Paper detail

Omega from the skewness of the cosmic velocity divergence

We propose a method for measuring the cosmological density parameter $Ω$ from the statistics of the divergence field, $θ\equiv H^{-1} ÷v$, 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 $ <θ^3> \propto -Ω^{-0.6} <θ^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 $26/7-γ$, where $γ=-d\log <θ^2> / d\log R$. If the power spectrum is a power law, $P(k)\propto k^n$, then $γ=3+n$. A Gaussian window yields similar results. The resulting method for measuring $Ω$ 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 $Ω\sim 1$. 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 $Ω$.