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Binary galaxies discussed in chapter 13 are a special case of multiplicity and clustering among galaxies. Large-scale clustering is discussed in chapter 15. The present chapter discusses multiple systems: groups, clusters, and clouds of intermediate size (D appeq 1-3 Mpc) and population (n appeq 10-100). Such systems can be identified and best studied individually in our immediate neighborhood (Delta < 20 Mpc). The nearer galaxies used in the calibration of the distance scale and in assessing the detailed properties of galaxies are generally members of nearby groups.

By ``group'' is meant a number n > 2 of distinct galaxies that are bound gravitationally for periods of the order of 109 years or greater (star cluster analogy) or perhaps are genetically related as products of a common explosive formative event during the past 109 years or so even though they may not be gravitationally bound at present (stellar association analogy).

These concepts, however, are not suitable as operational definitions. In practice a ``group'' will be a ``small'' number of galaxies, say n appeq 10, brighter than M = -16 (perhaps of a specified class only, either elliptical and lenticular, or spiral and irregular) occupying a volume of space V in which the average density rhon = n / V, say rhon 10 per Mpc3, is at least one order of magnitude greater than the average density < rho1 > in a surrounding volume of space of diameter one order of magnitude greater than that of the group. In other words, the significant factor is the contrast with the surrounding field, not the absolute densities or numbers. Note that number density is considered, not mass density (which would exclude the galactic equivalent of stellar associations).

Space density, however, is not an observable, and the basic observational criterion of clustering is surface density in the apparent distribution. Since dwarf galaxies (dE, dIm) are inconspicuous or invisible in all but the nearest groups, a group is first identified by its brightest members. Further criteria of group membership inc]ude a small velocity range and a general similarity of morphological types, apparent magnitudes, and diameters.