We investigate the effect of redshift-space distortions in the power spectrum parallel and perpendicular to the observer ’ s line of sight , P ^ { S } ( k _ { \parallel } , \mathbf { k } _ { \perp } ) , 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 due to 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 \beta \approx \Omega _ { 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 \Omega _ { m } = 1 universe , we find values for the one-dimensional pairwise velocity dispersion of \sigma _ { p } = 410 \pm 170 km s ^ { -1 } , and \beta = 0.38 \pm 0.17 .
An open \Omega _ { m } = 0.3 , and a flat \Omega _ { m } = 0.3 , \Omega _ { \Lambda } = 0.7 universe yield \sigma _ { p } = 420 km s ^ { -1 } , \beta = 0.40 , and \sigma _ { p } = 440 km s ^ { -1 } , \beta = 0.45 respectively , with comparable errors .
These results are consistent with estimates using the two-point galaxy correlation function , \xi ( \sigma, \pi ) , and favour either a low-density universe with \Omega _ { m } \sim 0.3 if galaxies trace the underlying mass distribution , or a bias factor of b \sim 2.5 if \Omega _ { m } = 1 .