Astron. Astrophys. 337, 655-670 (1998)

Structure formation: a spherical model for the evolution of the density distribution

P. Valageas

¹ Service de Physique Théorique, CEA Saclay, F-91191 Gif-sur-Yvette, France
² Theoretical Astrophysics Center, Juliane Maries Vej 30, DK-2100 Copenhagen 0, Denmark

Received 25 November 1997 / Accepted 12 May 1998

Abstract

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

This article contains no SIMBAD objects.

Contents

• 1. Introduction
• 2. Quasi-linear regime: density contrast
  • 2.1. Critical universe:
    • 2.1.1. Lagrangian point of view
    • 2.1.2. Eulerian point of view
  • 2.2. Open universe:
    • 2.2.1. Lagrangian point of view
    • 2.2.2. Eulerian point of view
  • 2.3. Comparison with numerical results
• 3. Quasi-linear regime: velocity divergence
• 4. Spherical density fluctuations
• 5. Non-linear regime
  • 5.1. Spherical collapse
    • 5.1.1. Counts-in-cells
    • 5.1.2. Density profile of virialized halos
  • 5.2. Underdensities
    • 5.2.1. Density profile of underdensities
    • 5.2.2. Contact of underdensities
    • 5.2.3. Adhesion model
    • 5.2.4. Non-spherical corrections
  • 5.3. General picture
• 6. Conclusion
• References

© European Southern Observatory (ESO) 1998

Online publication: August 27, 1998
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