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

¹ Laboratoire AIM, IRFU/Service d'Astrophysique – CEA/DSM – CNRS – Université Paris Diderot, Bât. 709, CEA-Saclay, 91191 Gif-sur-Yvette Cedex, France e-mail: gabriel.pratt@cea.fr
² Max-Planck-Institut für extraterrestriche Physik, Giessenbachstraße, 85748 Garching, Germany
³ School of Physics and Astronomy, University of Birmingham, Edgbaston, Birmingham B15 2TT, UK
⁴ School of Physics and Astronomy, University of Southampton, Southampton, Hampshire, SO17 1BJ, UK
⁵ Department of Physics and Astronomy, Michigan State University, East Lansing, MI 48824-2320, USA
⁶ Dipartimento di Astronomia dell'Università di Trieste, via Tiepolo 11, 34131 Trieste, Italy
⁷ Institute for Computational Cosmology, Department of Physics, Durham University, South Road, Durham DH1 3LE, UK

Received: 16 September 2009
Accepted: 10 November 2009

Abstract

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 R₁₀₀₀ in all systems and out to R₅₀₀ 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 R₅₀₀, 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 R₅₀₀. 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 K₀. However, we are unable to distinguish between a bimodal or a left-skewed distribution of K₀ 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 R₁₀₀₀, 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.