Non-linearity and stochasticity in the density-velocity relation

F. Bernardeau, M. J. Chodorowski, E. L. Łokas, R. Stompor, A. Kudlicki

Research output: Contribution to journalArticle

18 Citations (Scopus)

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, extended here for a top-hat filter, and numerical simulations. In particular, we derive the quantitative (complete as possible up to third-order terms) and qualitative predictions for constrained averages and constrained dispersions - which describe the non-linearities and the stochasticity properties beyond the linear regime - and compare them against numerical simulations. We find overall a good agreement for constrained averages; however, the agreement for constrained dispersions is only qualitative. Scaling relations for the Ω-dependence of these quantities are satisfactorily reproduced. Guided by our analytical and numerical results, we finally 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 analyse galaxy survey data in order to test the gravitational instability paradigm beyond the linear regime and to put useful constraints on cosmological parameters. In particular, we show how the non-linearity in the density-velocity relation can be used to break the so-called Ω-bias degeneracy in cosmic density-velocity comparisons.

Original languageEnglish (US)
Pages (from-to)543-555
Number of pages13
JournalMonthly Notices of the Royal Astronomical Society
Volume309
Issue number2
StatePublished - Oct 21 1999
Externally publishedYes

Fingerprint

stochasticity
nonlinearity
probability distribution functions
simulation
gravitational instability
divergence
perturbation theory
perturbation
galaxies
filter
filters
scaling
acoustics
prediction
predictions
distribution
parameter

Keywords

  • Cosmology: theory
  • Galaxies: clusters: general
  • Galaxies: formation
  • Large-scale structure of Universe

ASJC Scopus subject areas

  • Space and Planetary Science

Cite this

Bernardeau, F., Chodorowski, M. J., Łokas, E. L., Stompor, R., & Kudlicki, A. (1999). Non-linearity and stochasticity in the density-velocity relation. Monthly Notices of the Royal Astronomical Society, 309(2), 543-555.

Non-linearity and stochasticity in the density-velocity relation. / Bernardeau, F.; Chodorowski, M. J.; Łokas, E. L.; Stompor, R.; Kudlicki, A.

In: Monthly Notices of the Royal Astronomical Society, Vol. 309, No. 2, 21.10.1999, p. 543-555.

Research output: Contribution to journalArticle

Bernardeau, F, Chodorowski, MJ, Łokas, EL, Stompor, R & Kudlicki, A 1999, 'Non-linearity and stochasticity in the density-velocity relation', Monthly Notices of the Royal Astronomical Society, vol. 309, no. 2, pp. 543-555.
Bernardeau F, Chodorowski MJ, Łokas EL, Stompor R, Kudlicki A. Non-linearity and stochasticity in the density-velocity relation. Monthly Notices of the Royal Astronomical Society. 1999 Oct 21;309(2):543-555.
Bernardeau, F. ; Chodorowski, M. J. ; Łokas, E. L. ; Stompor, R. ; Kudlicki, A. / Non-linearity and stochasticity in the density-velocity relation. In: Monthly Notices of the Royal Astronomical Society. 1999 ; Vol. 309, No. 2. pp. 543-555.
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