On the deprojection of clusters of galaxies combining X-ray, Sunyaev-Zeldovich temperature decrement and gravitational lensing maps

Knowledge of the intrinsic shape of galaxy clusters is very important in investigating cosmic structure formation and astrophysical processes. The reconstruction of the 3D structure usually relies on deprojecting 2D X-ray, Sunyaev-Zeldovich (SZ) and/or gravitational lensing observations. As known, a joint analysis of these data sets can provide the elongation of the cluster along the line of sight together with its length and width in the plane of the sky. An unbiased measurement of the Hubble constant can be also inferred. Due to some intrinsic degeneracies, the observational constraints obtained from such projected data sets are not enough to allow an unique inversion. In general, the projected maps can be at the same time compatible with prolate, oblate and with many triaxial configurations. Even a prolate cluster might be interpreted as an oblate system and vice versa. Assuming that the cluster is axially symmetric is likely to overestimate the intrinsic ellipticity, whereas the system always looks rounder performing the inversion under the hypothesis of a triaxial cluster aligned with the line of sight. In general, analysing triaxial clusters under the prolate or oblate assumption may introduce strong biases even when the clusters are actually near to axial symmetry whereas the systematics introduced assuming the cluster to be aligned with the line of sight are more under control.