7.2. The Next Steps in Modeling

In the next few years computer power will undoubtedly continue to increase rapidly, but there are many challenges remaining in ring galaxy simulation, and it is unlikely that the computers will be powerful enough to solve them all directly. Nonetheless, we can expect substantial progress in an evolutionary, and perhaps even revolutionary, sense. To begin with, there is still a good deal of work to be done with current simulation tools. This includes detailed modeling of specific systems, especially those that have been studied at many wavelengths. It also includes more complete explorations of the effects of varying target galaxy structural parameters, and orbital parameters. This is especially true for off-center collisions, where all indications are that the wave structure depends very sensitively on the parameters. Finally, the long-term evolution of ring galaxies, including companion capture and merger, has just begun to be investigated.

With regard to modeling specific systems, the first question that arises is - which ones? The simplest answer is to choose ones with the most observational data available, especially the larger ring galaxies which are probably the most dynamically evolved. In particular, the existence of kinematic data (especially HI observations) is of special value to the modeler. For example, there is still important work to be done on the Cartwheel ring. The models in Struck-Marcell and Higdon (1993) were based on low-resolution VLA 21 cm data. Since that time Higdon (1992) has produced higher resolution velocity maps. Models designed to fit the high resolution velocity data should also give us a better idea of how warped the Cartwheel disk is. New Hubble Space Telescope observations have also been obtained (by K. Borne, R. Lucas (STScI) and ourselves) and observations such as these will guide future models. Additional fully self-consistent combined N-body/gas simulations are needed. Overall, the Cartwheel is a good system to model with three-body simulations because the potential is probably halo dominated, and the companions are relatively small, so the halo perturbation is minimal. However, self-gravity is needed to study the growth of local gravitational instabilities in the disk, and some differences can be expected with "live" halos and disks. In addition, the behavior of the collisional effect of a gas-rich intruder galaxy will probably be best studied with a responsive self-gravitating disk.

As discussed above, a good deal of data is currently being acquired on many other systems. The Lindsey-Shapley ring, Arp 10, Arp 147, VIIZw466 and a number of others will deserve detailed modeling efforts in the next few years. One specific hope we maintain is that new observations will provide further information on the mystery of spokes. Either they will be discovered in other systems with more sensitive, higher resolution data, or tighter constraints will be placed on their existence. This information, in conjunction with detailed modeling, would help enormously in determining whether the theoretical ideas discussed above are correct.

Even aside from models of specific systems, there is much general unfinished business in the realm of ring galaxy simulation - e.g., so much parameter space and so little time! Of course, the advantage of ring galaxies is that their symmetry eliminates or reduces the importance of some dimensions of parameter space. To begin with only relatively cursory explorations have been made of the effect of varying the disk/halo/bulge ratios (Huang and Stewart 1988; Wallin and Struck-Marcell 1988; Horellou and Combes 1994). As usual, kinematic models should provide a good guide to ring structure in purely symmetric collisions, but they should be tested, and the variations in phenomena like disk warping should be elucidated. Another factor that deserves further study is the effect of the gas to old star mass ratio in the target disk. Some idea of the effects of the gas on the disk stars can be gleaned from the work of Gerber (1993), and Hernquist and Weil (1993), but not enough models have been run to determine the systematics.

Similarly, we do not yet have a systematic guide to the morphological zoo of ring relatives formed in slightly off-center, slightly retrograde, prograde or direct collisions. As emphasized above and in Appendix 2, kinematic (and restricted three-body) models could also be a useful guide in this area. However, because of the extreme parameter sensitivity, producing a thorough morphological map by any means will be laborious. It seems likely that this goal will continue to be accomplished piecemeal, e.g., by assembling the results of studies of individual (asymmetric) systems.

Another fundamental parameter is time. By and large published simulations are not run long enough to determine the long term fate of the ring galaxy. Since in most cases where there is kinematic data available for the companion the system appears bound, we can expect an eventual merger. Merger simulations lead us to expect that this will occur after no more than two or three encounters. Some of the possible effects through the second encounter in nearly symmetric cases are reviewed in Section 4.3 and Appendix 1. The studies of Lotan and Struck-Marcell described there are the only work we are aware of to date. If the initial collision is significantly off-center or the inclination differs significantly from 90°, we expect that the evolving system will become increasingly asymmetric, and have little relation to the ring galaxy phenomenon after the second collision. However, these preliminary results and reasonable conjectures await confirmation with more detailed and extensive modeling.

Moreover, the long term evolution of unbound or marginally bound systems is not without interest. An intriguing example was given in the thesis of Lotan-Luban (1990). She found that in direct, off-center collisions, and also in off-center, slightly inclined (retrograde) collisions, a one-armed leading spiral wave formed and persisted for a very long time. A similar phenomenon was found earlier in retrograde tidal interactions by Thomasson et al. (1989) and Athanassoula (1978). Lotan-Luban tested a variety of parameter values with her restricted three-body simulations, and discussed the parameter dependencies in some detail. Studies with kinematic models (CS unpublished) seem to indicate that the one-arm is the locus of overlap of very high order ring caustic edges. This is consistent with the fact that the one-arm has not been seen to form in simulations of gas disks, where the ringing tends to damp out after about the third ring. Coupled N-body plus gas simulations are needed to answer the question of whether the one-arm appears in a self-consistent stellar disk in the presence of dissipative gas.

How dissipative is the gas, e.g., how does it respond to compression? This is not merely a question of the immediate (e.g., postshock) compressibility of the gas, but equally of the heating and cooling processes at work within it, the resulting (time and spatially varying) thermal phase structure. We will not repeat the discussion of Section 6.5 where some preliminary explorations of cooling/heating were presented, but we want to reiterate that those models as well as the cloud fluid models of Struck-Marcell and Appleton (1987) highlight the importance of such processes in the wake of a starburst ring. The issues of the role of these processes and how best to treat them in numerical simulations extend far beyond the limited field of ring galaxies. However, in all cases it is clear that their inclusion will introduce at least several additional parameters, i.e., new dimensions of model phase space, much additional computational complexity, and inevitable disagreements between workers following different approaches. It seems likely that cooling/heating effects will be one of the main frontiers of numerical simulation of galaxies for at least another decade. Once again, we expect that the relative simplicity and symmetry of collisional ring galaxies will guarantee them an important role in this field. The propagating single burst nature of their disk star formation is very simple, and thus attractive to modelers, compared with the complexity of, e.g., merging gas disks. High resolution observations of large-scale cooling shocks or (heated) superbubbles in rings would be extremely useful and exciting to modelers, and such discoveries are probably imminent.

It is becoming clear that to model and understand individual interacting galaxies requires the inclusion of much relevant physics. We believe that this must include, at some level of approximation, stellar and gas dynamics of the multi-component galaxies with self-gravity, pressure and heating/cooling effects. In particular, to model most real ring galaxy systems, this will eventually require that the simulations include non-isothermal gas disks in both primary and companion galaxies. There are several reasons these simulations should include cooling and heating. The first is that the strong shocks resulting from direct collisions between gas elements in different galaxies may heat the gas to such high temperatures that radiative cooling is not essentially immediate. The second is that the adiabatic expansion cooling of gas pulled out of the disks may be so strong that the temperature of that gas falls below its original value, an effect which could be very important to the occurrence of star formation in extended tidal features. A third reason is that the thermal effects of gas falling back onto the primary disk may be very important.

The upshot is that as simulations get more realistic they will get much more complex, and because of computational limitations, it will not be possible to include all the relevant processes in a unique way, based on well-understood physical principles. Approximations and phenomenological treatments will still be necessary. Consequently, model predictions will have to be handled with care, and continually checked and constrained by observation. Nonetheless, in conjunction with future multiwavelength observations (especially in the X-ray and far-infrared) the next generations of models should substantially advance our understanding of star formation and the thermal physics of the interstellar gas in ring galaxies in particular and interacting galaxies in general.

Acknowledgments

We thank the following people for supplying material, in some cases in advance of publication: K. Borne (STScI), R. Buta (U. of Alabama), F. Combes (Meudon), A. Garcia (IAC-Spain), R. Gerber (NASA-Ames), F. Ghigo (NRAO-GB), L. Hernquist (Lick Obs.), J. Higdon (NRAO-AOC), C. Horellou (OSO-Sweden), M. Joy (NASA-Marshall), S. Lamb (U. of Illinois), S. Majewski (Carnegie-Pasadena), A. Marston (Drake U.- Iowa), J. C. Mihos (Lick Obs.), R. Norris (ATNF-Australia), J. Rodriguez Espinosa (IAC-Spain), B. Smith (U. of Texas) and J. Wallin (GMU). For stimulating conversations on ring galaxies we also wish to thank F. Ghigo, K. Borne, J. Wallin, J. Higdon and C. Horrelou and R. Gerber. PNA wishes to thank the hospitality of Cathy Horrelou and Fransoise Combes (Meudon) during a recent visit to Paris in which molecular observations were discussed. We are especially grateful for the insightful comments and extensive suggestions of A. Toomre and those of an anonymous referee. We also thank B. Elmegreen for additional suggestions. The latter part of this work was partially funded under NSF grant AST 9319596.