6.3. Models of the Cartwheel
There has been much recent observational work on the Cartwheel which has long been the ring galaxy prototype (see especially Section 3). It is, thus far, the most studied of all the ring galaxies. A rotation curve and ring expansion rate derived from the 21 cm. data (Higdon 1993, Struck-Marcell and Higdon 1993) provides a basis for any modeling effort. The color and emission line data, discussed earlier, yielded the very exciting result that the material behind the ring appears to be well represented as a sequence of aging stellar populations (Marcum, Appleton and Higdon 1992). More surprising is the result that there is little evidence for an older stellar disk in most of the region contained within the large ring. The ring wave has evidently triggered the first SF in much of the gas disk. Of all the ring galaxies discussed in this article, the Cartwheel may well be the most appropriate for pure hydrodynamic modeling.
The wealth of new observations stimulated a new modeling effort by Struck-Marcell and Higdon (1993). Several techniques were used ranging from semi-analytic calculations of stellar orbits in the KIA model to restricted three-body numerical hydrodynamical simulations of the Cartwheel disk. These models were able to produce a reasonable fit to the morphology and kinematics of the Cartwheel by assuming a slightly off-center impact with a 20% mass companion. Specifically, the relative sizes of the two rings and the shape of the azimuthally averaged rotation curve were reproduced by an iterative process. This process consisted of estimating the form of the (initial) halo potential from the 21 cm. rotation curve, comparing the resulting post-collision rotation curve at the relevant time in the model disk to the data, and then updating the halo potential and repeating the process until a reasonable fit was achieved. Mean radial velocity profiles were found to be very sensitive to the way the averaging was performed, and to the time since impact. Improved fits were obtained in the later analysis of the 21 cm. data given in Higdon (1993).
Another basic result of the models of Struck-Marcell and Higdon (1993) is that the first ring wave is weak in galaxies with a slightly rising rotation curve like the Cartwheel. Many of the physical mechanisms suggested as star formation triggers in interacting galaxies cannot reconcile the vigorous starburst in the ring with the small density perturbation. Specifically, the wave is not strong enough to generate either shocks or a nonlinear increase in cloud collisions. Thus, neither direct triggering by cloud collisions, which is the basis of many popular models of star formation in interacting galaxies (e.g., Noguchi 1990; Olson and Kwan 1990a, b), nor density dependencies without a threshold (e.g., Mihos et al. 1992, 1993) can account for the starburst ring. Instead, the nonlinear response in the ring (first suggested by Davies and Morton 1982 and discussed recently by Charmandaris, Appleton and Marston 1993) argues strongly for a threshold (density) effect. The simulations of Struck-Marcell and Higdon show that when the precollision disk is not too far from the gravitational instability threshold the wave triggers strong cloud buildup in the ring, and spoke formation downstream. An alternate model in which the observed ring is actually the second wave is discussed below. Because the companion is slightly less massive, the second ring is similar to the wave described by Struck-Marcell and Higdon.
On the other hand, as noted above, Gerber, Lamb and Balsara (1992) describe evidence of the existence of strong shocks and shock-induced star formation in another ring, Arp 147. The physics of wave-induced star formation is complicated and the role of different processes probably varies from system to system, depending on, e.g., companion size and the perturbation amplitude. The main lesson of the Cartwheel example is that it demonstrates what kind of information can be obtained about modes of star formation from the rings.
Another aspect of the Cartwheel ring galaxy that has yet to be modeled in detail is the fact that most of the star formation occurs in the southern quadrant of the galaxy (see also discussion in Section 3.4). The early models of Appleton and Struck-Marcell (1987b) were able, with the threshold star formation models, to provide some explanation for why only parts of the ring are fully activated, yet neither these models, nor the recent SPH/Schmidt law algorithms of Mihos and Hernquist (1994a, b) can explain the absence of star formation in the second inner ring. Perhaps the explanation lies in the highly asymmetric distribution of the large-scale HI emission (Higdon 1992) which may indicate that a substantial amount of HI has been "punched" out of the center during the collision (see Foster 1986; Horellou and Combes 1994).