Massive galaxies in cooling flow clusters display clear evidence of feedback from Active Galactic Nuclei (AGN). Joint X-ray and radio observations have shown that AGN radio jets push aside the surrounding hot gas and form cavities in the hot intracluster medium (ICM). These systems host complex, kiloparsec-scale, multiphase filamentary structures, from warm ionized (10,000 K) to cold molecular ($<$100 K). These striking clumpy filaments are believed to be a natural outcome of thermally unstable cooling from the hot ICM, likely triggered by feedback processes while contributing to feeding the AGN via Chaotic Cold Accretion (CCA). However, the detailed constraints on the formation mechanism of the filaments are still uncertain, and the connection between the different gas phases has to be fully unveiled. By leveraging a sample of seven X-ray bright cooling-flow clusters, we have discovered a tight positive correlation between the X-ray surface brightness and the H$α$ surface brightness of the filaments over two orders of magnitude, as also found in stripped tails.

Accepted for publication in Nature Astronomy, 32 pages, 10 figures