Structure of superclusters and supercluster formation - V. Spatial correlation and voids

Galaxian spatial correlation function is calculated for various observational samples having different sample volume. It is demonstrated that the correlation length, $$r_0$$, increases with sample volume. For volumes considerably smaller than the size of the Local Supercluster the correlation length is about half the conventional value, $$5h^{-1}$$ Mpc, which corresponds to sizes of intermediate samples, containing the whole supercluster. Samples containing several superclusters have correlation lengths twice the conventional one. Similar calculations have been carried out for various theoretical models. Samples representing luminous matter in a neutrino-dominated universe and having different sample volumes have correlation length $$r_0$$ which increases with volume until the sample size reaches the average size of voids. Further increase in the sample size does not change the correlation length, indicating that fair samples of the model universe have been reached. These calculations and simple theoretical estimates indicate that the value of the correlation length reflects the filling factor of the sample and the presence of large voids in galaxy distribution. The observed correlation function of galaxies reflects the distribution of luminous matter. After correcting for the difference between the correlation functions of true mass and galaxies, the correlation length for a fair sample of the Universe is estimated to be $$r_0=10h^{-1}$$ Mpc.