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One of the driver to propose cold H2 as a dark matter candidate is our increasing knowledge about evolution of galaxies along the Hubble sequence (e.g. Pfenniger, Combes & Martinet, 1994). Because of spiral waves and bars, galaxies progressively concentrate their mass towards the center, and the late-type galaxies evolve to early-types in the sequence. Besides, HI observations of rotation curves have shown that the fraction of dark matter in the total mass is larger in late-type galaxies: therefore, some of the dark matter must be transformed into stars during evolution (cf Pfenniger, this conference).

4.1. Baryonic mass fraction

The quantity of baryons in the Universe (and more precisely the fraction of the critical density in baryons Omegab) is constrained by the primordial nucleosynthesis to be Omegab = 0.013 h-2, with h = H0 / (100 km/s/Mpc) is the reduced Hubble constant. With h = 0.5, Omegab is 0.09, and more generally Omegab is between 0.01 and 0.09 (Walker et al. 1991, Smith et al. 1993), while the visible matter corresponds to Omega* ~ 0.003 (M/L/5) h-1 (+ 0.006 h-1.5 for hot gas). Therefore, most of the baryons (90%) are dark.

In rich clusters of galaxies, the baryons are more visible, under the form of hot gas, they constitute ~ 30% of the total mass (White et al. 1993). Since clusters must be representative of the baryonic fraction of the Universe, this implies that the total mass cannot be larger than 3 times the baryons mass (or Omegam < 0.3).

4.2. The smallest fragments

The existence of a large number of gas clumpuscules (of ~ 10 AU in size) in the Galaxy has already been invoked to explain the observed ESE (Extreme Scattering Events) in front of quasars, by Fiedler et al. (1987, 1994). About 300 QSOs were observed during a few years, 150 over 12 yrs. More than 10 ESE events were detected, due to diffraction or refraction by a region of high electronic density (ne). From the duration of the events, sizes of ~ 10 AU are derived, and from their frequency, the number of clumpuscules in the Galaxy must be about 103 the number of stars. The neutral density of these objects is still a matter of debate. Their stability is best explained in the hypothesis that they are self-gravitating. The mass of one clumpuscule is then of the order of 10-3 Msun. Walker & Wardle (1998) have recently built models of self-gravitating clouds, with envelopes ionised by the interstellar radiation field: they found for the electronic density the right order of magnitude to account for the observed ESE. This hypothesis is supported by direct observations through HI VLBI in absorption in front of remote radio sources (Diamond et al. 1989, Davis et al. 1996, Faison et al. 1998); large column densities (~ 1021 cm-2) are observed with sizes of ~ 10 AU, leading to HI densities of 106 cm-3 or more.

4.3. Gamma-rays

Dixon et al. (1998) from EGRET observations have recently detected an excess of diffuse gamma-ray emission in the galactic halo. This could be interpreted in several ways: either coming from un-resolved sources associated to the Galaxy; or being due to high-latitude inverse compton emission; or finally to extra molecular gas in the halo, through cosmic ray/nucleon reaction giving pi0 then gamma-rays. This has been developped by de Paolis et al. (1999) and Kalberla et al. (1999), see also Shchekinov (this conference). Cosmic rays are stopped by thick clumpuscules, that have enough column density to be opaque for both cosmic rays and gamma rays. Sciama (1999) proposes that cosmic rays are fragmented in clouds, heat the clouds, and are responsible for the their FIR emission (Sciama 1999). However, the absorbed energy is non negligeable, and since clouds in these halo models are assumed to move through the optical plane (in their z-ocillations), sweep up high-metallicity gas, and therefore contain CO molecules, they should be visible through CO emission.

4.4. Various models of H2 as dark matter

The first model proposes to prolonge the visible gaseous disk towards large radii, with thickening and flaring, following the HI disk. The cold and dark H2 component is supported by rotation, exists only outside the optical disk, where it is required by rotation curves (Pfenniger et al 1994, Pfenniger & Combes 1994). The gas is stabilised through a constantly evolving fractal structure, experiencing Jeans instabilities at all scales, in thermal equilibrium with the cosmic background radiation at T = 2.7 (1 + z) K.

Other models distribute the dark molecular gas in a spherical or flattened halo, with no hole within the optical disk. The molecular gas is not so cold, and is associated with clusters of brown dwarfs or MACHOS (de Paolis et al. 1995, Gerhard & Silk 1996, Shchekinov, this conference).

In the clumpuscule model, the HI gas can be considered as a tracer, the interface between the molecular clumps and the extra-galactic radiation field. Beyond the HI disk, there could be an ionization front, and the interface might become ionized hydrogen. In this context, there should exist a distribution correlation between the dark matter and the HI gas. This is indeed the case, as already remarked by Bosma (1981), Broeils (1992) or Freeman (1993): there is a constant ratio between the surface density of dark matter, as deduced from the rotation curves, and the HI surface density, SigmaDM / SigmaHI = 7-10 (cf figure 3, and a recent work by Hoekstra et al. 1999). This ratio is constant with radius in a given galaxy, and varies slightly from galaxy to galaxy, being larger in early-types. However, the dark matter does not dominate the mass in the latter, and therefore the estimate of its contribution is more uncertain. The correlation is the most striking in dwarf galaxies, which are dominated by dark matter. The observed velocity curve is almost exactly proportional to the velocity curve expected from the HI component alone. Figure 3 shows the example of NGC 1560, from Broeils (1992). Let us note that dwarf galaxies represent a hard test for all models of dark matter, since the stellar component does not dominate the mass. They rule out cold dark matter (CDM) profiles (Burkert & Silk 1997), and hot dark matter (HDM) models are also unable to concentrate as much as is observed (Lake 1989, 1990, Moore 1996). Baryonic dark matter is thus required.

Figure 3

Figure 3. Left: HI rotation curve of NGC 1560 (dots +error-bars), with the rotation curve due to the HI itself (dotted line) and the stellar component (dash). The full line is the resulting expected rotation curve, when the HI mass has been multiplied by 6.2. Right: The ratio of surface densities of dark matter to HI required to explain the rotation curve of galaxies, as a function of type. Data from 23 galaxies have been taken from Broeils (1992) and references therein.

4.5. Detection possibilities

If there exists a transition region where the cold H2 is mixed in part with evolved gas with enough metallicity and dust, it might be possible to detect cold dust emission. Encouraging results have been found by the COBE satellite, concluding to the existence of a cold (4-7K) component with column densities 10 times that of the warm component (at 18K), and more confined to the outer Galaxy (Reach et al. 1995).

Another promising tool for detection is H2 absorption in the UV electronic lines. The main problem is the low expected surface filling factor of the cold gas (~ 1%). H2 has already been detected in front of QSO through intervening galaxies (Foltz et al. 1988, Ge et al 1997); but these observations suffer from severe confusion problem in the Lyalpha forest. With the Hubble Space telescope, it was not possible to observe the fundamental lines at zero redshift, but it will be possible with FUSE. Let us remark that heavy lines of sight will be impossible to observe, due to obscuration of the background source (e.g. Combes & Pfenniger 1997). Finally, observations of the lowest pure rotational lines of H2 have suggested some clues for the existence of large quantities of H2 in galaxies (Valentijn & van der Werf 1999) and should be pursued in external galaxies, at much further radius than was possible with ISO.

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