Annu. Rev. Astron. Astrophys. 1994. 32: 531-590
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9.2. Pregalactic and Protogalactic Cooling Flows

Although cooling flows provide a natural way of turning gas into low mass stars with high efficiency, those observed in the centers of clusters could not themselves be responsible for either the cluster dark matter (since this is distributed throughout the cluster) or the halo dark matter in galaxies outside clusters. In order to account for the usual dark matter problems, one therefore needs cooling flows on the scale of galaxies or below. Only the most massive cluster galaxies exhibit cooling flows at the present epoch - but it would not be surprising if smaller scale cooling flows occurred at earlier cosmological epochs since X-ray data already suggest that cooling flows evolve hierarchically to larger scales (Evrard 1990, Katz & White 1993).

These considerations prompted Ashman & Carr (1988) and Thomas & Fabian (1990) to consider the circumstances in which one could expect high-pressure quasi-static flows to occur at pregalactic and protogalactic epochs. The situation is best illustrated for the hierarchical clustering scenario, in which, as time proceeds, increasingly large gas clouds bind and virialize. The mass fraction of a cloud cooling quasi-statically is maximized when the cooling time tc is comparable to the free-fall time tf: Collapse does not proceed at all for tc >> tf, whereas it is not quasi-static for tc << tf. In any particular variant of the hierarchical clustering scenario, one can specify the mass binding as a function of redshift. For a cloud of mass M, the dynamical time will just be of order the Hubble time at that redshift, whereas the cooling time will depend upon the density and virial temperature of the cloud (which are themselves determined by M and z). Thus, one can specify a region in the (M, z) plane of Figure 8 in which bound clouds will cool within a dynamical time. This applies above a lower mass limit associated with molecular hydrogen or Lyman-alpha cooling and below an upper mass limit associated with atomic hydrogen cooling (Rees & Ostriker 1977) or the Compton cooling of the microwave background.

Figure 8

Figure 8. The (M, Z) region within which a cloud of mass M binding at a redshift z will cool within a Hubble time. The other lines show how the binding mass evolves with redshift for the CDM scenario with or without bias (solid and broken lines) and for the isocurvature model. A lot of gas may be processed through a cooling flow where the binding curve hits the cooling curve. This happens at both a pregalactic and protogalactic era in the CDM case, but the pressure is too low to make LMOs in the former case. In the isocurvature case, only protogalactic cooling flows occur.

The condition tc ~ tf will be satisfied at the boundary of the region (shown shaded) and the intersection of this boundary with the binding curve M(z) singles out two characteristic mass-scales and redshifts. These correspond to what Ashman & Carr term "Pervasive Pregalactic Cooling Flows" (PPCFs) and what Thomas & Fabian term "Maximal Cooling Flows" since the amount of gas cooling quasi-statically is maximized. The associated mass-scales are always of order 104-108 Msun and 1011 Msun, but the redshifts depend on the particular scenario. Figure 8 shows the binding curves corresponding to the Cold Dark Matter scenario, the broken curve corresponding to the biased version, and the baryon-dominated isocurvature scenario (with eta specifying the exponent in the mass dependence of the density fluctuations at decoupling).

One might anticipate most of the dark matter being made on the smaller scale because much of the gas will have been consumed by the time atomic cooling becomes important. However, this does not happen in the Cold Dark Matter picture because the spectrum of fluctuations is very flat on subgalactic scales and, in the isocurvature models, M(z) may never be small enough for low mass PPCFs to occur after decoupling. Both these features are indicated in Figure 8. Ashman & Carr (1991) therefore argue that most of the dark matter would need to be made by high mass protogalactic PPCFs. Another argument in favor of the protogalactic PPCFs is that the pressure is probably too low to make LMOs on the smaller scale.

One problem with invoking protogalactic cooling flows to make the dark matter is that one might expect most of the gas to have gone into clouds with tc < tf and such clouds should make ordinary stars. This "cooling catastrophe" raises the question of whether there could be enough gas left over to make ordinary galaxies (White & Frenk 1991, Blanchard et al 1992). One way around this is to invoke supernovae to reheat the gas so that most of it can avoid cooling until the protogalactic epoch (Thomas & Fabian 1990). Another way is to argue that even clouds with tc < tf can make a lot of dark matter (Ashman 1990). The idea here is that gas always drops out at such a rate as to preserve the PPCF condition tc ~ tf for the surviving gas. One thus gets a two-phase medium, with cool dense clouds embedded in hot high-pressure gas. This was originally proposed as a mechanism to make globular clusters at a protogalactic epoch (Fall & Rees 1985), but Ashman (1990) argues that sufficiently small clouds would fragment into dark clusters rather than visible clusters in the presence of molecular hydrogen. By applying the same idea to other galaxies, he predicts that the fraction of dark mass in spirals should increase with decreasing disk mass and this may be observed (Persic & Salucci 1990).

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