This review has focused on understanding the mechanisms that underlie the various instabilities and processes that affect the structure of galaxy disks. The discussion has referred extensively to simulations that are sufficiently simple that they clearly illustrate each particular aspect of the behavior. A complementary, and powerful, approach is to add additional physical processes to simulations, with the aim of improving realism to address otherwise inaccessible questions. However, the increased complexity of the behavior that comes with increasing realism, makes a deep understanding of the results harder to achieve. Hopefully, the behavior described here will form a solid basis on which to build as the challenges presented by more realistic systems are addressed.
A contrast with accretion disk theory seems appropriate here. Shakura & Sunyaev (1973) proposed a scaling relation for turbulent viscosity that led to rapid progress in modeling accretion disks some 25 years before the likely origin of the viscosity was identified (Balbus & Hawley 1998). A theory for the structural evolution of galaxies seems much farther away. While most of the important physical processes may have been identified, exactly how they drive evolution is still not fully understood, and even the evolutionary path remains vague. In the absence of this understanding, simplifying scaling laws cannot be identified with confidence and it seems best to work at improved understanding of the mechanisms at play.
Galaxy dynamics has made immense strides in the 45 years since the chapter by Oort (1965) in the corresponding volume of the preceding series. Understanding of local wave mechanics (Section 3) and the mechanisms for the principal global gravitational instabilities (Sections 4 & 6) is well advanced. Bending waves and global buckling modes (Section 8) are mostly understood, but not at quite the same level, while lop-sided modes (Section 5) perhaps still require some more concerted effort. Understanding of bar structure (Section 9) and the role of bars in galaxy evolution has developed beyond recognition, and disk heating (Section 10) seems more solidly understood, with our confidence being strongly boosted by the extremely valuable data from Nordström et al. (2004).
But answers to a number of major questions of galaxy dynamics are still incomplete. Although the bar-forming instability is now understood (Section 4.1), it does not provide a clear picture of why only a little over half of all bright disk galaxies are barred (Section 9.2). After bars, spirals arms are the second most prominent feature of disk galaxies and are probably responsible for the most dynamical evolution (Section 10), yet a deep understanding of their origin (Section 7) remains elusive. The good progress made in recent years to understand the warps of galaxy disks (Section 8) still has not supplied a satisfactory account of their incidence.
Many of these outstanding issues may be bound up with how galaxies form, our understanding of which is currently making particularly rapid progress.
The author is indebted to James Binney, Victor Debattista, Agris Kalnajs, Juntai Shen, Alar Toomre, and Scott Tremaine for numerous valuable comments on a draft of this review.