ERGO-ML and how to directly infer the multi-temperature nature of intra-cluster gas: simulation-based inference with TNG-Cluster

Though galaxy clusters are virialized and mostly in thermodynamic equilibrium, their internal gas thermodynamics are complex. The hot gas is multiphase and spatially inhomogeneous. The exact state of the gas contains important information about the internal physics governing clusters, however, measuring the multiphase distribution of the X-ray emitting gas is hard if not impossible with current observational methods. In this work (part of the ERGO-ML series), we present a direct inference method of the multiphase temperature distribution of the gas in the intra-cluster medium (ICM), applicable over a large range of spatial and mass scales. It works using different spectral resolutions (XRISM-like and Chandra-like) and realistic photon noise. Our method is an application of simulation-based inference. We train a neural-network on X-ray spectra in the range 0.1-10 keV, generated for about 10 5 sightlines of massive clusters (M 200c = 10 14.2-15.2 M) from the TNG-Cluster cosmological MHD galaxy simulation. We show that our method recovers the mass-weighted temperature of both individual sightlines and entire clusters with an average prediction error of < 0.01 dex, and the total gas mass within 0.04 dex. On top of that it gives accurate measures of the fraction of sub- and super-virial gas. Our method is capable of extracting the cooler gas phase even if the flux contribution is 3 orders of magnitude below that of the virial gas phase. We then show that we can accurately recover the spatial distribution of multi-phase gas both in relaxed and merging systems. This opens the way to studies of the multiphase nature of the ICM and the violent physics of feedback, accretion and merging.