A number of authors have speculated on the role that hydrostatic pressure plays in the formation of molecular clouds in the centers of galaxies (Helfer and Blitz, 1993; Spergel and Blitz, 1992), and galactic disks (Elmegreen, 1993; Wong and Blitz, 2002; among others). Blitz and Rosolowsky (2004) showed that if hydrostatic pressure is the only parameter governing the molecular gas fraction in galaxies, then one predicts that the location where the ratio of molecular to atomic gas is unity occurs at constant stellar surface density. They probed this prediction and found that the constancy holds to within 40% for 30 nearby galaxies.
The functional form of the relationship between hydrostatic pressure and molecular gas fraction has recently been investigated by Blitz and Rosolowsky (2006) for 14 galaxies covering 3 orders of magnitude in pressure. Hydrostatic pressure is determined by
The quantities vg, the gas velocity dispersion, and h*, the stellar scale height, vary by less than a factor of two both within and among galaxies (van der Kruit and Searle, 1981a, b; Kregel et al., 2002). The quantities *, the stellar surface density, and g, the gas surface density, can be obtained from observations. The results for 14 galaxies is given in Fig. 10.
Figure 10. Plot of the ratio of molecular to atomic surface density as a function of hydrostatic pressure for 14 galaxies. The plot covers 3 magnitudes in pressure and molecular fraction.
The figure shows that the galaxies all have similar slopes for the relationship: H2 / HI P0.92, very nearly linear. Moreover, except for three galaxies, NGC 3627, NGC 4321, and NGC 4501, all have the same constant of proportionality. The three exceptional galaxies all are interacting with their environments and may be subject to additional pressure forces. It is important to point out that we expect this pressure relation to break down at some lower scale no smaller than the scale of a typical GMC, ~ 50 pc. However, on the scale of the pressure scale height, typically a few hundred parsecs, the pressure should be more or less constant both vertically and in the plane of a galaxy.
The two axes in Fig. 10 are not completely independent; both are proportional to H2. However, each axis is also dependent on other quantities such as HI and *. Since * varies by a larger amount in a given galaxy than H2, because HI dominates at low pressures (P / k < 105 cm-3 K) and because both axes have different dependencies on H2, the constancy of the slopes and the agreement of the intercepts cannot be driven by the common appearance of H2 on each axis. A more detailed discussion of this point is given in Blitz and Rosolowsky (2006).
As of this writing we do not know how the LMC and the SMC fit into this picture; no good map giving the stellar surface density for these objects is currently available. Although we do not know the stellar scale heights for these galaxies, because of the weak dependence on h* in Equation 3, this ignorance should not be much of a difficulty. The results for the SMC are particularly interesting because of its low metallicity and low dust-to-gas ratio (Koorneef, 1984; Stanimirovic et al., 2000). Since the extinction in the UV is significantly smaller than in other galaxies, one might expect higher pressures to be necessary to achieve the same fraction of molecular gas in the SMC, though care must be taken since CO may be compromised as a mass tracer in such environments.
The following picture for the formation of molecular clouds in galaxies is, then, suggested by the observations. Density waves or some other process collects the atomic gas into filamentary structures. This process may be the result of energetic events, as is thought to be the case for IC 10, or dynamical processes, as is primarily the case for M33. Depending on how much gas is collected, and where in the gravitational potential of the galaxy the gas is located, a fraction of the atomic hydrogen is turned in molecular gas. In very gas-rich, high pressure regions near galactic centers, this conversion is nearly complete. But some other process, perhaps instabilities, collects the gas into clouds. Whether this is done prior to the formation of GMCs, or after is not clear.