Astronomy and Astrophysics – Astrophysics
Scientific paper
1998-07-02
Astronomy and Astrophysics
Astrophysics
17 pages, 4 figures To be published in A&A
Scientific paper
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 $\Sigma \sim 1$. Moreover, it allows one to recover the exact series of the cumulants of the probability distribution of the density contrast in the limit $\Sigma \to 0$ 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.
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