Deprojection of galaxy cluster X-ray, Sunyaev-Zeldovich temperature decrement, and weak-lensing mass maps

A general method of deprojecting two-dimensional images to reconstruct the three-dimensional structure of the projected object (specifically, X-ray, Sunyaev-Zeldovich [SZ], and gravitational lensing maps of rich clusters of galaxies), assuming axial symmetry, is considered. Here we test the applicability of the method for realistic, numerically simulated galaxy clusters, viewed from three orthogonal projections at four redshift outputs. We demonstrate that the assumption of axial symmetry is a good approximation for the three-dimensional structure in this ensemble of galaxy clusters. Applying the method, we demonstrate that a unique determination of the cluster inclination angle is possible from comparison between the SZ and X-ray images and, independently, between SZ and surface density maps. Moreover, the results from these comparisons are found to be consistent with each other and with the full three-dimensional structure inclination angle determination. The radial dark matter and gas density profiles as calculated from the actual and reconstructed three-dimensional distributions show a very good agreement. The method is also shown to provide a direct determination of the baryon fraction in clusters, independent of the cluster inclination angle.