The non-linear redshift-space power spectrum: Omega from redshift surveys

We examine the anisotropies in the power spectrum by the mapping of real space to redshift space, Using the Zel'dovich approximation, we obtain an analytic expression for the non-linear redshift-space power spectrum in the distant observer limit. For a given unbiased galaxy distribution in redshift space, the anisotropies in the power spectrum depend on the parameter f(Ohm)approximate to(0.6), where Ohm is the density parameter. We quantify these anisotropies by the ratio, R, of the quadrupole and monopole angular moments of the power spectrum. In contrast to linear theory, the Zel'dovich approximation predicts a decline in R with decreasing scale. This departure from linear theory is due to non-linear dynamics and is not a result of incoherent random velocities. The rate of decline depends strongly on Ohm and the initial power spectrum, However, we find a scaling relation between the quantity R/R(lin) (where R(lin) is the linear theory value of R) and the dimensionless variable k/k(nl), where k(nl) is a wavenumber determined by the scale of non-linear structures. The scaling is weakly dependent on the initial power spectrum and is in good agreement with a large N-body simulation. This universal scaling relation greatly extends the scales over which redshift distortions can be used as a probe of Ohm. The scaling relation is in agreement with the observed quadrupole-to-monopole ratio from the 1,2-Jy IRAS survey, with a best estimate of Ohm(0.6)/b(lin)=0.6+/-0.2 where b(lin) is the linear bias parameter.