Annu. Rev. Astron. Astrophys. 1982. 20: 399-429 Copyright © 1982 by Annual Reviews. All rights reserved

5. SUMMARY AND PROSPECTS

Despite rapid progress in recent years, our understanding of spheroidal components remains imperfect. Some of the more important questions that have to be answered are the following.

1. What is the structure of the nuclei of spheroidal systems? How common are cusps of brightness at the centers of galaxies? Are the structures of these cusps affected by massive black holes at their foci? What relationship have these stellar structures to active galactic nuclei and quasars? High-resolution, high signal-to-noise photometry and further work on the dynamics of systems whose distribution functions are of the form f (E, J) are required to elucidate these questions.

2. Do normal giant elliptical galaxies have massive halos? The rotation curves of disk galaxies tell us that the mass distributions of these galaxies are more extensive than the light distributions of their bulges. Dynamical arguments (Ostriker & Peebles 1973, Efstathiou et al. 1982) suggest that this additional mass is not associated with the disks, so we may conclude that these bulges have massive halos. Furthermore, radial velocities of cluster galaxies suggest that the mean mass-to-light ratio near the centers of rich clusters is very much higher (M / L_B 200; Faber & Gallagher 1979) than the mass-to-light ratios (M / L_B 10) that are indicated by the internal motions of the galaxies. Since most of the light from the central region of a compact rich cluster (such as that in Coma) comes from spheroidal components, it is probable that these spheroidal components either possess or have possessed massive halos. However, the uncertainties associated with interpreting velocity, dispersion profiles in dynamical terms, and the difficulty of pushing spectroscopic observations to very low surface brightnesses, are such that it has not been demonstrated that any normal elliptical galaxy has a massive halo. Dressler's (1979) work on the cD galaxy in the cluster Abell 2029 presents the strongest case for a massive halo around an elliptical galaxy.

3. Are spheroidal components normally triaxial? Further observations of gas disks and dust lanes within and around elliptical galaxies should help us to elucidate this fundamental question, as would a better understanding of the dynamics of triaxial systems. Do the apparent major axes of the bulges of many disk galaxies run, like that of the bulge of M31, not exactly parallel to the major axis of the surrounding disk? If spheroidal components are triaxial, are they predominantly oblate or prolate?

4. What are the pattern speeds of triaxial spheroidal components, and how do these speeds relate to the observed streaming motions within elliptical galaxies and the bulges of disk galaxies? It has yet to be demonstrated that triaxial systems are possible that (like giant elliptical galaxies) have nearly singular central densities and rather flat rotation curves, and yet have no obvious features in their density profiles at the characteristic radii of resonances. The very nearly featureless brightness profiles of elliptical galaxies suggest that the speeds at which their figures rotate must be very small, and it is not clear that such small pattern speeds will permit appreciable rotation very close to the centers. One possibility is that spheroidal components become axisymmetric oblate bodies at a radius that is smaller than the radius of the first important resonance.

5. Why do the bulges of disk galaxies rotate rapidly and giant elliptical galaxies slowly? Does this difference in rotation speeds reflect only the different luminosities of the two types of system? Can one account in detail for the observations of bulges with models in which the velocity dispersion tensor is isotropic?

It may be many years before we possess a satisfactory understanding of the shapes and internal motions of most spheroidal components. The two most urgent theoretical tasks involve the construction of axisymmetric models, which remain of great interest since many spheroidal components may turn out to be axisymmetric, and the structure of axisymmetric models is anyway likely to help us understand nearly axisymmetric triaxial galaxies. Two types of axisymmetric models are urgently needed. Recent observations of the bulges of disk galaxies and of dwarf ellipticals call for models based on distribution functions f (E, J_z) . The problem here is choosing a distribution function that generates a model whose isodensity surfaces are nearly similar ellipsoids and whose rotation curve is rather flat. Observations of giant elliptical galaxies and of the kinematics of stars in the solar neighborhood call for more general models in which <v_R²> <v_z²> and the distribution function is not a function of just the classical integrals E and J_z .

In the observational area the greatest need is now for high-quality surface photometry of all types of spheroidal components. Photometric observations are every bit as vital as spectroscopic measurements for developing our understanding of the dynamics of spheroidal components, and there is a strong case for correcting the imbalance that has arisen in the allocation of scarce telescope time between spectroscopic and photometric observations.

Acknowledgments

It is a pleasure to thank J. P. Ostriker for advice on the outline, and G. T. Bath and S. M. Fall for comments on a draft of this article.