Basic Questions

Early analyses (e.g., Gregory and Thompson, 1978; Kirshner et al., 1981; Fairall et al., 1990; Fairall, 1998) of modern magnitude-limited galaxy catalogs revealed large empty regions, originally called voids. These regions filled in somewhat as more sensitive surveys found fainter galaxies (e.g., Kirshner et al., 1987), but they remained underpopulated. Cosmological many-body simulations gave a probability f0(V) for finding such empty regions (Aarseth and Saslaw, 1982), even before their theoretical distribution function was calculated. Soon it became clear that these voids and underdense regions were part of a more general distribution function description.

In retrospect, we may regard many analyses of observed spatial distribution functions as attempts to answer several basic questions. Although these questions are not yet fully answered, and relations among them are not always apparent, we will use them to guide our discussion here.

1. Is the observed form of f(N, V) generally consistent with gravitational quasiequilibrium clustering? If so, does it rule out other possibilities such as particular dark matter distributions or initial conditions?

2. Do the two-dimensional distribution functions for projections onto the sky give a good estimate of f(N, V) or do we need the full three-dimensional distribution function?

3. How does b(r) depend on spatial scale? Can this dependence restrict possible models significantly?

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