The mass distribution in a collapsing merging spherical cluster of objects

We consider a statistical model in which given objects (the particles of the generalized gas) interact with one another and merge to form more massive objects. These gas clouds form a self-gravitational field, causing the collapse of the initial spherical distribution. We show numerically, that the upper part of the distribution has an asymptotic shape of the following form: N(m) ∼ (m/m̄)^-λ exp (-βm/m̄), where both λ and β depend on the parameter α of the cross section merging, and unlike the zero-dimensional case, they depend on the initial geometry. The mean mass is denoted by m̄. For evolved systems, the time dependence is only through m̄. The results can be applied to the protogalaxy mass distribution in the formation phase of a cluster of galaxies.