Multiphase gas offsets in the atmospheres of central galaxies and their consequences for SMBH activation I. The hot and warm ionized gas phases

We investigate the spatial relationships between multi-phase 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 \textit{Chandra}, VLT/MUSE, and VLBA, we robustly locate the position, respectively, of the X-ray peak of the intracluster medium (ICM), of the H$α$ 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 $\langleΔ^{\text{SMBH}}_{\text{X-ray}}\rangle = 4.8$ kpc (dispersion of $3.8$ kpc). In contrast, the peak of warm ionized gas traced by H$α$ exhibits much smaller offsets ($\langleΔ^{\text{SMBH}}_{\text{H}α}\rangle = 0.6$ 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 AGN-driven uplift contributing in some systems.Importantly, systems with H$α$ - SMBH offsets of $\geq$1 kpc uniformly lack detectable radio cores on VLBA scales, with upper limits on the 5~GHz power of $P_{5\,\text{GHz}} \leq 10^{21-22}$ W Hz$^{-1}$, while those without such offsets exhibit radio powerful AGN with pc-scale radio emission up to $P_{5\,\text{GHz}} \sim 10^{24-25}$ 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, multi-wavelength observations for understanding the interplay between multiphase gas cooling and AGN fueling in central galaxies.