Alexeï Molin, Simon Dupourqué, Nicolas Clerc, Étienne Pointecouteau, François Pajot, Edoardo Cucchetti

Context. The NewAthena mission planned for launch in the mid-2030s will carry X-IFU, an integral field unit spectrometer that will enable unique insight in the X-ray hot universe through its combination of spectral and spatial capabilities. The high spectral resolution will allow a mapping of turbulent velocities of the hot gas in galaxy clusters, providing an unrivaled way to study the complex dynamics within galaxy clusters. Aims. This is the fourth in a series of papers aimed at forecasting the ability to investigate turbulence in the intracluster medium through the observation of the centroid shift caused by turbulent motions of the gas. In this paper we improve on previous methods by investigating the ability of simulation-based inference (SBI) to constrain the underlying nature of velocity fluctuations through the use of standard observational diagnostics, such as the structure function. Methods. We rely on a complex architecture of neural networks in order to model the likelihood and posterior distributions relevant to our case. We investigate its capability to retrieve the turbulence parameters on mock observations, and explore its capability to use alternative summary statistics. Conclusions. Our trained models are able to infer the parameters of the intracluster gas velocity power-spectrum in independently simulated X-IFU observations of a galaxy cluster. We evaluated the precision of the recovery for different models. We show the necessity to use methods such as SBI to avoid an under-estimation of the sources of variance by comparing the results to our previous paper. We confirm that sample variance severely impacts the precision of recovered turbulent features. Our results demonstrate the need for advanced modeling methods to tackle the complexity of the physical information nested within future observations expected from X-IFU/NewAthena.