### 7. STATISTICAL PROPERTIES OF NEARBY GROUPS

7.1 Completeness of Survey

The frequency distribution of distance moduli of the 54 groups in Table 2 plus the Local Group is given in Table 5.

 Figure 5. Cumulative frequency distribution of distance moduli of nearby groups (including Local Group).

A plot of the cumulative frequencies N = n (fig. 5) is consistent with the relation N 3, i.e., log N = a + 0.6 µ0, expected for a statistically uniform space density of cluster centers in the range 30 < µ0 < 31. There is an apparent excess of nearby groups for µ0 < 30 due in part to a genuine higher density near the Local Group and in part to the fact that a finer division of groups is possible in our immediate neighborhood; at larger distances an increasing proportion of groups have been included in larger clouds. To compensate for this effect let us visualize (figs. 8 and 9) the region of the Local Group observed from a great distance, say, from the Virgo cluster; then the M81, Sculptor, and Local Groups might appear merely as condensations in the same cloud (our Local Cloud) and the NGC 5128 chain might be unnoticed. The circles and dashed line in figure 5 correspond to the corrected frequency function allowing for this effect. The presence of a Local Cloud is still in evidence, but the approximation to the 3 law is quite good for µ0 > 29 and apparently right up to the limit of the survey at µ0 31. This is because in preparing this chapter all identifiable groups with µ0 < 32 (and many beyond) were considered and only those with µ0 31.0 (31.2 to allow for accidental errors) are discussed here. Hence the survey should be substantially complete out to µ0 = 31.0 ( = 16 Mpc) except, of course, for the obscured galactic belt (about one-fifth of the sky area).

 26.0 27.0 28.0 29.0 29.5 30.0 30.5 31.0 µ0 <26 26.9 27.9 28.9 29.4 29.9 30.4 30.9 31.2 n 1 1 2 3 3 4 7 18 16 N = n 1 2 4 7 10 14 21 39 55

* Including Local Group.