Annu. Rev. Astron. Astrophys. 1998. 36: 267-316
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4.4. Gravitational Confinement: Cold Dark Matter Minihalos

The properties of gas clouds under the influence of the gravitational field of dark matter have been investigated by Umemura & Ikeuchi (1985), and, more specifically in terms of the "minihalo" model by Rees (1986) and Ikeuchi (1986). In this picture, Lyalpha clouds are a natural by-product of the CDM structure formation scenario. Photoionized gas settles in in the potential well of an isothermal CDM halo. The gas is stably confined, if the potential is sufficiently shallow to avoid gravitational collapse but deep enough to prevent the warm gas from escaping. The CDM minihalos are more compact than the self-gravitating baryonic clouds of Black (1981) because of the larger dark matter gravity. The detailed structure of the halo depends on the relative spatial distribution of baryons and CDM. The models can be parametrized by the intensity of the radiation field J, the central overdensity delta(r = 0), and the ratio of baryonic to dark matter (Ikeuchi et al 1989). The minihalo model has the attractive feature of providing a natural explanation for the overall shape of the observed column density distribution function (CDDF). The large observed dynamic range in column density reflects the strong density variations as a function of impact parameter, rather than a range in cloud properties. For the general case where the baryon distribution is an isothermal sphere (nb propto r-2), the HI density in the highly ionized region of the minihalo drops like nHI propto r-4 with radius r, and the resulting column density distribution seen by random lines of sight through a population of such halos obeys dcalN / dNHI propto NHI-1.5 (Rees 1988; Milgrom 1988). The largest column densities, including damped Lyalpha systems, are caused by the neutral cores in the shielded centers of the clouds (Murakami & Ikeuchi 1990). Thus minihalos can produce a column density power law over almost nine decades, providing a physical basis for Tytler's (1987a) suggestion of a common origin for all QSO absorbers. Evolution with redshift is caused by a number of processes (Rees 1986): When loosing pressure support as the ionizing flux decreases, gas may settle deeper into the potential well, thus reducing the geometric absorption cross-section. once stars are forming the UV flux may rise again, and stellar winds may blow out the gas (Babul & Rees 1992), thus increasing the absorption cross-section. Halos are produced by a continuing turn-around of density peaks, and are destroyed by merging.

A non-stationary version of the minihalo model was studied by Bond et al (1988), who examined the hydrodynamics of a collapsing spherical top-hat perturbation. If the accreting baryonic component escapes gravitational collapse (and subsequent star formation) it may reexpand under the influence of photoionization heating and even recollapse after the UV intensity has ebbed (see also Murakami & Ikeuchi 1993).

In order to investigate the relative importance of various confinement mechanisms Petitjean et al (1993a) have studied a hybrid model, of spherical clouds with or without dark matter, bounded by an external pressure. These models show that pure baryonic clouds (as discussed by Black 1981), in order to be stable against the outer pressure, tend to overproduce high column density systems. Many of the observed features of the Lyalpha forest clouds can be explained with a single type of minihalo, but to match the fine structure of the column density distribution function halos may be required to exhibit a range of central densities (Murakami & Ikeuchi 1990; Petitjean et al 1993b). Two separate populations, one for low column density Lyalpha clouds, and one for the higher column density metal systems, give a better fit to the CDDF (Petitjean et al 1993b).

Charlton et al (1993, 1994) have studied gravitational condensations with a different geometry, modelling Lyalpha clouds as equilibrium slab models that are subject to the pull of CDM gravity and to an external pressure. It was found that the change of slope in the column density distribution function (near log N(HI) ~ 15) can be explained by a transition between pressure and gravitational confinement, in the sense that at higher column densities gravity takes over and imposes a steeper dependence of the neutral column density with total column density.

NON-EQUILIBRIUM AND OTHER EFFECTS POINTING BEYOND THE SIMPLE HALO MODEL

With the adoption of the CDM based models researchers could avail themselves of the analytical apparatus developed to describe the dark matter distribution, especially the important concept of "halos" (Babul 1990; Mo et al 1993). Of course, there is a limit to the degree of realism with which a counting scheme for dark matter condensations or spherical collapse can describe the observed properties of gas clouds, and even the notion of distinct "objects", dear to traditional astronomy, may fail. Hydrodynamic simulations (see below) show that in a hierarchical universe at intermediate redshift (~ 2) most baryonic matter may not have settled in spherical, or rotationally supported virialized objects, as suggested by the word "halo". Virial radii of objects capable of stably confining HI clouds are ~ 10 kpc (Rees 1986). The coherence lengths of Lyalpha systems from gravitational lensing constraints (Smette et al 1992, 1995) are much larger, implying that only few LOS ever hit the virialized region. Thus, minihalos may not only be embedded in regions of uncollapsed gas, they may still be accreting matter at the epoch where we observe the Lyalpha forest. Thus it makes sense to look for signs of non-equilibrium, especially departures from thermal line line profile caused by the bulk motion of the infalling gas (Miralda-Escudé & Rees 1993). Meiksin (1994) has traced the formation and internal structure of minihalos and slabs with hydrodynamical simulations to search for such observable non-equilibrium effects. For a slab or pancake geometry, noticeable deviations from Voigt profiles are predicted, but they would be hard to detect for spherical clouds.

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