The mass distribution in a merger model

We consider a statistical model in which gas clouds (the particles of the generalized gas) interact with one another and merge to form larger objects. We derive the particle mass distribution for such a gas. Our assumptions are equivalent to the basic assumptions of the statistical mechanics of sticky gas. We show, numerically, that the upper part of the mass distributions has an asymptotic shape of the following form: N(m) ∼ (m/<m>)^-λ exp (-βm/<m>, where λ= λ(α) and β= β(α) depend on the parameter α of the cross section for merger and <m> is the mean mass. The only time dependence is via the dependence of <m> on time, which is found to be a power law. The distribution has a maximum, namely there is a mass that is the most frequent one. The results are applied to protogalaxy mass distribution in the formation phase of a cluster of galaxies. Several predictions are made.