Annu. Rev. Astron. Astrophys. 1994. 32: 277-318
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The intracluster gas is, of course, densest in the core of a cluster and therefore the radiative cooling time, tcool, due to the emission of the observed X rays, is shortest there. (For X-radiation from hot gas, tcool propto Talpha / n, where -1/2 ltapprox alpha ltapprox 1/2 and n is the gas density.) A cooling flow is formed when tcool is less than the age of the system, say ta ~ H0-1. In the cases considered here, tcool exceeds the gravitational free-fall time, tgrav within the cluster, so

Equation 1 (1)

and gas can be considered to be in quasi-hydrostatic equilibrium. The flow takes place because the gas density has to rise to support the weight of the overlying gas. It is essentially pressure-driven.

To see this clearly, consider the gaseous atmosphere trapped in the gravitational potential well of a cluster or galaxy to be divided into two parts at the radius rcool, where tcool = ta. The gas pressure at rcool is determined by the weight of the overlying gas, in which cooling is not important. Within rcool, cooling reduces the gas temperature and the gas density must rise in order to maintain the pressure at rcool. The only way for the density to rise (ignoring matter sources within rcool, which is a safe assumption in a cluster of galaxies) is for the gas to flow inward. This is the cooling flow. Although in principle the cooling could instead be balanced by sources of heat, we show below that this is neither physically nor astrophysically plausible, nor is it consistent with observations of cooler, X-ray line-emitting gas.

If the initial gas temperature exceeds the virial temperature of a central galaxy (which is generally the case for rich clusters but not for poor ones or individual galaxies) then the gas continues to cool as it flows inward. When the gas temperature has dropped to the virial temperature of the central galaxy, adiabatic compression of the inflowing gas under the gravitational field of the galaxy, i.e. the release of gravitational energy, counterbalances the radiative heat loss and can sustain, or even raise, the gas temperature as it flows further inward. Radiative heat loss causes a continual reduction in the entropy of the inflowing gas, but not necessarily in its temperature. The gas temperature can eventually drop catastrophically in the core of the galaxy if the gravitational potential flattens there. The net result is that the gas within rcool radiates its thermal energy plus the PdV work done on it as it enters the region and the gravitational energy released within rcool.

This is the behavior of an idealized, spherically symmetric, homogeneous cooling flow, in which the gas has a unique temperature and density at each radius. X-ray observations of real cooling flows indicate that they are inhomogeneous and must consist of a mixture of temperatures and densities at each radius. The homogeneous flow still gives fair approximations for many properties of the mean flow. The physics of the cooling flow mechanism is very simple, although the details of its operation are not.

The primary evidence for cooling flows comes from X-ray observations. There is less evidence at other wavelengths, and none of it supports the large mass deposition rates of 100s Msun yr-1 inferred from the X-ray data for some clusters. We discuss this point more fully later, but it should be stressed that large amounts of distributed low-mass star formation need not be detectable at other wavelengths if the gas is initially at X-ray emitting temperatures. This is, perhaps, the crux of the controversial aspect of cooling flows: It is difficult to prove or disprove their existence with observations in wavebands other than the X-ray. The lack of clear evidence at other wavebands does not make the X-ray evidence any less compelling, though it does challenge our observational and theoretical ingenuity in those other wavebands.

It was Uhuru observations of clusters that first showed the mean cooling time of the gas in the cores of clusters to be close to a Hubble time (Lea et al 1973). These, and other early X-ray measurements described later, and theoretical considerations, led Cowie & Binney (1977), Fabian & Nulsen (1977), and Mathews & Bregman (1978) to independently consider the effects of significant cooling of the central gas, i.e. cooling flows. The process was noted by Silk (1976) as a mechanism for the formation of central cluster galaxies from intracluster gas at early epochs and as a mechanism for general galaxy formation by Gold & Hoyle (1958). General reviews of cooling flows have been made by Fabian et al (1984b, 1991) and Sarazin (1986, 1988) and some other points of view may be found in the Proceedings of a NATO Workshop (Fabian 1988a).

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