Fourier analysis of redshift-space distortions and the determination of Ω

The peculiar velocities of galaxies distort the pattern of galaxy clustering in redshift space, making the redshift-space power spectrum anisotropic. In the linear regime of gravitational instability models, the strength of this distortion depends only on the ratio $\beta\equiv f(\Omega)/b\approx\Omega^{0.6}/b$, where Ω is the cosmological density parameter, and b is the bias parameter. We derive a linear-theory estimator for β, based on the harmonic moments of the redshift-space power spectrum. Using N-body simulations, we examine the impact of non-linear gravitational clustering on the power-spectrum anisotropy and on our β-estimator. Non-linear effects can be important out to wavelengths $\lambda\sim50\enspace h^{-1}$ Mpc or larger; in most cases, they lower the quadrupole moment of the power spectrum, and thereby depress the estimate of β below the true value. With a sufficiently large redshift survey, the scaling of non-linear effects may allow separate determinations of Ω and b. We describe a practical technique for measuring the anisotropy of the power spectrum from galaxy redshift surveys, and we test the technique on mock catalogues drawn from the N-body simulations. Preliminary application of our methods to the 1.2-Jy IRAS galaxy survey yields $\beta_\text{est}\sim 0.3-0.4$ at wavelengths $\lambda\sim30-40 h^{-1}$ Mpc. Non-linear effects remain important at these scales, so this estimate of β is probably lower than the true value.