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Expanding X-ray cavities observed in hot gas atmospheres of many galaxygroups and clusters generate shock waves and turbulence that are primaryheating mechanisms required to avoid uninhibited radiatively cooling flowswhich are not observed. However, we show here that the evolution of buoyantcavities also stimulates radiative cooling of observable masses oflow-temperature gas. During their early evolution, radiative cooling occurs inthe wakes of buoyant cavities in two locations: in thin radial filamentsparallel to the buoyant velocity and more broadly in gas compressed beneathrising cavities. Radiation from these sustained compressions removes entropyfrom the hot gas. Gas experiencing the largest entropy loss cools first,followed by gas with progressively less entropy loss. Most cooling occurs atlate times, $\sim 10^8-10^9$ yrs, long after the X-ray cavities have disruptedand are impossible to detect. During these late times, slightly denser lowentropy gas sinks slowly toward the centers of the hot atmospheres where itcools intermittently, forming clouds near the cluster center. Single cavitiesof energy $10^{57}-10^{58}$ ergs in the atmosphere of the NGC 5044 group create$10^8 - 10^9$ $M_{\odot}$ of cooled gas, exceeding the mass of extendedmolecular gas currently observed in that group. The cooled gas clouds wecompute share many attributes with molecular clouds recently observed in NGC5044 with ALMA: self-gravitationally unbound, dust-free, quasi-randomlydistributed within a few kpc around the group center.

Hot gaseous atmospheres in galaxy groups and clusters are both heated and cooled by X-ray cavities