Idealized observations: ζ_x at the corresponding true r_x whilst varying models and other factors (different gas electron density models: interpolation model, modified β-model with one β-component, binned model (upper left); different dark-matter mass models: NFW model, GNFW model, Einasto model (upper right); different binnings (lower left); different center positions for the fit: determined center according to Sect. 3.1, true position of the minimum of the gravitational potential according to the simulations (lower right)). If not stated otherwise, we assume an interpolation model for the gas electron density and an NFW model for the dark-matter mass. The data points at the true r₂₀₀ that are based on an extrapolation of the fitted profile are shown as empty symbols. More information can be found in the text.