## Halo correlations in nonlinear cosmic density fields
The question we address in this paper is the determination of the correlation properties of the dark matter halos appearing in cosmic density fields once they underwent a strongly nonlinear evolution induced by gravitational dynamics. A series of previous works have given indications that kind of non-Gaussian features are induced by nonlinear evolution in term of the high-order correlation functions. Assuming such patterns for the matter field, i.e. that the high-order correlation functions behave as products of two-body correlation functions, we derive the correlation properties of the halos, that are assumed to represent the correlation properties of galaxies or clusters. The hierarchical pattern originally induced by gravity is shown to
be conserved for the halos. The strength of their correlations at any
order varies, however, but is found to depend only on their internal
properties, namely on the parameter
where Various illustrations of our general results are presented. As a
function of the properties of the underlying matter field, we
construct the count probabilities for halos and in particular discuss
the halo void probability. We evaluate the dependence of the halo mass
function on the environment: within clusters, hierarchical clustering
implies the higher masses are favored. These properties solely arise
from what is a natural bias (
This article contains no SIMBAD objects. ## Contents- 1. Introduction
- 2. The nonlinear behavior
- 3. Generating functions for conditional cell counts
- 3.1. Biased two-body correlation function
- 3.2. The bias for many-body correlations
- 3.3. General properties of the galaxy and cluster correlation functions
- 3.4. The halo correlation functions
- 3.4.1. The general expression of the vertices
- 3.4.2. The normalization properties
- 3.4.3. The validity limits
- 3.5. The rare halo correlation functions
- 3.5.1. Counting overdense cells
- 4. Models for the matter correlations
- 4.1. Specific models for
- 4.2. The minimal tree hierarchical model
- 4.2.1. Small
*x*limit
- 4.2.1. Small
- 4.3. The Hamilton model and extensions
- 4.3.1. Count-in-cells
- 4.3.2. The halo correlations
- 4.3.3. Other forms of in the minimal tree-hierarchical model
- 4.4. The factorized tree-hierarchical model
- 4.4.1. Large
*x*behavior - 4.4.2. Small
*x*limit - 4.4.3. A very special case
- 4.4.1. Large
- 4.5. Hierarchical models and tree-hierarchical models, comments
- 5. The observational consequences
- 6. Conclusion
- Appendices
- References
© European Southern Observatory (ESO) 1999 Online publication: September 13, 1999 |