NON-GAUSSIAN FLUCTUATIONS AND THE STATISTICS OF GALAXY CLUSTERING

We investigate the formation of large-scale structure by gravitational instability from Gaussian and non-Gaussian initial conditions, using cosmological N-body simulations. Our non-Gaussian models are characterized by a one-point probability distribution, P(delta), with either a long tail of positive fluctuations (skew-positive), a long tail of negative fluctuations (skew-negative), or extended tails of both positive and negative fluctuations (broad). Skew-positive models, which qualitatively resemble models based on global texture or global monopoles, form structure by accreting mass on to rare high peaks of the density field, leaving large volumes essentially unperturbed. Skew-negative models possess deep density minima which develop into expanding bubbles; they qualitatively resemble explosion models in which blast waves sweep matter on to dense shells. Models with a broad but symmetric P(delta) share characteristics of both skew-positive and skew-negative models. We attempt to isolate the effects of non-Gaussian initial fluctuations from other factors by considering a range of initial power spectra, flat (OMEGA = 1) and open (OMEGA = 0.2) cosmologies, and unbiased and biased galaxy formation. We apply a variety of statistical clustering measures to all of our models, and we assess the viability of each model by comparing these results to observational data wherever possible. Our diverse set of models serves to illustrate the behaviour, sensitivity and usefulness of each of these clustering statistics. The Gaussian model with OMEGA = 1, biased galaxy formation, and a power spectrum slope n = - 1 is the most successful at reproducing the full range of observational data. Skew-positive models are less successful than Gaussian models in nearly every respect: they tend to produce lumpy, voidless structure, high galaxy pairwise velocities, and galaxy clusters with excessive velocity dispersions. Skew-negative models can create attractive spatial structure without biased galaxy formation, but their dynamical properties do not match observations: if OMEGA = 1 then the mass-to-light ratios of galaxy clusters are too high, and if OMEGA = 0.2 then the cluster velocity dispersions are too low. These models also produce excessively large voids and a 'bubbly' topology that does not match observations. On the whole our results support the hypothesis of Gaussian primordial fluctuations, and they show that galaxy clustering data are already sufficient to rule out many models of large-scale structure.