Gas Distributions in an Unbiased Sample of Low-z Galaxy Clusters

We present an improved technique for the deprojection and PSF-deconvolution of X-ray surface brightness profiles of galaxy clusters. Our method is tested using simulated profiles, XMM-Newton and Chandra data, and is shown to result in unbiased gas density profiles that retain full information about the gas distribution. We then apply the method to surface brightness profiles of an unbiased sample of nearby clusters from the XMM Legacy Project for the Study of Galaxy Cluster Structure, and discuss the scaling properties of the gas density profiles. 1. AN IMPROVED TECHIQUE FOR MEASURING GAS DENSITY PROFILES We have developed a regularisation procedure for the direct deprojection and PSF-deconvolution of X-ray surface brightness profiles. Our technique allows us to obtain accurate gas density profiles in a straightforward manner from X-ray observations, avoiding a priori assumptions about the functional form of the density distribution and making full use of the information in the surface brightness profile, unlike the use of analytical models. Our regularisation procedure is adapted from the Philips-Towmey method used by Bouchet (1995) for the deconvolution of gamma-ray spectra. The effects of projection and PSF blurring can be expressed as a 2D redistribution matrix, determined from geometrical calculations and detector characteristics, which is multiplied by the emitted profile to produce an observed surface brightness profile. Since directly solving this equation for the emitted profile is an inverse problem, we minimise the amplification of errors in the derived emitted profile by constraining the solution to be smooth (minimising the sum of the squares of the 2nd derivatives about each point), using a cross-validation technique to systematically choose a regularisation coefficient based on distinguishing between smooth (i.e. physically plausible) variations and noise (e.g. Wahba 1978). In Fig 1 we show the results of Monte Carlo simulations of profiles obtained by projection and PSF convolution of the simulated emission from model density distributions. We used the AB model of Pratt & Arnaud (2002), a modified β-model that can also fit central cusps: