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

The peculiar velocities of galaxies distort the pattern of galaxy clus tering in redshift space, making the redshift-space power spectrum ani sotropic. In the linear regime of gravitational instability models, th e strength of this distortion depends only on the ratio beta = f (OMEG A)/ b almost-equal-to OMEGA0.6/b, where OMEGA is the cosmological dens ity parameter, and b is the bias parameter. We derive a linear-theory estimator for beta, based on the harmonic moments of the redshift-spac e power spectrum. Using N-body simulations, we examine the impact of n on-linear gravitational clustering on the power-spectrum anisotropy an d on our beta-estimator. Non-linear effects can be important out to wa velengths lambda approximately 50 h-1 Mpc or larger; in most cases, th ey lower the quadrupole moment of the power spectrum, and thereby depr ess the estimate of beta below the true value. With a sufficiently lar ge redshift survey, the scaling of non-linear effects may allow separa te determinations of OMEGA and b. We describe a practical technique fo r 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-J y IRAS galaxy survey yields beta(est) approximately 0.3-0.4 at wavelen gths lambda approximately 30-40 h-1 Mpc. Non-linear effects remain imp ortant at these scales, so this estimate of beta is probably lower tha n the true value.