Feedback in Cluster Cores: The Life of Multiphase Filaments

Galaxy cluster cores are exceptional laboratories for probing the baryon cycle that regulates galaxy evolution and active galactic nucleus (AGN) feedback. They provide a unique window into how the intracluster medium (ICM) cools, fuels central galaxies, sustains star formation, and ultimately triggers feedback from the Universe's most massive black holes. In this talk, I present a newly identified correlation between the surface brightness of the hot and warm gas phases within filamentary structures in cluster centers, based on MUSE, SITELLE, and Chandra observations. Remarkably, this correlation closely resembles those observed in the tails of jellyfish galaxies, revealing an unexpected connection between cluster-scale filaments and ram-pressure-stripped systems. I further demonstrate that AGN feedback plays a crucial role in shaping the filaments morphology, pressure balance, and metallicity, highlighting their dynamic, multiphase nature. Finally, I present new high-resolution ALMA observations of a filament in the Perseus cluster to investigate the impact of AGN feedback on cold molecular clouds and their potential for star formation.