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The gas clouds out of which galaxies, groups, and clusters form were heated by the energy released during their initial gravitational collapse. Some of the gas then cooled to form the objects readily observed today. In the case of ordinary galaxies much of the gas cooled rapidly, but in massive galaxies and clusters the gas cooled more slowly and a quasi-hydrostatic atmosphere formed. The mass of uncooled hot gas exceeds that in visible stars in groups and clusters of galaxies. The temperature of the atmosphere is close to the virial temperature (typically several million K and greater) and is directly observable only in the X-ray waveband. The hot atmosphere continues to lose energy by the emission of radiation (principally X rays); in the central region, where the atmosphere is naturally densest, a cooling flow forms. This region, which grows with time, is where the cooling rate of the gas is sufficiently high that the gas particles lose their energy to radiation. The weight of the overlying gas then causes a slow, subsonic inflow; inhomogeneities in the gas cause cooled matter to drop out and form cold clouds or stars throughout the flow. The net result is that cold matter continues to be slowly deposited over a large volume in the core of the massive galaxy, group, or cluster.

This idealized picture represents the main features of cooling flows, which are found to be common in massive elliptical galaxies, groups, and clusters of galaxies through X-ray observations. The surface brightness and spectrum of the X rays show that the gas particles lose much of their thermal energy to X-radiation in the central region of many of these objects, implying that the cooling process necessary for the formation of galaxies has extended until the present time and that the central massive galaxies are continuing to grow now. Most of this growth is not in terms of visible stars, however, since the radiative cooling rates in nearby rich clusters of 10s to 100s Msun yr-1 would then make the central galaxies much bluer and brighter than even a superficial optical inspection allows. The cooled gas must somehow condense into optically dark objects, or some other process must come into play. Detailed observations at optical and other wavebands do reveal anomalies in the centers of cooling flows and confirm that the gas has a high density, a high pressure, and short cooling time, but so far do not reveal the cooled component. The only thing we know for certain is that gas is leaving the hot phase, where it is detectable in X rays, and is becoming some form of dark matter.

After a very brief overview of the intracluster medium, the X-ray properties of nearby cooling flows are discussed in some detail. We review the evidence, derived from X-ray images and spectra, that the gas really cools and that cooling flows are common. Therefore they must be long-lived and steady. Recent data clearly show the temperature of the gas dropping towards the center of many clusters. The spectra also require X-ray absorption, in excess of Galactic line-of-sight values, consistent with widespread cold gas which may be one signature of the cooled component of the flow. After reviewing the appearance of cooling flows in other wavebands, we discuss some theoretical issues on cooling flows, such as the lack of thermal conduction and the required multiphase nature of the gas. Much of the behavior of the cooling gas is very uncertain once it has dropped below X-ray emitting temperatures, with magnetic fields surely important, and in place of a secure theoretical discussion, we outline one possible picture of what is occurring. Finally we move onto distant cooling flows and their evolution before returning to galaxy formation.

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