Publication
Context. Observations of the hot gas in distant clusters of galaxies, though challenging, are key to understanding the role of intense galaxy activity, supermassive black hole feedback, and chemical enrichment in the process of massive halo assembly.|Aims. Using X-ray hyperspectral data alone, we assess the feasibility of retrieving the thermodynamical hot gas properties and chemical abundances of a z = 2 galaxy cluster of mass M-500 = 7 x 10(13) M-circle dot, extracted from the Hydrangea hydrodynamical simulations.|Methods. We created mock X-ray observations of the future X-ray Integral Field Unit (X-IFU) on board the Athena mission. By forward-modelling the measured 0:4 1 keV surface brightness, the projected gas temperature and abundance profiles, we reconstructed the three-dimensional distribution for the gas density, pressure, temperature, and entropy.|Results. Thanks to its large field of view, high throughput, and exquisite spectral resolution, one X-IFU exposure lasting 100 ks enabled the reconstruction of density and pressure profiles with 20% precision out to a characteristic radius of R-500, accounting for each quantity's intrinsic dispersion in the Hydrangea simulations. Reconstruction of abundance profiles requires both higher signal-to-noise ratios and specific binning schemes. We assess the enhancement brought by longer exposures and by observing the same object at later evolutionary stages (at z = 1 and 1.5).|Conclusions. Our analysis highlights the importance of scatter in the radially binned gas properties, which induces significant e ffects on the observed projected quantities. The fidelity of the reconstruction of gas profiles is sensitive to the degree of mixing of the gas components along the line of sight. Future analyses should aim to involve dedicated hyper-spectral models and fitting methods that are able to grasp the complexity of such three-dimensional, multi-phase, di ffuse gas structures.