Bulk vs. turbulent motions at the centres of galaxy clusters: AGN-driven turbulence according to TNG-Cluster
The highly dynamic intracluster medium (ICM) influences cluster thermodynamic evolution and probes key physical processes. Quantifying the non-thermal motions is therefore essential for understanding cluster physics and interpreting high spectral-resolution X-ray observations from telescopes like {\it XRISM}. We quantify bulk and turbulent gas motions in 352 galaxy clusters at $z=0$ (${\rm M_{200c}=10^{14.3-15.4}\, M_\odot}$) from the TNG-Cluster suite of magneto-hydrodynamical galaxy simulations. We use a multi-scale filtering Reynolds decomposition to separate total gas velocities into bulk (coherent) and turbulent (small-scale fluctuations) components. We primarily focus on the hot X-ray emitting gas in the central core regions. According to TNG-Cluster, majority of the ICM has subsonic turbulence but with broad velocity distributions reaching $\mathcal{M}_{\rm Turb}\sim 10$ and large cluster-to-cluster variations. In cluster centres, turbulence contributes less than half of the total velocity dispersion $(\sigma_{v\rm,Turb } \sim 0.5 ~\sigma_{v,\rm Total})$ for most clusters, with typical turbulent velocity dispersions of $50-75$ km s$^{-1}$ across the mass range, and with sub per cent levels of turbulent pressure support. Clusters that are strong cool cores, or have X-ray cavities, or experienced recent SMBH feedback energy injections exhibit systematically larger turbulent velocity dispersions and more prominent turbulent velocity tails. On average, the turbulent velocity dispersion peaks in cluster centres, decreases slightly to a minimum at $0.1-0.2 \, R_{\rm500c}$, then rises again. Our analysis shows that SMBH feedback is a key driver of turbulence in cluster cores, generating strong but short-lived motion alongside high-velocity outflows. It also calls for caution for interpreting {\it XRISM} observations.