Publication : t99/006

Nonlinearity and stochasticity in the density-velocity relationship

Bernardeau F. (CEA, DSM, SPhT (Service de Physique Théorique), F-91191 Gif-sur-Yvette, FRANCE)
Chodorowski M.J. (Copernicus Astronomical Center, Polish Academy of Sciences, Bartycka 18, PL-00-716 Warsaw, POLAND)
Lokas E.L. (Copernicus Astronomical Center, Polish Academy of Sciences, Bartycka 18, PL-00-716 Warsaw, POLAND)
Stompor R. (Center for Particle Astrophysics (CfPA), UC Berkeley, 366 Le Conte Hall, MC 7300, Berkeley, CA 94720-7304, USA)
Kudlicki A. (Copernicus Astronomical Center, Polish Academy of Sciences, Bartycka 18, PL-00-716 Warsaw, POLAND)

Abstract:
We present results of the investigations of the statistical properties of a joint density and velocity divergence probability distribution function (PDF) in the mildly non-linear regime. For that purpose we use both perturbation theory results (complete as possible up to third order terms), obtained analytically for a Gaussian filter and extended for a top-hat filter, and numerical simulations. {In particular we derive the quantitative and qualitative predictions for constrained averages and constrained dispersions -- which describe the nonlinearities and the stochasticity properties beyond the linear regime -- and compare them against numerical simulations. We find overall a good agreement with scaling relations for the $\Omega$-dependence of these quantities satisfactory reproduced.} {Finally, guided by our analytical and numerical results, we construct a robust phenomenological description of the joint PDF in a closed analytic form. The good agreement of our formula with results of N-body simulations for a number of cosmological parameters provides a sound validation of the presented approach. } {Our results} provide a basis for a potentially powerful tool with which it is possible to analyze galaxy survey data in order to test the gravitational instability paradigm beyond the linear regime and put useful {constraints} on cosmological parameters.

Année de publication : 1999
Revue : Mon. Not. R. Astron. Soc. 309 543-555 (1999)
Preprint : arXiv:astro-ph/9901057
Keywords : cosmology: theory, galaxie large-scale structure of the Universe
Langue : Anglais

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