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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 = sigmagas kappa / (pi G Sigmagas), where sigmagas is the gas velocity dispersion and kappa 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 Halpha (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 sigmagas. This ignores, however, the stellar component's contribution to Q. Using IRAC 4.5 µm data we find that the stellar mass surface density (Sigma*) everywhere exceeds that of gas (i.e., Sigma* > SigmaHI + SigmaH2). A gravitational stability parameter combining stars and gas can be written Qtot = (kappa / pi G) ( Sigmagas / sigmagas + Sigma* / sigma*)-1 (Wang & Silk 1994), where the ring's radial Halpha profile constrains sigma* ltapprox 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

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 (SigmaSFR) and the surface density of cold gas in galaxies, i.e., the "Schmidt Law", written SigmaSFR = beta SigmagasN. In M 51 for example, H2 and SFR / area obey SigmaSFR propto SigmaH21.37 ± 0.03 (Figure 4). HI is uncorrelated with SigmaSFR, 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 SigmaSFR in most of the ring, though with a small N. The exponent becomes negative (i.e., anti-correlated) where SigmaSFR 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 SigmaSFR, which is completely the opposite from M 51. How can H2 be so apparently disconnected from star formation?

Figure 4

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 SigmaSFR. 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 (ident log(LHalpha / MH2)) from S0 to Scd ( approx -1.8 Lodot / Modot). Later types show higher SFE, peaking at -0.8 Lodot / Modot 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 Lodot / Modot, 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.

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