  Galaxy clusters are the most massive collapsed structures in the universe
whose potential wells are filled with hot, X-ray emitting intracluster medium.
Observations however show that a significant number of clusters (the so-called
cool-core clusters) also contain large amounts of cold gas in their centres,
some of which is in the form of spatially extended filaments spanning scales of
tens of kiloparsecs. These findings have raised questions about the origin of
the cold gas, as well as its relationship with the central active galactic
nucleus (AGN), whose feedback has been established as a ubiquitous feature in
such galaxy clusters. Here we report a radiation hydrodynamic simulation of AGN
feedback in a galaxy cluster, in which cold filaments form from the warm,
AGN-driven outflows with temperatures between $10^4$ and $10^7$ K as they rise
in the cluster core. Our analysis reveals a new mechanism, which, through the
combination of radiative cooling and ram pressure, naturally promotes outflows
whose cooling time is shorter than their rising time, giving birth to spatially
extended cold gas filaments. Our results strongly suggest that the formation of
cold gas and AGN feedback in galaxy clusters are inextricably linked and shed
light on how AGN feedback couples to the intracluster medium.

Astrophysics of Galaxies;Cosmology and Nongalactic Astrophysics;High Energy Astrophysical Phenomena