Chasing ICM cooling and AGN feedback from the macro to the meso scales in the galaxy cluster ZwCl 235

We aim to investigate the AGN/ICM interplay in ZwCl 235, a galaxy cluster with high X-ray flux, an extended central radio galaxy, and evidence of multi-phase gas at its center. Using archival data from the Chandra telescope, the VLASS survey, the LOTSS survey and the VLBA telescope, we perform a complete study of ZwCl 235, dissecting the dynamics of the ICM, the thermodynamic state of the central gas, and the properties of the BCG. By means of radial profiles and 2D spectral maps, we measure the temperature, entropy and cooling time of the ICM, and we compare the morphology of the central radio galaxy with the surrounding medium. We find evidence that ZwCl 235 is a sloshing cool core cluster in which the activity of the central galaxy has excavated a pair of cavities and possibly uplifted enriched gas to an altitude of ~30 kpc. In the cluster core, the lowest entropy ICM is preferentially found in a 20 kpc-long filament tangential to the southern radio lobe of the AGN. We argue that the observed cool (~1.3 keV) filament is likely produced by a combination of sloshing and stimulated ICM cooling, that may be fueling the central supermassive black hole. Additionally, we determine that the X-ray emission of the BCG originates from a ~1.4 keV plasma kernel which extends for 5 kpc in radius and has a short cooling time (~240 Myr), and could represent the thermal corona of the BCG. Overall, we propose that several sources (the large scale ICM, the low entropy filament and the ~1.4 keV kernel) of cold material are currently feeding the central AGN, and that the ICM cooling cycle expectations are met from the macro scales (between 5 - 100 kpc) to the meso scales (<5 kpc) of AGN feedback.