Omega from the skewness of the cosmic velocity divergence

Details Omega from the skewness of the cosmic velocity divergence Omega from the skewness of the cosmic velocity divergence

1994-04-22

arxiv.org/abs/astro-ph/9404052v1

Mon.Not.Roy.Astron.Soc. 274 (1995) 20-26

Astronomy and Astrophysics

Astrophysics

16 pages + 2 figures, uuencoded postscript file, also available by anonymous ftp from ftp.cita.utoronto.ca in directory /cit

Scientific paper

We propose a method for measuring the cosmological density parameter $\Omega$ from the statistics of the divergence field, $\theta \equiv H^{-1} \div v$, the divergence of peculiar velocity, expressed in units of the Hubble constant, $H \equiv 100 h km/s/Mpc$. The velocity field is spatially smoothed over $\sim 10 h^{-1} Mpc$ to remove strongly nonlinear effects. Assuming weakly-nonlinear gravitational evolution from Gaussian initial fluctuations, and using second-order perturbative analysis, we show that $ <\theta^3> \propto -\Omega^{-0.6} <\theta^2>^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 $\gamma=-d\log <\theta^2> / d\log R$. If the power spectrum is a power law, $P(k)\propto k^n$, then $\gamma=3+n$. A Gaussian window yields similar results. The resulting method for measuring $\Omega$ is independent of any assumed biasing 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 $\Omega$.

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