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Structure formation: a spherical model for the evolution of the density distribution
Received 25 November 1997 / Accepted 12 May 1998
Within the framework of hierarchical clustering we show that a simple Press-Schechter-like approximation, based on spherical dynamics, provides a good estimate of the evolution of the density field in the quasi-linear regime up to . Moreover, it allows one to recover the exact series of the cumulants of the probability distribution of the density contrast in the limit which sheds some light on the rigorous result and on "filtering". We also obtain similar results for the divergence of the velocity field.
Next, we extend this prescription to the highly non-linear regime, using a stable-clustering approximation. Then we recover a specific scaling of the counts-in-cells which is indeed seen in numerical simulations, over a well-defined range. To this order we also introduce an explicit treatment of the behaviour of underdensities, which takes care of the normalization and is linked to the low-density bubbles and the walls one can see in numerical simulations. We compare this to a 1-dimensional adhesion model, and we present the consequences of our prescription for the power-law tail and the cutoff of the density distribution.
Key words: large-scale structure of Universe galaxies: clusters: general
© European Southern Observatory (ESO) 1998
Online publication: August 27, 1998