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2.2. Distribution of Clusters with Richness and Distance

An illustration of the distribution of rich clusters with richness and distance is summarized in Table 2. The table refers to the statistical sample of the Abell (1958) cluster catalog (i.e., richness class R geq 1, corresponding to a richness threshold count of NR geq 50 galaxies within 1.5h-1 Mpc radius and magnitude m leq m3 + 2m (see Table 1); redshift range z appeq 0.02 to 0.2; and sky coverage delta > -27° and |b| gtapprox 30°). The Abell catalog covers ~ 1/3 of the entire sky to z ltapprox 0.2. Recent smaller automated surveys from digitized plates are reported by the Edinburgh-Durham catalog (EDCC; Lumsden et al. 1992), and the APM survey (Dalton et al. 1992). A large automated cluster catalog will be available in the near future from the Sloan Digital Sky Survey (SDSS). This and other planned surveys will allow a more accurate determination of the distribution of rich clusters with richness and distance and other statistical studies of clusters.

Table 2. Distribution of Abell Clusters with Distance and Richness.a

Distance distribution Richness distribution
D <zest> Ncl(R geq 1) R NR Ncl

1 0.0283 9 (0)b (30-49) (~ 103)
2 0.0400 2 1 50-79 1224
3 0.0577 33 2 80-129 383
4 0.0787 60 3 130-199 68
5 0.131 657 4 200-299 6
6 0.198 921 5 geq 300 1
Total 1682 Total (R geq 1) 1682

Nearby redshift samplec, d Distant projected sampled
D leq 4 D = 5 + 6

Ncl(total) 104 1574
Ncl(b geq 30°) 71 984
Ncl(b leq - 30°) 33 563
Ncl(R = 1) 82 1125
Ncl(R geq 2) 22 422

a Statistical sample. |b| boundaries as given in Table 1 of Abell (1958). Notation: D = distance group (defined by the estimated redshifts of the clusters); <zest> = average estimated redshift from the magnitude of the tenth brightest galaxy; Ncl = number of clusters; R = richness class; NR = number of galaxies brighter than m3 + 2m within RA = 1.5h-1 Mpc (richness count).
b R = 0 clusters are not part of the statistical sample.
c Redshifts by Hoessel et al. (1980).
d This sample is limited to |b| geq 30° in addition to the |b| boundaries of the statistical sample.

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