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 β≡f(Ω)/b≃Ω 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 λ∼50 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