FOURIER-ANALYSIS OF REDSHIFT-SPACE DISTORTIONS AND THE DETERMINATION OF OMEGA

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 = f (OMEGA)/ b almost-equal-to OMEGA0.6/b, where OMEGA is the cosmological density parameter, and b is the bias parameter. We derive a linear-theory estimator for beta, 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 beta-estimator. Non-linear effects can be important out to wavelengths lambda approximately 50 h-1 Mpc or larger; in most cases, they lower the quadrupole moment of the power spectrum, and thereby depress the estimate of beta below the true value. With a sufficiently large redshift survey, the scaling of non-linear effects may allow separate determinations of OMEGA 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(est) approximately 0.3-0.4 at wavelengths lambda approximately 30-40 h-1 Mpc. Non-linear effects remain important at these scales, so this estimate of beta is probably lower than the true value.