6. OPEN QUESTIONS AND CONCLUDING REMARKS

In conclusion, I'd like to enumerate a few questions regarding the chemical evolution of galaxies that seem to need further investigation.

• What are the primary mechanisms determining the shape and slope of abundance gradients in spiral galaxies? We have seen that chemical evolution models tend to predict that composition gradients should get shallower in the inner disks spirals, but this has not been observed in real galaxies. Does viscous evolution play a role in maintaining an exponential gradient, by transferring new gas into the inner disk? This is essentially a hydrodynamical problem. It is also important to determine how closely composition gradients follow an exponential profile, since the H II region abundance scale is still uncertain for high metallicity. IR spectroscopy will make a significant contribution to constraining the abundance calibrations in the metal-rich regime.
• How homogeneous are abundances in galaxies at a given place and time? Conflicting studies have argued for significant (±0.2-0.3 dex) variations in abundances on small scales, or for a very homogeneous composition (< 0.1 dex variations). The question is relevant to the time scales for cooling and mixing of stellar ejecta with the ambient ISM. Most chemical evolution models assume instantaneous mixing, but is this a good approximation? Detailed tudies of abundance variations across small (< 1 kpc) regions of galaxies will tell us how homogeneous the ISM composition is.
• Is infall of gas presently occuring in galaxies, and how does the rate evolve with time? This is a big unknown, since most chemical evolution models use relatively slow, ongoing infall of metal-poor gas to suppress the fraction of metal-poor G dwarfs. Observational evidence for classical infall is sketchy. The high-velocity clouds seen at high latitudes may represent infall, or may be part of a Galactic fountain flow, or may be associated with interaction between the Galaxy and its satellite galaxies.
• What galaxies may be losing metals to the IGM, and how much do they contribute? Is there a threshold mass above which galaxies retain metals?
• Does galaxy environment influence composition? The Virgo cluster studies need to be followed up by larger samples in a wider variety of cluster environments. The spiral-rich Ursa Major cluster and the Coma cluster are two obvious choices for continued study.
• Is there zero metallicity gas (or stars for that matter) in galaxies? Pre-enrichment by an initial stellar Population III also provides a solution to the G-dwarf problem and to the origin of metals seen in Ly forest clouds. What is the composition of the huge gas reservoirs in the outer parts of spirals and irregulars?

For abundance work in ionized nebulae, we need to understand better the effects of dust on the thermal and ionization balance. The calculated ionizing spectra from massive stars are still in a state of flux, as more physics and opacity are included; this is an area that will continue to require attention as computing power grows. The effects of inhomogeneous structure on the observed emission-line spectrum of H II regions also needs to be addressed.

Stellar nucleosynthesis also needs continuing attention. The biggest remaining problem in theoretical stellar evolution and nucleosynthesis continues to be the treatment of convective mixing, which affects both structure and nucleosynthesis. This is also a hydrodynamical problem requiring improved computing power, and should provide a source of entertainment (and argument) for some time.

We are seeing great improvements in the study of abundances in nearby galaxies, particularly with the new space-based UV and IR observatories, which are greatly improving the data for elements besides oxygen. With these new data, we are in a better position to connect the present-day abundance patterns in galaxies with those observed in high-redshift gas clouds. Eventually, emission-line spectroscopy of distant galaxies should greatly expand our information on heavy element abundances at early times, and allow us to trace the evolution of metallicity in the universe in greater detail. This will be an important complement to the absorption line work on DLAs, as the connection between the emission-line gas and the stellar component is much more clear, and the disk component can be sampled more completely than with absorption studies.

For nearby galaxies one challenge for observers is to compile a homogeneous reference set of abundance data, to provide a statisically significant sample for outlining the relationships between abundances, galaxy mass, and Hubble type, and for understanding the effects of environment on abundance profiles. Some Hubble types are poorly represented in the database, particularly very early Hubble types (Sa-Sab), and very late types (Sd). Basic structural data for nearby galaxies also need improvement. The amount and distribution of molecular gas is one area for improvement. Stellar mass-to-light ratios and the stellar mass surface density distribution is another. Wide-field imaging in the infrared should help reduce the uncertainty in the mass of the stellar component.

One might have noticed that many of the theoretical questions mentioned above come down to hydrodynamics. Understanding star formation, the evolution of galaxies, and the structure of stars all involve hydrodynamics at fundamental levels, so I believe that improved hydrodynamical modeling of all of these phenomena will be the key to a better understanding of galaxy evolution. Understanding the mechanisms which connect abundances in galaxies to galaxy structure should provide a continuing challenge to galaxy evolution theorists.

I am grateful to the organizers of this Winter School for the opportunity to meet and interact with the young scientists (on both the galactic and stellar side) whose research papers I have been enjoying in the past couple of years. Special thanks go to Eric Bell for producing Figure 5 for me, and for informative discussions of the properties of galaxy colors and population synthesis models. The review presented here has also benefitted by numerous conversations over the past years with Daniela Calzetti, Mike Edmunds, Gary Ferland, Claus Leitherer, John Mathis, Andy McWilliam, and Verne Smith. Finally, I must also acknowledge my various collaborators on galaxy abundances (Reginald Dufour, Rob Kennicutt, Greg Shields, Evan Skillman, Manuel Peimbert, and Silvia Torres-Peimbert) who have contributed greatly to many of the results I have presented in these lectures. My work on abundances in galaxies has been supported the past four years by NASA grant NAG5-7734.