The non-Gaussian distribution of galaxy gravitational fields

We perform a theoretical analysis of the observational dependence between angular momentum of galaxy clusters and their mass (richness), based on the method introduced in our previous paper. For that we obtain the distribution function of gravitational fields for astronomical objects (like galaxies and/or smooth halos of different kinds) due to their tidal interaction. By applying the statistical method of Chandrasekhar, we are able to show that the distribution function is determined by the form of interaction between objects and for multipole (tidal) interaction it is never Gaussian. Our calculation permits demonstrating how the alignment of galaxy angular momenta depends on cluster richness. The specific form of the corresponding dependence is due to assumptions made about cluster morphology. Our approach also predicts the time evolution of stellar object angular momenta within CDM and ΛCDM models. Namely, we have shown that angular momentum of galaxies increases with time.