2025ApJ...994..247U

We investigate the spatial relationships between multiphase gas components and supermassive black hole (SMBH) activity in a sample of 25 cool-core galaxy groups and clusters. Using high-angular-resolution observations from Chandra, the Very Large Telescope/Multi Unit Spectroscopic Explorer, and the Very Long Baseline Array (VLBA), we robustly locate the positions, respectively, of the X-ray peak of the intracluster medium, of the Hα peak of the warm ionized gas, and of the SMBH radio core, on parsec scales. We identify spatial offsets between the X-ray peak of the hot gas and the SMBH in 80% of the systems, with an average displacement of $\langle {{\rm{\Delta }}}_{\rm{X-ray}\,}^{\,\rm{SMBH}}\rangle =4.8$ kpc (dispersion of 3.8 kpc). In contrast, the peak of warm ionized gas traced by Hα exhibits a much smaller offset ($\langle {{\rm{\Delta }}}_{\rm{H}\,\alpha }^{\,\rm{SMBH}}\rangle =0.6$ kpc; dispersion of 1.4 kpc) and a lower incidence of displacement (15%). Our findings suggest that hot-gas sloshing primarily drives the observed spatial offsets, with active galactic nucleus (AGN)-driven uplift contributing in some systems. Importantly, systems with Hα-SMBH offsets of ≥1 kpc uniformly lack detectable radio cores on VLBA scales, with upper limits on the 5 GHz power of P_5GHz​​​​​ ≤ 10^21–22 W Hz^–1, while those without such offsets exhibit radio-powerful AGNs with parsec-scale radio emission up to P_5GHz ∼ 10^24–25 W Hz^–1. This correlation indicates that centrally concentrated warm gas is critical for sustaining radio-loud SMBH activity, possibly supporting scenarios of cold-mode accretion. Overall, our results highlight the importance of high-angular-resolution multiwavelength observations for understanding the interplay between multiphase gas cooling and AGN fueling in central galaxies.