Self-similar gravitational clustering

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Abstract
We consider the evolution of gravitational clustering and derive several new scaling relations for the multiplicity function. These include generalizations of the Press–Schechter theory to different densities and cosmological parameters. We then test the theory against multiplicity function and correlation function estimates for a series of 1000-body experiments. The results are consistent with the theory and show some dependence on initial conditions and cosmological density parameter. The statistical significance of the results, however, is fairly low because of several small number effects in the experiments. There is no evidence for a non-linear bootstrap effect or a dependence of the multiplicity function on the internal dynamics of condensed groups. Empirical estimates of the multiplicity function by Gott and Turner have a feature near the characteristic luminosity predicted by the theory. The scaling relations allow us to infer from estimates of the galaxy luminosity function that galaxies must have suffered considerable dissipation if they originally formed from a self-similar hierarchy. We also develop a method for relating the multiplicity function to similar measures of clustering, such as those of Bhavsar, for the distribution of galaxies on the sky. These are shown to depend on the luminosity function in a complicated way.

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