5. Lyman- clouds
The description of gravitational clustering used in this article allows one to build a model for Lyman- clouds (Valageas et al.1999a). We shall take advantage of this possibility to include these objects in the present study. Indeed, although at high redshifts they do not contribute significantly to the total opacity (which comes mainly from the uniform component of the IGM) since only a small fraction of baryonic matter has been allowed to form bound objects, at redshifts close to the reionization epoch they already provide a non-negligible opacity. We identify Lyman- absorbers as three different classes of objects, which we shall briefly describe below.
5.1. Lyman- forest
We assume that after reionization the gas within low-density halos is reheated by the UV flux to a temperature K. Hence in such shallow potential wells, baryonic density fluctuations are erased over scales defined as in (22) but with the temperature . This builds our first class of objects defined by their radius and virial temperatures . The multiplicity function of these mass condensations is again obtained from (2). The fraction of neutral hydrogen at low z is evaluated by assuming photo-ionization equilibrium. At high z prior to reionization, when the UV flux is very small and cannot heat the gas, we simply take while the fraction of neutral hydrogen is unity. Since the baryonic density is roughly uniform within these objects (by definition) we consider that each halo produces one specific mean column density on any intersecting line-of-sight (we neglect the small dependence on the impact parameter due to geometry). At low z this population can be identified with the Lyman- forest. Note that, as explained in details in Valageas et al. (1999a), our approach is also valid for clouds which are not spherical objects of radius but filaments of thickness and length . This is due to the growth of the density fluctuations on smaller scales (along with ) and to the direction jumps of filamentary structures.
Here we note that models for the Lyman- forest are often classified in two categories: 1) mini-halo models and 2) IGM density fluctuations. In case 1), one considers that Lyman- absorbers are discrete clouds formed by bound collapsed objects (or halos confined by the IGM pressure) which occupy a small fraction of the volume. On the other hand, in case 2) (which is currently favored) one assumes that absorption comes from a continuous medium (the IGM) with relatively small density fluctuations. Although in our model we identify distinct patches of matter (of size ) as in 1), the underlying picture corresponds to the case 2). Indeed, as we consider regions with an "overdensity" from down to , defined below in (24), which can be as low as , see Fig. 13, we take into account all the volume of the universe. Hence our Lyman- forest absorbers are made of a broad range of density fluctuations within the IGM which fill all the space between galactic halos (which we describe below as they form Lyman-limit and damped systems and only occupy a negligible fraction of the volume, as seen in Fig. 12). Note that this would not be possible if we were to consider density fluctuations defined by a constant density threshold since this would imply that we probe at most a fraction of the volume of the universe. We identify the lowest density regions (i.e. with a density contrast ), which are also the most numerous and fill most of the volume, with the IGM. A patch of matter with this density would only make up a column density cm-2 on a scale at .
5.2. Lyman-limit systems
Potential wells with a large virial temperature do not see their baryonic density profile smoothed out and they also retain their individuality. Thus, we define a second class of objects identified to the ionized outer shells of virialized halos, characterized by their density contrast and satisfying . The deepest of these potential wells (such that ) corresponds to the galactic halo described in Sect. 3. We assume that the mean density profile is a power-law (with ) so that each object can now produce a broad range of absorption lines, as a function of the impact parameter of the line-of-sight. This population can be identified with the Lyman-limit systems.
5.3. Damped systems
The deep cores of the virialized halos described above which are not ionized because of self-shielding (at low z) form our third population of objects. One halo can again produce various absorption lines for different impact parameters. At high z, prior to reionization, halos are entirely neutral so that the previous contribution of ionized shells disappears and we only have two classes of objects: these neutral virialized halos and the "forest" objects.
© European Southern Observatory (ESO) 1999
Online publication: June 18, 1999