HIERARCHICAL FRAGMENTATION MODEL FOR THE EVOLUTION OF SELF-GRAVITATING CLOUDS

We develop a hierarchical model for the fragmentation of cold, self-gravitating gas clouds and apply the model to the collapse of matter accumulated at the boundaries of large-scale voids in the universe. In this model the mass function for fragment sizes and the correlation function for fragment positions are naturally related. Using this relationship, we derive the mass function for galaxies from the observed galaxy-galaxy two-point correlation function. Assuming that galaxy masses and luminosities are proportional to one another, the derived luminosity function agrees with the empirical Schecter function at low luminosity. We argue that the correlation function itself may be a natural outcome of large-scale gravitational instability at each stage of the hierarchy.