The bulk of molecular hydrogen in a galaxy is cold, around 10-20K, and therefore invisible. The first rotational level, accessible only through a quadrupolar transition, is more than 500 K above the fundamental. The presence of H2 is inferred essentially from the CO tracer. The carbon monoxyde is the most abundant molecule after H2; its dipole moment is small (0.1 Debye) and therefore CO is easily excited, the emission of CO(1-0) at 2.6mm (first level at 5.52K) is ubiquitous in the Galaxy.
1.1. The H2/CO conversion ratio
To calibrate the H2/CO ratio, the most direct and natural is to compare the UV absorption lines of CO and H2 along the same line of sight (Copernicus, e.g. Spitzer & Jenkins 1975; ORFEUS, cf Richter et al., this conference). However, only very low column densities are accessible, in order to see the background source, and therefore these observations sample only the diffuse gas, which is not representative of the global molecular component. It is well known now that the conversion ratio might vary considerably from diffuse to dense gas (see below). The CO molecule is excited by H2 collisions, and should be a good tracer; but its main rotational lines are most of the times optically thick. One can then think of observing its isotopic substitutes 13CO or C18O, but these are poor tracers since they are selectively photodissociated, and trace only the dense cores.
The main justification to use an H2/CO conversion ratio is the Virial hypothesis: in fact, the CO profiles do not yield the column densities, but they give the velocity width V of molecular clouds. Once the latter are mapped, and their size R known, the virial mass can be derived, proportional to V2 R. There exists a good relation between the CO luminosity and the virial mass, as shown in Figure 1. The relation has a power-law shape, but with a slope different from 1. Both are not proportional, and the conversion ratio should vary by more than a factor 10 from small to Giant Molecular Clouds (GMC). In external galaxies, the observations provide only an average over many clouds, and it has been hoped that the clouds are of the same nature from galaxy to galaxy. If Tb is the brightness temperature of the average cloud, the conversion ratio X should vary as n1/2 / Tb, where n is the average density of the cloud. This does not take into account the influence of the gas metallicity. And the CO luminosity varies with the metallicity Z, sometimes more than linearly. In the Magellanic Clouds, LMC or SMC (Rubio et al 1993), the conversion ratio X might be 10 times higher than the "standard" ratio. The ratio can be known for local group galaxies, since individual clouds can be resolved, and virial masses computed (Wilson 1995).
Figure 1. Virial mass versus CO luminosity for molecular clouds in the Milky Way. The fit corresponds to MV LCO0.76. The data are from Dame et al. (1986); Solomon et al. (1987); Heithausen (1996); Magnani et al. (1985); Williams et al. (1994); Falgarone et al. (1992); Wang et al. (1995); Ward-Thompson et al. (1994); Lemme et al. (1995).
Dust as a tracer
At millimetric wavelengths, in the Rayleigh-Jeans domain, dust emission depends linearly on temperature, and its great advantage is its optical thinness. In some galaxies, CO and dust emission fall similarly with radius, like in NGC 891 (Guélin et al. 1993). In other, such as NGC 4565 (Neininger et al. 1996), the dust emission falls more slowly than CO, although more rapidly than HI emission. This can be interpreted by the exponential decrease of metallicity with radius. The dust/HI ratio follows this dependency, while CO/HI is decreasing more rapidly (either due to metallicity, or excitation problems).
Their emission is proportional to the product of the Cosmic Ray density and the gas density. But both densities, and their radial profiles are not known independently. The -ray radial distribution is however much more extended than that of the supernovae remnants, the source of cosmic ray acceleration (e.g. Bloemen 1989). Recently: EGRET onboard GRO has observed an excess of gamma-rays in the halo of our Galaxy (see below).
Direct H2 observations
Of course, H2 can also be observed directly when it is warm. Starbursts and mergers reveal strong 2.2 µm emission, like in NGC 6240 (DePoy et al 1986). The source of excitation has long been debated (X-ray heating, UV fluorescence, shocks ...) and it was recently concluded that global shocks were responsible (van der Werf et al. 1993, Sugai et al. 1997). Pure rotational lines have been observed with ISO. In Arp220, as much as 10% of the ISM could be in the warm phase, i.e. 3 109 M (Sturm et al. 1996) while CO observations conclude to a total M(H2) = 3.5 1010 M (Scoville et al. 1991). In normal galaxies, the warm H2 could be less abundant (Valentijn et al. 1996). At least, the warm CO component does not affect the H2 / CO ratio.