Feeding the Black-Holes : From cooling filaments to H2 accretion disks

Brightest Cluster Galaxies (BCGs) are unique direct evidence of AGN-feedback caught in the act. The large cavities inflated by the AGN-radio lobes have pushed the hot intra-cluster medium and made gigantic bubbles raising buoyantly in the ICM. BCGs lying at the center of cool core clusters (short cooling time) are also surrounded by a huge network of kpc-scale filaments, visible in the optical and detected in warm H2 and cold CO. Those cold filaments are likely formed via thermal instabilities in the low-entropy cluster core. There is strong evidence that AGN-jets themselves play an important role in the local compression and cooling of this gas. BCGs are thus the best objects to study this key piece of the feedback. Once cooled the gas can settle down in the galaxy and feed the central Black Hole, powering the feedback engine. To understand the detailed circulation of the cold gas is of prime importance. The spatial resolution and sensitivity of JWST with MRS and MIRI can (i) map the H2 lines tracing the bulk of the mass in the filaments and seek warm dust at large scales; it can also help (ii) determine the main excitation processes in the filaments (and confirm the important role of shocks) via mid-IR line diagnostics and (iii) map the expected central molecular disks, a yet unobserved element of the feedback cycle.