The Durham/UKST galaxy redshift survey - VI. Power spectrum analysis of clustering

We present the power spectrum analysis of clustering in the Durham/UKST Gal axy 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 d own to a magnitude limit of b(J) similar to 17 from COSMOS scanned UK Schmi dt Telescope plates. Our measurement of the power spectrum is robust for wa venumbers in the range 0.04 h Mpc(-1) less than or equal to k less than or equal to 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 ex pressed as the rms variance in the number of galaxies in spheres of radius 8 h(-1) Mpc as sigma(8) = 1.01 +/- 0.17. We find remarkably good agreement between the power spectrum measured for the Durham/UKST Survey and those ob tained from other optical studies on scales up to lambda = 2 pi/k similar t o 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 estima ted from the Las Campanas Redshift Survey. The Durham/UKST Survey power spe ctrum has a higher amplitude than the power spectrum of IRAS galaxies on la rge scales, implying a relative bias between optically and infrared selecte d samples of b(rel) = 1.3. We apply a simple model for the distortion of th e pattern of clustering caused by the peculiar motions of galaxies to the A PM 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 spectr um of the Durham/UKST Survey. This implies beta = Ohm(0.6)/b = 0.60 +/- 0.3 5, where b is the bias between fluctuations in the galaxy and mass distribu tions, and also suggests a one-dimensional velocity dispersion of sigma = 3 20 +/- 140 km s(-1). We compare the Durham/UKST power spectrum with cold da rk matter (CDM) models of structure formation, including the effects of non linear growth of the density fluctuations and redshift-space distortions on the theoretical power spectra. We find that for any choice of normalizatio n, the standard CDM model has a shape that cannot be reconciled with the Du rham/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 r ange of wavenumbers for which we have a robust measurement of the power spe ctrum, we find the best agreement is obtained for a critical-density CDM mo del in which the shape of the power spectrum is modified.