On the Spatial Distribution of Galaxies: a Specific Model.

Counts of galaxies in 1 X 1 squares obtained at the Lick Observatory are used to test whether the serial correlations between these counts are compatible with the hypotheses that (1) 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 p of galaxies per cluster is a variable following an unspecified probability law with mean v and standard deviation (iv) the distribution of position of galaxies within a cluster follows a symmetric normal distribution with standard deviation CT. The outcome of the test is favorable to the hypotheses enumerated. We note that the parameter CT 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, CT 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 CT varying from 3 x 10 to 14 X 10 parsecs, according to the assumptions conceraing the distribution of absolute magnitudes of the galaxies with CT = 3.7 x 10 parsecs as the tentative best- fitting estimate. Further numerical results, combined with certain plausible hypotheses, imply that pi, the average number of galaxies per cluster, is less than 287; that the standard deviation CT of the number of galaxies per cluster is less than 1 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 p - 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 CTM = 1.25 mag.