Galaxy clustering in two dimensions: Some analytic results

The key results of Fall, Saslaw, and Kandrup regarding the early stages of galaxy clustering are reformulated here for the model problem of two-dimensional gravity with anr ^–1-interaction force. This should lead to new insights into the various physical processes involved and, more importantly, may prove of some use in interpreting numerical results obtained from two-dimensionalN-body simulations. The calculations suggest that, for a two-, rather than three-dimensional system, the correlational energy density should grow more rapidly with time, but should exhibit only a weak logarithmic dependence upon the typical particle speed. Various other measures of the clustering are independent of the dimensionality.