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We discuss mathematical methods for analysis of the X-ray observational data to obtain a distribution of the main physical parameters of X-ray galaxy clusters. First of all, this is the binning of galaxy cluster imagery on the concentration rings around the central parts. It allows us to calculate the integrated amount of pixels, which contain the information on temperature and other parameters of hot diffuse gas, cooling flows etc., as well as to detach the central engine of galaxy cluster. The another approach is the so-called “contour binning algorithm”, which allows us to select contours on an adaptively smoothed map in such a manner that the generated bins closely fit the surface brightness. This method is mostly informative when the spectral properties follow surface brightness and/or their distribution is not smooth. We compare these methods using the Chandra observational data for A2029, A2107, and A2151 galaxy clusters. We consider a wavelet analysis likely the “Mexican Hat” as an additional and important approach for the X-ray image processing to determine not only the regions of cores in clusters but also substructures occupied by galaxies and ICM regions while processing their X-ray image contour binning. We confirm that the detachment of substructures should precede further research because of the existence of subclustering imposes doubt in the validity of the hydrostatic eqilibrium hypothesis of the X-ray gas when the dynamical matter distribution and the profiles of various physical parameters along radii are considered. A combined application of these three techniques can significantly complement our understanding of the physical processes that occur in X-ray galaxy clusters.

NEW APPROACH FOR ANALYSIS OF THE X-RAY DATA IN CORES OF GALAXY CLUSTERS: BINNING ON THE CONCENTRATION RINGS, CONTOUR BINNING, AND WAVELET TRANSFORMS