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Colloquium on the Age of the Universe, Dark Matter, and Structure Formation
due to atomic or molecular radiative processes—clouds that couldn’t cool would simply remain in equilibrium, being later incorporated in a larger scale of structure as the hierarchy built up. On the other hand, clouds that can cool radiatively will deflate. Most cooling mechanisms are more efficient at higher temperatures, as well as at higher densities. Once collapse starts, it proceeds almost isothermally, so that the internal Jeans mass falls as the density rises. A virialized, self-gravitating cloud that can cool radiatively would eventually go into free-fall collapse and (perhaps after a disc phase) fragment into smaller pieces.
Three “cooling regimes” are relevant during successive phases of the cosmogonic process, each being associated with a characteristic temperature.
For a H-He plasma the only effective cooling at low temperatures (<104 K) comes from molecular hydrogen. Even this process cuts off below a few hundred degrees; but above that temperature it allows contraction within the cosmic expansion timescale. The H2 fraction is never high, and it is, in any case, not a very efficient coolant—indeed, systems that collapse at z<10 fail to form enough molecules for effective cooling [e.g., see figure 1 of Tegmark, et al. (1)]—but molecular cooling almost certainly played a role in forming the very first objects that lit up the universe
If H2 is prevented from forming, so that molecular cooling is ineffective, then a H-He mixture behaves adiabatically unless T is as high as 8,000–10,000°, when excitation of Lyman a by the Maxwellian tail of the electrons provides efficient cooling whose rate rises steeply with temperature. Because of this steep temperature dependence, gas in this regime contracts almost isothermally, so that its Jeans mass decreases as the density rises.
The UV from early stars will photoionize some (and eventually almost all) of the diffuse gas. When this happens, the HI fraction is suppressed to a very low level, so there is no cooling by collisional excitation of Lyman lines; moreover, the energy radiated whenever a recombination occurs is quickly canceled by the energy input from a photoionization, so the only net cooling is via bremsstrahlung. The cooling is, in effect, then reduced by a factor of 100 (see, for instance, ref. 2). The minimum temperature (below which there is a net heating from the UV) depends on the UV spectrum and on whether the He is doubly ionized: it is in the range of 20,000–40,000°. (These three regimes refer to a H-He plasma. When heavy elements are present they can dominate the low-T cooling; ionization is still important in suppressing the most efficient channels for cooling.)
The Role of Molecular Hydrogen and the UV Feedback. The role of molecular cooling at early cosmic epochs has been considered by many authors, dating back to the 1960s; recent discussions are given, for instance, by Tegmark et al. (1) and Haiman. Rees, and Loeb (3). The exact efficiency depends on the density and, therefore, on the redshift when the first collapse occurs.
However, even at high redshifts, H2 cooling would be quenched if there were a UV background able to dissociate the molecules as fast as they formed. Photons of hv>11.18 eV can photodissociate H2. as first calculated by Stecher and Williams (4). These photons can penetrate a high column density of HI and destroy molecules in virialized and collapsing clouds. (If the incident spectrum has a nonthermal component extending up to KeV energies, there is a counterbalancing positive feedback because the number of photoelectrons is increased, and this enhances molecule formation.)
Only a small fraction of the UV that ionized the IGM could have been produced in systems where star formation was triggered by molecular cooling. Most must have formed in systems large enough to have been able to cool by atomic line effects. There is then a further transition when the medium breaks through and becomes completely ionized: the UV background intensity gets a boost, because the contributions from remote regions (which dominate in Olbers-type integrals) are less severely attenuated. The UV is then enough to maintain the very high mean ionization implied by transparency of the IGM beyond the Lyman limit. This means that it can maintain high ionization of a cloud until it has either collapsed to an overdensity exceeding the IGM ratio of ions to neutrals or until it becomes self-shielding (which happens at more modest overdensities for large clouds). Until that happens the cooling rate will be reduced by the lack of bound electrons and consequent elimination of the (otherwise dominant) “line” contribution to the cooling.
When this third phase is reached, the thermal properties of the uncollapsed gas will resemble those of the structures responsible for the observed Lyman-forest lines in high-z quasars spectra—these are mainly filaments, draining into virialized systems. Such systems have velocity dispersions of 50 km/sec and are destined to turn into galaxies of the kind whose descendants are still recognizable. I shall return (section 4) to discuss the detectability of these early galaxies.
Evidence for Diffuse Gas at Highz
CMB Fluctuations as a Probe of the Ionization Epoch. If the intergalactic medium were suddenly reionized at a redshift z, then the optical depth to Thomson scattering back would be
(the generalization to a more realistic scenario of gradual reionization is straightforward). Even when this optical depth is far below unity, the ionized gas constitutes a “fog” that attenuates the fluctuations imprinted at the recombination era; the photons that are scattered at <zi then manifest a different pattern of fluctuations, characteristically on larger angular scales. This optical depth is consequently one of the parameters that can, in principle, be determined from CMB anisotropy measurements. It is feasible to detect a value as small as 0.1—polarization measurements may allow even greater precision, because the scattered component would imprint polarization on angular scales of a few degrees, which would be absent from the Sachs-Wolfe fluctuations on that angular scale originating at trec.
Twenty-one-centimeter Emission, Absorption, and Tomog raphy. The 21-cm line of HI at redshift z would contribute to the background spectrum at a wavelength of 21 (1+z) cm. This contribution amounts to a brightness temperature of order 0.05 (1+z)1/2. This is very small compared with the 2.7 K of the CMB and smaller still compared with the nonthermal background, which swamps the CMB, even at high galactic latitudes, at the long wavelengths where high-z HI should show up. Nonetheless, inhomogeneities in the HI may be detectable, because they would give rise not only to angular fluctuations but also to spectral structure (5, 6). If the same strip of sky were scanned at two radio frequencies differing by (for example) 1 MHz. the temperature fluctuations due to the CMB itself, to galactic thermal and synchrotron backgrounds, and to discrete sources would track each other closely. Contrariwise, there would be no correlation between the 21-cm contributions, because the two frequencies would be probing “shells” in redshift space whose radial separation would exceed the correlation length. Consequently, it is not necessarily unfeasible to distinguish the 21-cm background, utilizing a radio telescope with a large collecting area. That line radiation allows three-dimensional tomography of the high-z HI renders this a specially interesting technique.