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The intracluster medium (ICM) of galaxy clusters encodes the impact of thephysical processes that shape these massive halos, including feedback fromcentral supermassive black holes (SMBHs). In this study we examine the gasthermodynamics, kinematics, and the effects of SMBH feedback on the core ofPerseus-like galaxy clusters with a new simulation suite: TNG-Cluster. We firstmake a selection of simulated clusters similar to Perseus based on total massand inner ICM properties, i.e. cool-core nature. We identify 30 Perseus-likesystems among the 352 TNG-Cluster halos at $z=0$. Many exhibit thermodynamicalprofiles and X-ray morphologies with disturbed features such as ripples,bubbles and shock fronts that are qualitatively similar to X-ray observationsof Perseus. To study observable gas motions, we generate XRISM mock X-rayobservations and conduct a spectral analysis of the synthetic data. Inagreement with existing Hitomi measurements, TNG-Cluster predicts subsonic gasturbulence in the central regions of Perseus-like clusters, with a typicalline-of-sight velocity dispersion of 200 km/s. This implies that turbulentpressure contributes $< 10\%$ to the dominant thermal pressure. In TNG-Cluster,such low (inferred) values of ICM velocity dispersion coexist withhigh-velocity outflows and bulk motions of relatively small amounts ofsuper-virial hot gas, moving up to thousands of km/s. However, detecting theseoutflows observationally may prove challenging due to their anisotropic natureand projection effects. Driven by SMBH feedback, such outflows are responsiblefor many morphological disturbances in the X-ray maps of cluster cores. Theyalso increase both the inferred, and intrinsic, ICM velocity dispersion. Thiseffect is somewhat stronger when velocity dispersion is measured fromhigher-energy lines.

X-ray inferred kinematics of the core ICM in Perseus-like clusters: insights from the TNG-Cluster simulation