Toward mapping turbulence in the intracluster medium

Context. The NewAthena mission planned for launch in the late 2030s will carry X-IFU, an integral field unit spectrometer that will obtain unique insights into the X-ray hot Universe through its combination of spectral and spatial capabilities. Its ability to deliver spatially resolved observations with a high spectral resolution will allow for detailed mapping of turbulent velocities in the hot gas of galaxy clusters, offering capabilities beyond those of previous missions to study their complex dynamics. 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 including masked autoencoders 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. Results. 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 underestimation of the sources of variance by comparing the results to our previous paper. We confirm that cluster-to-cluster variations in the stochastic velocity field (i.e., sample variance) severely impact 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 high-resolution spectroscopic X-ray observations, such as the ones expected from X-IFU/NewAthena.