Triaxiality in galaxy clusters: Mass versus Potential reconstructions

Accounting for the triaxial shapes of galaxy clusters is expected to become important in the context of the upcoming cosmological surveys. While the distribution of matter in galaxy clusters cannot be described with simple geometrical models without loss of information, their gravitational potential can be very well approximated by a sphere or a spheroid. We study the shape of the isodensity and isopotential contours in a relaxed and dynamically active simulated clusters, with both a principal component analysis (PCA) and an elliptical fitting procedure. We then analyze how the choice of the substructure removal algorithm and the representation of the data (cumulative vs thin shell) affect the results. For the matter distribution, we find that the orientation and axis ratio of the isodensity contours are highly degenerate with the presence of substructures and unstable against the representation of the data. In addition, we observe that as the derived cluster shape depends on the method used for removing the substructures, thermodynamic properties extracted from, for instance, the X-ray emissivity profile, suffer from this additional, and often underestimated, bias. In contrast, as the potential is smoother and more spherical than the matter density, the PCA results on the isopotential contours are robust against the choice of representations of the data, and converge toward simple geometrical models for both the relaxed and the dynamically active clusters. The fact that clusters potentials can be represented by simple geometrical models and reconstructed with a low level of systematics for both dynamically active and relaxed clusters (see Tchernin et al. 2020), suggests that by characterizing galaxy clusters by their potential rather than by their mass, dynamically active and relaxed clusters could be combined in cosmological studies, improving statistics and lowering scatter.[abr.]