2015ApJ...810..167S

We calculate the distribution function of astronomical objects' (like galaxies and/or smooth halos of different kinds) gravitational fields due to their tidal interaction. For that we apply the statistical method of Chandrasekhar, used originally to calculate the famous Holtzmark distribution. We show that in our approach the distribution function is never Gaussian, its form being dictated by the potential of interaction between objects. This calculation permits us to perform a theoretical analysis of the relation between angular momentum and mass (richness) of the galaxy clusters. To do so, we follow the ideas of Catelan & Theuns and Heavens & Peacock. The main difference is that here we reduce the problem to a discrete many-body case, where all physical properties of the system are determined by the interaction potential V(r_q). The essence of reduction is that we use the multipole (up to quadrupole here) expansion of Newtonian potential so that all hydrodynamic, ''extended'' characteristics of an object, such as its density mass, are ''integrated out,'' leaving its ''point-like'' characteristics, such as mass and quadrupole moment. In that sense we do not distinguish between galaxies and smooth components such as halos. We compare our theoretical results with observational data.