XRISM constraints on the velocity power spectrum in the Coma cluster

The velocity field of intracluster gas in galaxy clusters contains key information on the virialization of infalling material, the dissipation of AGN energy into the surrounding medium, and the validity of the hydrostatic hypothesis. The statistical properties of the velocity field are characterized by its fluctuation power spectrum, which is usually expected to be well described by an injection scale and a turbulent cascade. Here we propose a simulation-based inference technique to retrieve the properties of the velocity power spectrum from X-ray micro-calorimeter data by generating simulations of Gaussian random fields from a parametric power spectrum model. We forward model the measured bulk velocities and velocity dispersions by including the most relevant observational effects (projection, emissivity weighting, PSF smearing). We then train a neural network to learn the mapping between the power spectrum parameters and the generated data vectors. Considering a three-parameter model describing turbulent energy injection on large scales and a power-law cascade, we found that two XRISM/Resolve pointings are sufficient to accurately determine the turbulent Mach number and set interesting constraints on the injection scale. Applying our method to the Coma cluster data, we obtain a model that is characterized by a large injection scale that rivals the size of the cluster ($\ell_{inj}=2.2_{-1.0}^{+2.0}$ Mpc). When this power spectrum model is integrated over the cluster scales ($0<\ell