A case study of early galaxy cluster with the Athena X-IFU

Context: Observations of the hot gas in distant clusters of galaxies, though challenging, are key to understand the role of intense galaxy activity, super-massive black hole feedback and chemical enrichment in the process of massive halos assembly. Aims: We assess the feasibility to retrieve, using X-ray hyperspectral data only, the thermodymamical hot gas properties and chemical abundances of a $z=2$ galaxy cluster of mass M500=7 x $10^{13} M_{\odot}$, extracted from the Hydrangea hydrodynamical simulation. Methods: We create mock X-ray observations of the future X-ray Integral Field Unit (X-IFU) onboard the Athena mission. By forward-modeling the measured 0.4-1 keV surface brightness, the projected gas temperature and abundance profiles, we reconstruct 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 100ks enables reconstructing density and pressure profiles with 20% precision out to a characteristic radius of R500, 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 ($z=1-1.5$). Conclusions: Our analysis highlights the importance of scatter in the radially binned gas properties, which induces significant effects on the observed projected quantities. The fidelity of the reconstruction of gas profiles is sensitive to the degree of gas components mixing along the line-of-sight. Future analyses should aim at involving dedicated hyper-spectral models and fitting methods that are able to grasp the complexity of such three-dimensional, multi-phase, diffuse gas structures.