The Durham/UKST Galaxy Redshift Survey – VI. Power spectrum analysis of clustering

We present the power spectrum analysis of clustering in the Durham/UKST Galaxy Redshift Survey. The Survey covers 1450 square degrees and consists of 2501 galaxy redshifts. The galaxies are sampled at a rate of one in three down to a magnitude limit of b J ∼17 from cosmos scanned UK Schmidt Telescope plates. Our measurement of the power spectrum is robust for wavenumbers in the range 0.04  h  Mpc −1 k 0.6  h  Mpc −1 . The slope of the power spectrum for k >0.1  h  Mpc −1 is close to k −2 . The fluctuations in the galaxy distribution can be expressed as the rms variance in the number of galaxies in spheres of radius 8  h −1  Mpc as σ 8 =1.01±0.17. We find remarkably good agreement between the power spectrum measured for the Durham/UKST Survey and those obtained from other optical studies on scales up to λ =2π/ k ∼80  h −1  Mpc. On scales larger than this we find good agreement with the power measured from the Stromlo–APM Survey, but find more power than estimated from the Las Campanas Redshift Survey. The Durham/UKST Survey power spectrum has a higher amplitude than the power spectrum of IRAS galaxies on large scales, implying a relative bias between optically and infrared selected samples of b rel =1.3. We apply a simple model for the distortion of the pattern of clustering caused by the peculiar motions of galaxies to the APM Galaxy Survey power spectrum, which is free from such effects, and find a shape and amplitude that are in very good agreement with the power spectrum of the Durham/UKST Survey. This implies β =Ω 0.6 b =0.60±0.35, where b is the bias between fluctuations in the galaxy and mass distributions, and also suggests a one‐dimensional velocity dispersion of σ =320±140 km s −1 . We compare the Durham/UKST power spectrum with cold dark matter (CDM) models of structure formation, including the effects of nonlinear growth of the density fluctuations and redshift‐space distortions on the theoretical power spectra. We find that for any choice of normalization, the standard CDM model has a shape that cannot be reconciled with the Durham/UKST Survey power spectrum, unless either unacceptably high values of the one‐dimensional velocity dispersion are adopted or the assumption that bias is constant is invalid on scales greater than 20  h −1  Mpc. Over the range of wavenumbers for which we have a robust measurement of the power spectrum, we find the best agreement is obtained for a critical‐density CDM model in which the shape of the power spectrum is modified.