 |
 |
Astron. Astrophys. 331, 829-837 (1998)
The skewness and kurtosis of the projected density distribution function: validity of perturbation theory
E. Gaztañaga 1, 2 and
F. Bernardeau 3
1 Institut d'Estudis Espacials de Catalunya, Unidad Nixta
del CSIC, Edf. Nexus-104 - c/ Gran Capitan 2-4, E-08034 Barcelona,
Spain
2 NASA/Fermilab Astrophysics Center, Fermilab, Batavia, IL
60510, USA
3 Service de Physique Théorique, C.E. de Saclay,
F-91191 Gif-sur-Yvette cedex, France
Received 17 July 1997 / Accepted 10 November 1997
Abstract
We study the domain of validity of Perturbation Theory (PT), by
comparing its predictions for the reduced skewness,
![[FORMULA]](img1.gif)
, and kurtosis, ![[FORMULA]](img2.gif)
, of the
projected cosmological density field, with the results of N-body
simulations. We investigate models with different linear power spectra
and consider as physical applications both angular galaxy catalogues
and weak lensing surveys. We first find that the small-angle
approximation for the predicted skewness provides a good match to the
exact numerical PT results. On the other hand, results from non-linear
simulated catalogues agree well with PT results on quasi-linear
angular scales, which correspond to scales larger than about
![[FORMULA]](img3.gif)
in the applications we have considered. We also
point out that projection effects tend to attenuate the effects of
strong non-linearities in the angular skewness and kurtosis.
Key words: cosmic microwave
background 
dark matter
gravitational
lensing
large-scale structure of Universe
Send offprint requests to: F. Bernardeau (fbernardeau@cea.fr)
Contents
- 1. Introduction
- 2. The physical models
- 3. A Monte-Carlo integration for
- 4. The numerical N -body results
- 4.1. Sampling variance
- 4.2. Time evolution
- 5. Conclusion
- Acknowledgements
- Appendix A: the expression of the three-point correlation function in real space
- References
© European Southern Observatory (ESO) 1998
Online publication: March 3, 1998
helpdesk@link.springer.de