Understanding the processes that drive galaxy formation and shape the observed properties of galaxies is one of the most interesting and challenging frontier problems of modern astrophysics. We now know that the evolution of galaxies is critically shaped by the energy injection from accreting supermassive black holes (SMBHs). However, it is unclear how exactly the physics of this feedback process affects galaxy formation and evolution. In particular, a major challenge is unraveling how the energy released near the SMBHs is distributed over nine orders of magnitude in distance throughout galaxies and their immediate environments. The best place to study the impact of SMBH feedback is in the hot atmospheres of massive galaxies, groups, and galaxy clusters, which host the most massive black holes in the Universe, and where we can directly image the impact of black holes on their surroundings. We identify critical questions and potential measurements that will likely transform our understanding of the physics of SMBH feedback and how it shapes galaxies, through detailed measurements of (i) the thermodynamic and velocity fluctuations in the intracluster medium (ICM) as well as (ii) the composition of the bubbles inflated by SMBHs in the centers of galaxy clusters, and their influence on the cluster gas and galaxy growth, using the next generation of high spectral and spatial resolution X-ray and microwave telescopes.

10 pages, submitted to the Astro2020 decadal