Annu. Rev. Astron. Astrophys. 1988. 26: 509-560 Copyright © 1988 by Annual Reviews. All rights reserved

7. PROBLEMS AND PROSPECTS

It would be fair to say that the principal features of the general LF (i.e., summed over Hubble types in an "average" environment) are now well known, as distilled from the studies of field and cluster samples that were reviewed in previous sections. What then remains to be established and with what means?

Once we adopt the premise that the individual type-specific _T(M) functions are more fundamental than their sum in any particular environment (e.g. spiral-rich or spiral-poor), the emphasis then shifts to determining _T(M) rather than _{T T}(M). It is here that our present knowledge is least secure.

We would like to test if the shape of _T(M) depends on density; it was assumed not to be so in previous sections, but only because our present knowledge is incomplete. Measurements of _T(M) are relatively easy in clusters (taking note of the membership problem) because all galaxies are at the same distance. But cluster studies only touch the high-density end of any _T(M, D) relation. To sample the crucial low-density regime we must find _T(M) in various (and different) parts of the field, or, speaking as before, in the high and low Alpine valleys and passes away from the Matterhorns. It is this excursion deep into the field that will usher in the next era of the work.

The usual technical problems will remain, each to be solved for particular projects. These include measurements of apparent magnitudes, surface brightness, morphological types, and redshifts (or other distance indicators).

On the theoretical side, once the (M, D) functions are known for each T, what do these probability distributions tell us about galaxy formation and evolution? [The simplest example of a theoretical deduction from an observed _T(M) distribution is that because no dwarf spirals exist, formation of spiral arms requires that the galaxy mass (which governs the maximum rotational velocity for a disk structure) be larger than a particular value. To make such a statement requires the knowledge that _T(M) 0 as M for spiral types.]