On the Spatial Distribution of Galaxies: a Specific Model.

Abstract

Counts of galaxies in I o X I o squares obtained at the Lick Observatory are used to test whether the serial correlations between these counts are compatible with the hypotheses that (i) galaxies occur only in clusters; (ii) the spatial distribution of cluster centers is quasi-uniform and, to be specific, follows a Poisson law; (iii) the number of v of galaxies per cluster is a variable following an unspecified probability law with mean and standard deviation o-^; (iv) the distribution of position of galaxies within a cluster follows a symmetric normal distribution with standard deviation a. The outcome of the test is favorable to the hypotheses enumerated. We note that the parameter a measures, in a sense, the dimensions of the cluster. In order to obtain the most probable distance of the galaxy farthest from the cluster center, a should be multiplied by a factor usually between 3 and 4, depending on the number of galaxies in the cluster. Numerical results include estimates of a varying from 3 X 10 6 to 14 X 10 6 parsecs, according to the assumptions concerning the distribution of absolute magnitudes of the galaxies with of the number of galaxies per cluster is less than 144 and more than (probably much more than) 17 ; and that X, the average number of cluster centers per cubic parsec, is between 0.12 X 10-18 and 34 X 10~ 18. Tentative computations based on the assumption that v-1 follows a negative binomial distribution show that the theory is compatible with the fact that within the area studied there are identified a number of very small clusters and, at the same time, a few giant clusters. The best agreement between the theoretical and empirical serial quasi-correlations is obtained on the assumption that the standard deviation of the absolute magnitude of galaxies is o-j/ = 1.25 mag.