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) similar to (m/m ($) over bar)(-lambda) exp(-beta/m ($) over bar), where both lambda and beta depend on the parameter alpha of the cross section merging, and unlike the zero-dimensional case, they depend on the initial geometry. The mean mass is denoted by m ($) over bar. For evolved systems, the time dependence is only through m ($) over bar. The results can be applied to the protogalaxy mass distribution in the formation phase of a cluster of galaxies.