The nonlinear redshiftspace power spectrum: Omega from redshift surveys
Abstract
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 nonlinear redshiftspace 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(Omega)~=Omega^0.6, where Omega 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 nonlinear dynamics and is not a result of incoherent random velocities. The rate of decline depends strongly on Omega 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 nonlinear structures. The scaling is weakly dependent on the initial power spectrum and is in good agreement with a large Nbody simulation. This universal scaling relation greatly extends the scales over which redshift distortions can be used as a probe of Omega. The scaling relation is in agreement with the observed quadrupoletomonopole ratio from the 1.2Jy IRAS survey, with a best estimate of Omega^0.6/b_lin=0.6+/0.2 where b_lin is the linear bias parameter.
 Publication:

Monthly Notices of the Royal Astronomical Society
 Pub Date:
 March 1996
 DOI:
 10.1093/mnras/279.1.L1
 arXiv:
 arXiv:astroph/9510049
 Bibcode:
 1996MNRAS.279L...1F
 Keywords:

 COSMOLOGY: THEORY;
 LARGESCALE STRUCTURE OF UNIVERSE;
 Astrophysics
 EPrint:
 uuencoded compressed postscript. The preprint is also available at http://www.ast.cam.ac.uk/preprint/PrePrint.html