4.1. The Role of Gravitational Instabilities
The onset of robust star formation in gas disks can be described in terms of local gravitational stability parameters, e.g., Qgas = gas / ( G gas), where gas is the gas velocity dispersion and is the disk's epicyclic frequency (Quirk 1972). Regions of the disk where Qgas < 1 are Jeans unstable and prone to collapse, leading to the formation of molecular cloud complexes and eventually stars. The "bead on a string" morphology evident in H (Figure 1) suggests that the rings are gravitationally unstable. Are they?
The Cartwheel's ring is, even ignoring its (unknown) molecular component. However, Qgas > 1 essentially everywhere in L-S'a ring (Figure 3), due to the large gas. This ignores, however, the stellar component's contribution to Q. Using IRAC 4.5 µm data we find that the stellar mass surface density (*) everywhere exceeds that of gas (i.e., * > HI + H2). A gravitational stability parameter combining stars and gas can be written Qtot = ( / G) ( gas / gas + * / *)-1 (Wang & Silk 1994), where the ring's radial H profile constrains * 45 km s-1. Figure 3 shows that when the stellar component is included, Qtot < 1 and L-S's ring is everywhere Jeans unstable.
Figure 3. Azimuthal variations in Q for Cartwheel (left) and L-S (right). The Cartwheel's HI ring is largely sub-critical (Qgas < 1), but not L-S even after adding molecular gas. Only when stellar mass is included does the ring become gravitationally unstable (i.e., Qtot < 1) everywhere.
Conversely, the interior disks in both satisfy Qtot > 1, i.e., these regions are stable against the growth of gravitational instabilities and star formation is effectively quenched.
4.2. Evidence for Peculiar Star Formation Laws
A strong correlation exists between SFR / area (SFR) and the surface density of cold gas in galaxies, i.e., the "Schmidt Law", written SFR = gasN. In M 51 for example, H2 and SFR / area obey SFR H21.37 ± 0.03 (Figure 4). HI is uncorrelated with SFR, implying that it is a photo-dissociation product and not directly involved in the star formation process. We show star formation laws derived for the Cartwheel and L-S in the same figure. Both are peculiar. Unlike M 51, atomic gas in the Cartwheel correlates with SFR in most of the ring, though with a small N. The exponent becomes negative (i.e., anti-correlated) where SFR peaks. Would this peculiarity disappear if the molecular component were available? Not if L-S's ring is any guide: atomic gas obeys M 51's molecular Schmidt Law, but its cold molecular ISM is uncorrelated with SFR, which is completely the opposite from M 51. How can H2 be so apparently disconnected from star formation?
Figure 4. Star formation laws in the rings of L-S (left) and Cartwheel (right) relative to M 51 (Kennicutt et al. 2007). H2 in M 51 (black & green triangles) obeys a Schmidt Law, but HI (blue) is uncorrelated with SFR. In L-S the opposite is true: HI (red squares) obeys a Schmidt Law but H2 is uncorrelated (red circles & arrows). In Cartwheel atomic gas can be correlated (filled purple squares) or anti-correlated (empty squares) with SFR / area.
4.3. Enhanced Star Formation Efficiencies
Star formation efficiency (SFE) is the yield of massive stars per unit H2 mass. Young et al. (1996) find nearly constant SFE ( log(LH / MH2)) from S0 to Scd ( -1.8 L / M). Later types show higher SFE, peaking at -0.8 L / M for Irr. Detecting molecular gas in L-S's ring allows the first estimate of SFE in a ring galaxy. We find SFE = -0.7 ± 0.1 L / M, i.e., similar to an Irr and an order of magnitude higher than the (presumably ~ Sa) progenitor. This result depends, of course, on our ability to reliably measure H2 in the ring using 12CO emission.