This paper presents a new technique for reconstructing the spatial distributions of hydrogen, temperature and metal abundance of a galaxy cluster. These quantities are worked out from the X-ray spectrum, modeled starting from few analytical functions describing their spatial distributions. These functions depend upon some parameters, determined by fitting the model to the observed spectrum. We have implemented this technique as a new model in the XSPEC software analysis package. We describe the details of the method, and apply it to work out the structure of the cluster A1795. We combine the observation of three satellites, exploiting the high spatial resolution of Chandra for the cluster core, the wide collecting area of XMM-Newton for the intermediate regions and the large field of view of Beppo-SAX for the outer regions. We also test the validity and precision of our method by i) comparing its results with those from a geometrical deprojection, ii) examining the spectral residuals at different radii of the cluster and iii) reprojecting the unfolded profiles and comparing them directly to the measured quantities. Our analytical method yields the parameters defining the spatial functions directly from the spectra. Their explicit knowledge allows a straightforward derivation of other indirect physical quantities like the gravitating mass, as well as a fast and easy estimate of the profiles uncertainties.
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