3.4. Populations of Clusters

It is not possible to state with certainty whether particular objects in the field of a cluster of galaxies are actually members of that cluster. Even radial velocities do not provide an unambiguous answer because of the velocity dispersion that always exists within a cluster. Only statistically can we speak of cluster populations, and then we must define: (1) the magnitude range counted; (2) the way the cluster is presumed to be bounded; and (3) the way corrections are applied for the field of foreground and background objects (of course, the meaning of the "field" itself is open to question).

Populations are given by Zwicky and his collaborators in their Catalogue of Galaxies and Clusters of Galaxies. The population listed for a cluster is the number of galaxies visible on the red Palomar Sky Survey plate that are contained within the isopleth (drawn by eye estimate) at which the surface density of galaxies is twice that in the surrounding field; the cluster counts are corrected for the mean field count itself. It is clear that the populations are not independent of distance, since a greater magnitude range is counted in nearby clusters than in distant ones. Also, since an isopleth contains not all of its cluster, but only that part within which the surface density is twice that of the surrounding field, the entire cluster population is not counted, even in the magnitude range considered. Moreover, as has been shown by Abell (1962) and Scott (1962), the isopleth contains a smaller fraction of the projected image of a distant cluster than of a nearby one. Finally, Zwicky himself has called attention to the fact that his cluster populations may be affected by interstellar and possible intergalactic absorption. Having noted these various selection effects, we summarize the population listed in the first two volumes of the Catalogue in table 3. The data are segregated by Zwicky's morphological cluster classes (compact, medium compact, and open), and also according to his estimate of the relative cluster distances. The radial velocities corresponding to the distances separating the five distance classes - near, medium distant (MD), distant (D), very distant (VD), and extremely distant (ED) - are quoted as 15,000, 30,000, 45,000, and 60,000 km s^-1, respectively.

Table 3. Numbers of clusters of various populations in the first two volumes

Population	< 100	100-199	200-299	300-399	400-499	500-599	600
Near:
Compact	0	2	2	2	0	2	6
Medium compact	6	27	27	9	8	3	14
Open	9	41	27	19	7	1	14
MD:
Compact	1	9	10	3	2	2	1
Medium compact	25	120	48	26	14	7	10
Open	21	109	33	8	7	3	1
D:
Compact	19	36	9	3	1	1	3
Medium compact	86	198	60	11	5	3	1
Open	50	164	24	5	1	0	0
VD:
Compact	139	143	30	2	1	0	0
Medium compact	267	190	36	1	4	0	0
Open	95	97	12	0	0	0	0
ED:
Compact	465	132	11	0	1	0	0
Medium compact	307	159	10	1	0	0	0
Open	36	18	0	0	0	0	0

Another body of data comes from the writer's cluster catalog (Abell 1958). This study concerns only the very richest clusters, but those are chosen in such a way as to comprise a relatively homogeneous sample, and the "populations" are defined in a manner to be as independent as possible of distance. The population of a cluster in the Abell catalog is the number of galaxies brighter than m₃ + 2, where m₃ is the photo-red magnitude of the third brightest cluster member. All counts were made on the red Sky Survey plates, and include those galaxies in the prescribed magnitude range that are contained within a circle centered on the image of the cluster, minus the number in the same magnitude range contained within a circle of similar size in the nearby field. The circles used were large compared to the main concentrations of galaxies within the cluster. A circle radius, in millimeters, was 4.6 × 10⁵/cz, where cz, the velocity of recession in km s^-1, was estimated by comparing the tenth brightest cluster member with the tenth brightest members of clusters of measured redshift. The counts were thus extended to approximatually the apparent dependence of cluster richness on distance is not large, and is very sensitive to slight errors of observations that may also depend on distance. The possible role of such errors has been discussed quantitatively by Paá (1964), who shows that the Just effect can be explained without evolution if Abell failed to include in the homogeneous sample only about 10 percent of the most distant clusters. Paál suggests that such a loss of remote clusters could result from the fact that the diameters of the counting circles used by Abell are inversely proportional to the cluster redshifts, rather than reflecting the dependence of angular diameter on distance that is predicted by any particular cosmological theory. It is the judgment of the writer that further independent observations are required to establish whether the Just effect is real.

Table 4. Numbers of clusters of various populations in the abell catalog

Population	clusters
50-79	1224
80-129	383
130-199	68
200-299	6
300	1

The Abell and Zwicky data on cluster richnesses are not easy to compare because of the different ways in which cluster "populations" are defined. Both tables 3 and 4, however, show clearly that the numbers of clusters increase rapidly with decreasing population. It is unfortunate that data do not exist on the relative numbers of rich clusters and small groups; probably the latter are far more frequent. Multiplicity is common even among what appear to be "field" galaxies. According to Holmberg (1962a), only 47 percent of nearby systems have multiplicity 1 (that is, are single galaxies), and 53 percent are either double or multiple systems. It should be noted, however, that all of the systems investigated by Holmberg are within what may be a local supercluster (see Section 5); moreover, multiplicity exists even within irregular clusters.