XRISM constraints on the velocity power spectrum in the Coma cluster

¹ Department of Astronomy, University of Geneva, Ch. d’Ecogia 16, 1290 Versoix, Switzerland
² NASA/Goddard Space Flight Center, Greenbelt, MD 20771, USA
³ Center for Astrophysics | Harvard & Smithsonian, 60 Garden Street, Cambridge, MA 02138, USA
⁴ Department of Astronomy and Astrophysics, University of Chicago, Chicago, IL 60637, USA
⁵ RIKEN Nishina Center, Saitama 351-0198, Japan
⁶ Center for Space Sciences and Technology, University of Maryland, Baltimore County, 1000 Hilltop Circle, Baltimore, MD 21250, USA
⁷ Physics Program, Graduate School of Advanced Science and Engineering, Hiroshima University, 1-3-1 Kagamiyama, Higashi-Hiroshima, Hiroshima 739-8526, Japan
⁸ Department of Physics & Astronomy, University of Utah, 115 South 1400 East, Salt Lake City, UT 84112, USA

^⋆ Corresponding author: Dominique.Eckert@unige.ch

Received: 29 June 2025
Accepted: 19 October 2025

Abstract

The velocity field of intracluster gas in galaxy clusters contains key information on the virialization of infalling material, the dissipation of active galactic nuclei 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. The Resolve instrument on board XRISM allowed us for the first time to accurately measure Doppler shifts and line broadening in nearby clusters. 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 modeled the measured bulk velocities and velocity dispersions by including the most relevant observational effects (projection, emissivity weighting, and point spread function smearing). We then trained 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 (ℓ_inj = 2.2^+2.0_−1.0 Mpc). When this power spectrum model is integrated over the cluster scales (0 < ℓ < R₅₀₀ = 1.4 Mpc), the Mach number of the gas motions is ℳ_3D,500 = 0.45^+0.18_−0.13, which exceeds the value derived from the velocity dispersions only. Further observations covering a wider area are required to decrease the cosmic variance and constrain the slope of the turbulent cascade.