Annu. Rev. Astron. Astrophys. 1998. 36: 267-316
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4. THE FIRST GENERATION OF MODELS

Theoretical modelling of absorption systems can be traced back to Spitzer's (1956) prediction (expanded by Bahcall & Spitzer 1969) that normal galaxies have large gaseous halos giving rise to heavy element UV absorption lines. Bahcall & Salpeter (1965) considered groups of galaxies, Arons (1972) suggested forming low mass protogalaxies as the probable sites of Lyalpha absorption. The interpretation by Sargent et al 1980 of their observations of the Lyalpha forest alerted researchers to differences between metal and Lyalpha forest absorption systems, with the evidence pointing away from galaxies, to distinct astronomical objects, intergalactic gas clouds.

4.1. Lyalpha Clouds confined by the Pressure of an Intercloud Medium

If the Lyalpha absorbers correspond to overdense clumps of gas, their persistence throughout of the history of the universe must be either due to only a slow change in their properties, or to replenishment of the clouds on a shorter time scale. An apparent lack of rapid evolution in the properties of the forest (later shown to be a statistical fluke), and the short electron and proton relaxation time scales and mean free paths appeared to justify treating the clouds as "self-contained entities in equilibrium" (Sargent et al 1980). A two phase intergalactic medium was postulated, with the hot, tenuous intercloud medium (ICM) in pressure equilibrium with the cooler and denser Lyalpha clouds. The standard version of the pressure confinement model (Sargent et al 1980; Ostriker & Ikeuchi 1983; Ikeuchi & Ostriker 1986) considers spherical, and, since gravity is ignored, homogeneous clouds. This model is self-consistent, but there are no very compelling physical reasons for preferring pressure to gravitational confinement or to no confinement at all, and the possibility of self-gravitating clouds as an alternative was discussed soon (Melott 1980; Black 1981).

Nevertheless, the pressure confinement model for Lyalpha clouds is appealing for several reasons: It combines the concept of a multiphase structure of the intergalactic medium, familiar from the interstellar medium, with the idea of separate entities, "clouds", in analogy to, but different from galaxies. A hot intercloud medium may have been a possible source of the X-ray background. In addition the explosion scenario (see below) provided a theory of cloud formation. Finally, the model made testable predictions, a rare but risky undertaking for astrophysical theories, which paved the way to its eventual demise.

The basic properties of pressure confined clouds, as worked out in detail by Sargent et al (1980), Ostriker & Ikeuchi (1983), and Ikeuchi & Ostriker (1986) can be summarized as follows:

The Lyalpha clouds are supposed to be in photoionization equilibrium with an ionizing UV background. The gas is heated by photoionization, and cools via thermal bremsstrahlung, Compton cooling, and the usual recombination and collisional excitation processes. The cloud evolution consists of several phases, depending on the relative lengths of cooling and expansion time scales. The ICM is expanding adiabatically by the cosmic expansion at all times because the high degree of ionization does not allow for efficient photoionization heating. The denser clouds embedded in the hot ICM start out in isothermal expansion with a temperature fixed by thermal ionization equilibrium (Tc ~ 3 × 104K), until the density nc propto PICM / Tc propto (1 + z)5 has dropped sufficiently that photoheating cannot compensate for the work of expansion any longer, and the clouds begin to cool and to expand less rapidly. The sound speed drops even faster so ultimately pressure equilibrium with the ICM ceases and the clouds enter free expansion. The available range of cloud masses is constraint by the requirements that the clouds must be small enough not to be Jeans-unstable, but large enough not to be evaporated rapidly when heated by thermal conduction from the ambient ICM (Sargent et al 1980, Ostriker & Ikeuchi 1983). Clouds formed at z ~ 6 would survive down to accessible redshifts (~ 4) only if their masses range between 10 5 < Mc < 1010 Msun.

THE ORIGIN OF LYMAN ALPHA CLOUDS FROM COSMIC SHOCKS     The explosion scenario of structure formation (Schwarz et al 1975; Ostriker & Cowie 1981) provided a non-gravitational origin for the pressure confined Lyalpha clouds. Large scale explosions from galaxies (e.g., from starbursts) and QSOs may have driven shock waves into the intergalactic medium. These events may also have provided the energy for collisional re-ionization and heating of the ICM, since photoionization cannot produce temperatures high enough to maintain pressure confinement (Ikeuchi & Ostriker 1986). This way a two-phase medium of hot "cavities" enclosed by a system of cooler shells could have arisen (Ozernoy & Chernomordik 1976). Lyalpha absorption is caused by the fragmenting shells (Chernomordik & Ozernoy 1983; Vishniac et al 1985). Among the observational consequences may be pairs of Lyalpha lines that occur wherever the line of sight intersects an expanding, spherical shell. It has been argued that such pairs have been seen (Chernomordik 1988, and refs. therein); this may be the case in individual systems, but it is difficult to prove in a statistical sense because the two-point correlation does not show the expected signal at the relevant velocity scale, ~ 100 kms-1 (Rauch et al. 1992). A potential problem for this model is implied by the observed lack of a correlation with galaxies. If Lyalpha clouds are shells expelled by galaxies, the absorbers should be clustered in a manner similar to that of galaxies (Vishniac & Bust 1987). Neither the auto-correlation function among absorbers nor the cross-correlation with galaxies show a signal of the requisite strength (Barcons & Webb 1990).

A similar pattern of shell formation ensues if QSOs, in the initial event of reionization, surround themselves with Strömgren spheres (Arons & McCray 1969, Shapiro & Giroux 1987), which can lead to shocked shells of gas at the boundary of the HII regions. The shells fragment as in the explosion scenario and may be visible as Lyalpha absorbers (Madau & Meiksin 1991).

THE ELUSIVE INTERCLOUD MEDIUM     The need for a confining intercloud medium has led to a number of searches for a residual absorption trough between the absorption lines, caused by the HI in the intercloud space. These measurements came to be referred to in the literature as the Gunn-Peterson (GP) test, though Gunn & Peterson's (1965) original result of a 40% average absorption was a detection of the unresolved Lyalpha forest as a whole. Values for the residual (i.e., intercloud, or diffuse, as opposed to line) GP effect require (a) a precise knowledge of the unabsorbed QSO continuum level, and (b) either subtracting the contribution from Lyalpha "lines", or the use of line free regions (whatever that may be) for the estimate. Steidel & Sargent (1987b) measured the total flux decrement of a sample of 8 QSOs against continua extrapolated from the regions redward of Lyalpha emission. After subtracting a model population of discrete Lyalpha lines they obtained a residual tauGP < 0.02 ± 0.03 (< z > ~ 2.67), i.e., a null result. Giallongo et al (1992), and Giallongo et al (1994) have compared apparently line free regions with an extrapolated continuum, and they found tauGP < 0.013 ± 0.026(< z > ~ 3) and ( tauGP < 0.02 ± 0.03(< z > ~ 4.3), respectively. Given the line crowding at high redshift, the small error bars of the z > 4 work betray a certain degree of optimism.

The clean-cut decomposition into line and continuum absorption makes theoretical sense for pressure confined clouds, but observationally we can never be sure whether there is a flat continuum trough from diffuse gas, or whether there are many weak lines blended together. Jenkins & Ostriker (1991), and Webb et al (1992), acknowledging this problem, attempted to model the pixel intensity distribution with continuum absorption and variable contributions from discrete lines. Their results show that tauGP can be produced both ways, by blending of weak lines below the detection threshold, or by a constant pedestal of absorption.

In any case the weakness or non-detection of a residual GP trough puts an upper limit on the density of the ICM. A lower limit on the ICM pressure (propto nICM TICM) can be derived from the absorption line width (which gives an upper limit on the radius of the expanding cloud (Ostriker & Ikeuchi 1983). The condition that the cloud must be large enough not to evaporate gives an upper limit on the pressure. Another independent upper limit on the pressure of the ICM comes from the lack of inverse Compton distortions in the spectrum of the cosmic microwave background (CMB) (Barcons et al 1991). This result rules out the intergalactic medium as the source of the hard X-ray background. It also may spell trouble for the explosion model of galaxy formation, which is the origin of the two-phase IGM in the current picture) and of apparently non-existing structure in the CMB. When all the limits are combined all the limits only a relatively small corner of allowed (n, T) parameter space remains for the intercloud medium.

PROBLEMS WITH THE COLUMN DENSITY DISTRIBUTION     For pressure confined clouds the large range of neutral hydrogen column densities observed must correspond to a range in the parameter combination

Equation 15     (15)

To reproduce only the low column density systems between 13 < log N(HI) < 16 the mass has to vary by 9 orders of magnitude, or the radiation field by 3 orders, or the pressure by a factor of 63. To ensure cloud survival the mass range is limited to less than 4 dex (see above), and the temperature is constant; therefore, we may need to invoke pressure inhomogeneities (Baron et al 1989). However, Webb & Barcons (1991), looking for pressure related spatial correlations among the equivalent widths of Lyalpha forest lines excluded pressure fluctuations DeltaP / P > 14% at the 2sigma level, and a similar limit must hold for the radiation field J. Extremely flattened clouds would help somewhat in that they would increase the column density range, allowing a wider range of path lengths through the clouds (Barcons & Fabian 1987), but that may introduce other problems. Williger & Babul (1992) taking these constraints into account investigated pressure confined clouds with detailed hydrodynamical simulations and found that the small mass range leads not only to a failure in producing the column density range but also to a faster drop in the number of clouds with redshift, than observed.

To summarize, the pure pressure confinement model is unlikely to explain the Lyalpha forest as a whole, though it is clear that some LOS must go through sites where gas is locally confined by external hydrostatic or ram pressure. Low redshift gaseous galactic halos, the likely hosts of the dense Lyman limit absorbing clouds, may be such environments. Formed by local instabilities the dense clouds may be in pressure equilibrium with a hot gas phase at the virial temperature of the halo (Mo & Miralda-Escudé 1996, and references therein).

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