The Durham/UKST Galaxy Redshift Survey – VII. Redshift‐space distortions in the power spectrum

We investigate the effect of redshift‐space distortions in the power spectrum parallel and perpendicular to the line of sight of the observer, P S (k ∥ , k ⊥ ), using the optically selected Durham/UKST Galaxy Redshift Survey. On small, non‐linear scales anisotropy in the power spectrum is dominated by the galaxy velocity dispersion; the ‘Finger of God’ effect. On larger, linear scales coherent peculiar velocities caused by the infall of galaxies into overdense regions are the main cause of anisotropy. According to gravitational instability theory these distortions depend only on the density and bias parameters via β≈Ω m 0.6 b. Geometrical distortions also occur if the wrong cosmology is assumed, although these would be relatively small given the low redshift of the survey. To quantify these effects, we assume the real‐space power spectrum of the APM Galaxy Survey, and fit a simple model for the redshift‐space and geometrical distortions. Assuming a flat Ω m =1 universe, we find values for the one‐dimensional pairwise velocity dispersion of σ p =410±170 km s −1 , and β=0.38±0.17. An open Ω m =0.3, and a flat Ω m =0.3, Ω Λ =0.7 universe yield σ p =420 km s −1 , β=0.40, and σ p =440 km s −1 , β=0.45, respectively, with comparable errors. These results are consistent with estimates using the two‐point galaxy correlation function, ξ ( σ ,π), and favour either a low‐density universe with Ω m ∼0.3 if galaxies trace the underlying mass distribution, or a bias factor of b∼2.5 if Ω m =1.