The rings are gas rich but seemingly H2 poor. Since HI rapidly converts into H2, the low fmol cannot signal the consumption of the molecular gas reservoir. Nor can metallicity effects by themselves be responsible, at least in L-S. The gas phase pressure (PISM) might be a factor, as it directly affects the HI to H2 conversion rate. Elmegreen (1993) finds fmol (PISM / P)2.2 ( / )-1, where is the ambient UV-field. For L-S's ring we estimated with Spitzer and GALEX images, and PISM ( G/2)(gas2 + (gas / *) gas *), with the ring's stellar surface mass density derived with IRAC 4.5 µm data. We find very high gas phase pressures, with PISM / PISM,local 30-400, leading us to expect fmol 1 everywhere. L-S's ring should be dominated by molecular gas. Why isn't it?
We used photo-dissociation models in Allen et al. (2004) to estimate average gas volume densities (n) in L-S's ring given its HI and UV-field. In the northern half of the ring, n = 100-300 cm-3, implying an ISM dominated by the Cold Neutral Medium (CNM, T = 50-100 K), i.e., the precursor of cold molecular clouds. In the southwest, where SFR and HI are both much higher, the models give n 2 cm-3, which taken at face value, points to an ISM dominated by the Warm Neutral Medium (WNM, T 7000 K). How can you form stars out of this?
We believe the answer lies in fundamental differences in the environments of rings and spiral arms. Consider that molecular clouds spend 20 Myrs in the arms of grand design spirals like M 51, whereas the ISM is confined in rings, equally as dense and actively forming stars, for 200 Myr. While molecular cloud growth is enhanced in the high gas rings, the destructive effects of SNe and OB stars are also amplified. A dominant WNM might be expected as the molecular clouds become fragmented and "over-cooked" by shocks and sustained UV-fields. CO might in this case retreat to the inner-most cloud cores resulting in weak ICO and underestimates of H2. This might explain the peculiar Schmidt Laws and enhanced SFE. At the same time, higher cloud collision rates might favor the formation of unusually large molecular cloud complexes and more efficient star formation. More work remains though results from Cartwheel and L-S are intriguing.