Clustering of galaxies in redshift space: Velocity distortion of the power spectrum and correlation function

Large-scale N-body simulations are used to investigate the distorting effects of peculiar velocities on the shape of the power spectrum and correlation function of galaxies as measured in redshift space. The distortion effect is studied over a large range of scales, from the nonlinear small scales of ∼1 h^-1 Mpc to the linear regime of 400 h^-1 Mpc. The distortions cause the redshift space power spectrum to be steeper than the real spectrum: the redshift space spectrum is enhanced over the real spectrum on large scales, in agreement with linear theory (Kaiser 1987), and is suppressed on small scales. The transition scale to the linear regime depends on the density parameter, Ω. For Ω = 0.2, the redshift space power spectrum is linearly enhanced on scales ≥60 h^-1 Mpc; for Ω = 1, the linear enhancement is reached only for ∼200 h^-1 Mpc. An analytic expression relating the redshift space power spectrum to the real space spectrum is derived; it is a function of Ω and of scale. The ratio of the redshift to real space correlation functions for separations 1-20 h^-1 Mpc is also investigated. A comparison of observations with simulations in redshift space reveals that the power spectrum of IRAS and optical galaxies are consistent with the spectrum of the standard Ω = 1 CDM model, as well as with the power spectra of the Ω ≈ 0.2 CDM model and the Ω = 1 HDM model. Consistency is also found for the correlation functions.