Estimating Omega from galaxy redshifts: Linear flow distortions and nonlinear clustering

We propose a method to determine the cosmic mass density Omega from redshift-space distortions induced by large-scale flows in the presence of nonlinear clustering. Nonlinear structures in redshift space, such as fingers of God, can contaminate distortions from linear flows on scales as large as several times the small-scale pairwise velocity dispersion sigma(v). Following Peacock & Dodds, we work in the Fourier domain and propose a model to describe the anisotropy in the redshift-space power spectrum; tests with high-resolution numerical data demonstrate that the model is robust for both mass and biased galaxy halos on translinear scales and above. On the basis of this model, we propose an estimator of the linear growth parameter beta = Omega(0.6)/b, where b measures bias, derived from sampling functions that are tuned to eliminate distortions from nonlinear clustering. The measure is tested on the numerical data and found to recover the true value of beta to within similar to 10%. An analysis of IRAS 1.2 Jy galaxies yields beta = 0.8=(+0.4)(-0.3) at a scale of 1000 km s(-1), which is close to optimal given the shot noise and finite size of the survey. This measurement is consistent with dynamical estimates of beta derived from both real-space and redshift-space information. The importance of the method presented here is that nonlinear clustering effects are removed to enable linear correlation anisotropy measurements on scales approaching the translinear regime. We discuss implications for analyses of forthcoming optical redshift surveys in which the dispersion is more than a factor of 2 greater than in the IRAS data.