Synthesizing the Observed Distribution of Galaxies

We develop a technique, based on the galaxy distribution function, to synthesize the observed distribution of galaxies. It populates space with a Poisson distribution of cluster centers and places particles around each center according to a speciic prescription. We specify each cluster, assumed to be spherical, by three quantities: the number of particles in the cluster, its radius, and its radial density proole. The observed galaxy distribution function and its scale dependence gives the probability that a cluster has N associated particles and also constrains the distribution of cluster radii and the radial density prooles. In our most successful models, identical particles are arranged in Poisson distributed spherical clusters that do not overlap, the radial density proole of any cluster resembles an isothermal sphere, and the probability that a cluster has N associated particles is given by the observed gravitational quasi-equilibrium distribution function. Various statistical analyses (two-point correlation function, counts-in-cells distribution functions, percolation) all show that this model is remarkably similar to the observed distribution of galaxies. This technique also illustrates the constraints that galaxy distribution functions place on models of large-scale structure. All these models should be tested against the observed galaxy distribution function over a wide range of scales.