The growth of density correlation in an oscillating spherical stellar system

An attempt is made to study how density correlations in an oscillating stellar system grow with time. The method adopted here is a sort of generalization of the virial method used extensively in hydrodynamical problems to a system of BBGKY equations. As the first attempt we consider in this paper a simple case where the averaged state of the stellar system is spherically symmetric and oscillating with a nearly homogeneous density. The effects of discrete particle interaction are neglected compared with those of collective interactions. The ternary correlations are also neglected. The results demonstrate that the density correlation grows rapidly, especially when the system is oscillating with a large amplitude. A general method to study more general cases is briefly mentioned. (auth.)