Publication : t94/063

Omega from the skewness of the cosmic velocity divergence

Bernardeau F. (CEA, DSM, SPhT (Service de Physique Théorique), F-91191 Gif-sur-Yvette, FRANCE)
Juszkiewicz R. (Copernicus Astronomical Center, ul. Bartycka 18, Warszawa, POLAND and Institut d'Astrophysique de Paris, CNRS, 98 bis Bld Arago, 75014 Paris, FRANCE)
Dekel A. (Institut d\'Astrophysique de Paris, CNRS, 98 bis Bld Arago, 75014 Paris, FRANCE & Racah Institute of Physics, The Hebrew University, Jerusalem, 91904 Jerusalem, ISRAEL)
Bouchet F.R. (Institut d\'Astrophysique de Paris (IAP-CNRS), 98 bis Bld Arago, F-75014 Paris, FRANCE)
We propose a method for measuring the cosmological density parameter $ \Omega $ from the statistics of the expansion scalar, $ \theta \equiv H^{-1} {\bf \nabla} . {\bf v} , $ - the divergence of peculiar velocity, expressed in units of the Hubble constant, $ H\equiv 100 {\rm h\ km\ s}^{ {\rm -1}} {\rm Mpc}^{ {\rm -1}}. $ The velocity field is spatially smoothed over $ \sim 10 {\rm h}^{ {\rm -1}} {\rm Mpc} $ to remove strongly nonlinear effects. Assuming weakly-nonlinear gravitational evolution from Gaussian initial fluctuations, and using second-order perturbative analysis, we show that $ \left\langle \theta^ 3 \right\rangle \propto -\Omega^{ -0.6} \left\langle \theta^ 2 \right\rangle^ 2. $ The constant of proportionality depends on the smoothing window. For a top-hat of radius $ R $ and volume-weighted smoothing, this constant is $ 26/7+\gamma , $ where $ \gamma = {\rm d\ log} \left\langle \theta^ 2 \right\rangle / {\rm d\ log} \ R. $ If the power spectrum is a power law, $ P(k)\propto k^ {\bf n}, $ then $ \gamma =-(3+n). $ A Gaussian window yields similar results. The resulting method for measuring $ \Omega $ is independent of any assumed biaising relation between galaxies and mass. The method has been successfully tested with numerical simulations. A preliminary application to real data, provided by the POTENT recovery procedure from observed velocities favors $ \Omega \sim 1. $ However, because of an uncertain sampling error, this result should be treated as an assessment of the feasibility of our method rather than a definitive measurement of $ \Omega . $
Année de publication : 1995
Revue : Mon. Not. R. Astron. Soc. (1995)
Preprint : arXiv:astro-ph/9404052
Numéro Exterieur : CITA-94-15
Langue : Anglais
NB : 274, 20-26 (1995)


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