systems. We discuss a tentative scenario to explain the observed behaviour of the entropy and gas mass fraction in the REXCESS sample, in which a combination of extra heating and merger mixing maintains an elevated central entropy level in the majority of the population, and a smaller fraction of systems is able to develop a cool core.