B. Clusters of Galaxies
Clustering among the nebulous objects in high galactic latitudes excited the attention of the early observers, long before it was recognized that these nebulae are extragalactic. The distribution of nebulae was in particular explored by the Herschels who found pronounced concentrations in Virgo, Ursa Major, Pisces-Perseus and other parts of the sky. An interesting review of their results is to be found in Humboldt's "Cosmos" (11).
At the beginning of this century M. WOLF (12) discovered some of the more distant clusters such as the one in Coma which was to play a most important role in all later investigations on the large scale distribution of matter in the universe. With the advent of the large telescopes in the United States of America a series of beautiful distant clusters was found, including those in Corona Borealis, Ursa Major, Gemini, Bootes and Hydra II. As is well known these clusters served HUMASON and HUBBLE as stepping stones in their explorations with the 100-inch reflector of the universal redshift in dependence on distance (2). From the analysis of the apparent magnitudes of the members of the nearer clusters HUBBLE (2) also derived the luminosity function of nebulae with a maximum frequency at the absolute photographic magnitude -14.2 and a dispersion of only 0.65 magnitudes. As it was shown later on by ZWICKY's investigations (13) with the Palomar Schmidt telescopes, HUBBLE'S luminosity function which until recently was considered as well established by most investigators is based on a systematically biased selection of objects and is quite erroneous. Actually, because of the discovery of ever increasing numbers of dwarf stellar systems and of swarms of intergalactic stars it now appears that the luminosity function does not possess any maximum at all but is rising monotonely as the absolute brightness of the galaxies decreases (14).
Because of the large solid angles subtended by the nearby clusters of galaxies their structural features could not be effectively explored with the large reflectors. Here the invention of the Schmidt telescope twenty five years ago came to the rescue. These instruments have large fields of uniformly excellent image quality in all colour ranges. Because of their large focal ratios, F/2 and F/2.5 respectively for the 18-inch and 48-inch Schmidt telescopes on Palomar Mountain, these instruments possess very high speeds for the photography of extended luminous objects and they are therefore ideally suited for the investigation of agglomerations of galaxies. Twenty years of work with these telescopes have produced numerous significant results on the characteristics of clusters of galaxies. Some of these results are as follows.
1. Contrary to opinions previously held by astronomers (2) clusters and clouds of galaxies are the rule, rather than the exception. Isolated galaxies are clearly in the minority.
2. Clusters and clouds of galaxies are virtually space fillers. Some among them are open clouds or medium. compact swarms but, a surprisingly large fraction of the rich clusters are spherically symmetrical.
3. If mmax is the apparent photographic magnitude of its brightest member, a rich cluster may contain as many as ten thousand galaxies in the magnitude range from mmax to mmax + 7.
4. In many of the large spherical clusters the radial distribution of the brightest members can be closely approximated by the function representing the density distribution of matter as a function of the distance from the center of an isothermal gravitational gas sphere, as originally analyzed by R. EMDEN (10).
5. There occurs a radial segregation of the members of a cluster, both as to type and luminosity. Very bright nebulae of the types S0 and E are preponderantly concentrated toward the centers of the large clusters, while faint nebulae of all types are relatively more numerous toward the outskirts, where also most of the spirals are found. The outlying parts of a cluster may therefore also be expected to be the bluest in colour.
6. The large spherical clusters of galaxies are remarkably similar in structure, and their absolute dimensions as well as the absolute luminosity functions for their brightest members are closely the same.
7. The velocity dispersion within the large clusters of galaxies is of the order of 2000 km./sec.
8. Both luminous and dark intergalactic matter have been found to be concentrated with a slight radial gradient toward the centers of the large clusters. The large luminous clouds in which the cluster nebulae appear imbedded show surface brightness corresponding to a range of apparent photographic magnitude mp per square second of arc lying in the range +23 < mp / sq. second of arc < + 25. In the neighborhood of close multiple nebulae belonging to a large cluster, the surface brightness of the luminous intergalactic matter may be even greater and approach or surpass that of the night sky glow which is of the order of mp = + 22 per square second of arc. Such bright local clouds are for instance found near the center of the Coma cluster (R.A. 12h 57.5m, Decl. +28° 13.5', Epoch 1950.0), of the Corona Borealis cluster (R.A. 15h 20m 21s, Decl. +27° 54'), and the so-called A-cluster (R.A. 1h 6m 17s, Decl. -15° 38' 40"). In the latter case the cloud is quite asymmetrical and partly red and partly blue in colour (15). In most cases the large intergalactic clouds within clusters appear rather blue, similar in colour to the bridges between galaxies which we shall discuss in the following.
9. Clusters of galaxies appear to be distributed uniformly and randomly throughout an apparently flat and non-expanding universe. This somewhat surprising result was derived from studies of both the apparent distribution of the centers of clusters in the celestial regions least obscured by interstellar and intergalactic dust as well as from the analysis of the frequency distribution of the angular diameters of nearly one thousand rich clusters (14, 16).
10. From the study mentioned under 9, it also follows that there is no systematic clustering of clusters. Actually it can be shown that if gravitational interactions are transmitted with a finite velocity cg assumed to be equal to the speed of light c, no statistically well organized cluster of galaxies can be formed with a diameter materially greater than about twenty million light years (16). Also, if cg = c, or cg not materially greater than c, a uniform expansion of the universe appears to be theoretically impossible, since local instabilities will lead to avalanching collapses of matter. These processes would give rise to irregular swarm formations of galaxies and to vast lacunae devoid of matter, both of dimensions vastly greater than the observed regular clusters of galaxies (17). No swarms or lacunae of the type described, seem to exist.
11. The analysis of the large clusters in Coma, Hydra I, Perseus, Cancer and others led to the recognition by ZWICKY (14) in 1933 that the average masses of the first several hundred brightest member galaxies in these clusters are of the order of 2 × 1011 times the mass of the sun, that is two hundred times greater than the average masses originally derived by HUBBLE (2) and others from absolute luminosity criteria. HOLMBERG in 1937 in his study (7) which we discussed in section IIa arrived at similarly large values for the average masses of the components of double nebulae. Both the author's and HOLMBEEG'S mass determinations must of course be revised as soon as a new more reliable distance scale will become established.