On the Large Scale Distribution of Matter in the Universe

Abstract

The following considerations represent an attempt to analyze those effects which govern the large scale distribution of matter in the universe. It is proposed to discuss the problems of: (a) the frequency of occurrence of clusters of nebulae which contain different numbers of nebulae, (b) the relative numbers of nebulae in dependence of their intrinsic luminosity and mass, and (c) the frequency distribution of various types of stars in dependence of their mass and intrinsic luminosity. It is found observationally that clusters of nebulae become the more frequent the fewer nebulae they contain. On the other hand the data so far available indicate that the luminosity function for nebulae exhibits a frequency maximum at the absolute magnitude ${M}_{0}=\ensuremath{-}14.2$. Reasons are advanced which suggest that this result which was obtained from the purely observational approach to the problem of the general distribution of matter cannot be final. The theoretical analysis of the frequency distribution of various types of stars is largely complicated because of the interference of effects due to light pressure and the generation of energy through subatomic processes and cannot at the present be carried through. The analogous problems for the nebulae and the clusters of nebulae, however, lend themselves to a simple qualitative analysis which, starting from the assumption of a stationary universe, makes use of the principle of the conservation of energy, the virial theorem and the application of statistical considerations to distributions of the Boltzmann and the Smoluchowski types. The results obtained are in good agreement with the observed distribution of the clusters of nebulae. In addition an understanding is arrived at of the important fact that the velocities of field nebulae on the average are only about half as large as those of cluster nebulae. The theoretical considerations given, however, are in complete contradiction with the luminosity function now generally adopted for the nebulae inasmuch as the existence of a large number of intrinsically faint nebulae representing more than half of all of the matter in the visible universe is predicted which to date must have been overlooked. On the basis of this prediction various criteria are developed to facilitate the discovery of intrinsically faint stellar systems and a systematic search for such systems utilizing the 18-inch Schmidt telescope on Palomar Mountain is described. On the basis of the results achieved so far it is shown that the new distribution function of nebulae in the so-called local group of nebulae deviates markedly in the direction of the theoretical expectations from the luminosity function derived by previous observers. Practical methods are discussed, the application of which should make possible the construction of a more representative distribution function for nebulae over a large range of luminosities. In the final section some of the known observational facts are briefly reviewed which favor the assumption of a stationary rather than an expanding universe.