Non-parametric modeling of the intra-cluster gas using APEX-SZ bolometer imaging data

Aims. We aim to demonstrate the usability of mm-wavelength imaging data obtained from the APEX-SZ bolometer array to derive the radial temperature profile of the hot intra-cluster gas out to radius r(500) and beyond. The goal is to study the physical properties of the intra-cluster gas by using a non-parametric de-projection method that is, aside from the assumption of spherical symmetry, free from modeling bias. Methods. We use publicly available X-ray spectroscopic-imaging data in the 0.7-2 keV energy band from the XMM-Newton observatory and our Sunyaev-Zel'dovich Effect (SZE) imaging data from the APEX-SZ experiment at 150 GHz to de-project the density and temperature profiles for a well-studied relaxed cluster, Abell 2204. We derive the gas density, temperature and entropy profiles assuming spherical symmetry, and obtain the total mass profile under the assumption of hydrostatic equilibrium. For comparison with X-ray spectroscopic temperature models, a re-analysis of recent Chandra observation is done with the latest calibration updates. We compare the results with that from an unrelaxed cluster, Abell 2163, to illustrate some differences between relaxed and merging systems. Results. Using the non-parametric modeling, we demonstrate a decrease of gas temperature in the cluster outskirts, and also measure gas entropy profiles, both of which are done for the first time independently of X-ray spectroscopy using the SZE and X-ray imaging data. The gas entropy measurement in the central 100 kpc shows the usability of APEX-SZ data for inferring cluster dynamical states with this method. The contribution of the SZE systematic uncertainties in measuring T-e at large radii is shown to be small compared to XMM-Newton and Chandra systematic spectroscopic errors. The total mass profile obtained using the hydrostatic equilibrium assumption is in agreement with the published X-ray and weak lensing results; the upper limit on M-200 derived from the non-parametric method is consistent with the NFW model prediction from weak lensing analysis.