*Astron. Astrophys. 347, 757-768 (1999)*
## Non-linear gravitational clustering: smooth halos, substructures and scaling exponents
**
Patrick Valageas
**
Service de Physique Théorique, CEA Saclay, F-91191 Gif-sur-Yvette, France
*Received 22 January 1999 / Accepted 19 April 1999*
**Abstract**
Within the framework of hierarchical clustering scenarios, we
investigate the consequences for the properties of virialized halos of
the constraints provided by numerical simulations on the first few
correlation functions. Thus, we show that the density field *cannot
be described by a collection of smooth halos* with a universal
density profile. This implies that substructures within larger objects
play an important role (but a mean spherically averaged density
profile may exist). In particular, a possible interpretation is that
collapsed objects can be divided into an infinite hierarchy of smaller
objects with increasingly large densities (these substructures might
also be continuously destroyed and created by the long-range action of
gravity). Finally, we present multifractal models (restricted to
non-linear scales) which can describe in a natural way such non-linear
density fields with increasingly large fluctuations at smaller scales.
We relate their properties to the correlation functions and present a
few constraints they are expected to satisfy, using theoretical
considerations as well as constraints from numerical simulations.
Thus, the simplest realistic model is the *bifractal* model
described in Balian & Schaeffer (1989a). Moreover, we show that it
should provide (at least) a very good approximation of the
multifractal properties of the actual non-linear density field, hence
of the probability distribution of the density contrast. The
implications of this model (e.g. for galaxies) are detailed in other
studies.
**Key words:** cosmology: large-scale structure of
Universe
galaxies: clusters: general
This article contains no SIMBAD objects.
### Contents
© European Southern Observatory (ESO) 1999
Online publication: June 6, 1999
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