Galaxy clusters are filled with a hot plasma called the intracluster medium, or ICM. In roughly half of clusters, the radiative cooling time is much shorter than the age of the cluster, meaning that the ICM should have had plenty of time to cool and form stars. Instead, observations show little cold gas in these clusters and star formation rates at least an order of magnitude below what is predicted. This dissertation explores a theory known as the Precipitation-regulated Feedback Hypothesis. As the ICM cools, thermal instability leads the formation of cold clouds that accrete onto a supermassive black hole, powering active galactic nuclei (AGN) that reheat the cluster. This feedback loop balances cooling and keeps the cluster in a rough state of thermal equilibrium.
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