Andrew Ratcliffe

The Durham/UKST Galaxy Redshift Survey – IV. Redshift-space distortions in the two-point correlation function

We have investigated the redshift space distortions in the optically selected Durham/UKST Galaxy Redshift Survey using the 2-point galaxy correlation function perpendicular and parallel to the observer’s line of sight, �(�,�). We present results for the real space 2-point correlation function, �(r), by inverting the optimally estimated projected correlation function, which is obtained by integration of �(�,�), and find good agreement with other real space estimates. On small, non-linear scales we observe an elongation of the constant �(�,�) contours in the line of sight direction. This is due to the galaxy velocity dispersion and is the common “Finger of God” effect seen in redshift surveys. Our result for the one-dimensional pairwise rms velocity dispersion is 1/2 = 416 ± 36kms 1 which is consistent with those from recent redshift surveys and canonical values, but inconsistent with SCDM or LCDM models. On larger, linear scales we observe a compression of the �(�,�) contours in the line of sight direction. This is due to the infall of galaxies into overdense regions and the Durham/UKST data favours a value of ( 0.6 /b)�0.5, where is the mean mass density of the Universe and b is the linear bias factor which relates the galaxy and mass distributions. Comparison with other optical estimates yield consistent results, with the conclusion that the data does not favour an unbiased critical-density universe.

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 1 in 3 down to a magnitude limit of bJ � 17 from COSMOS scanned UK-Schmidt plates. Our measurement of the power spectrum is robust for wavenumbers in the range 0.04 hMpc 1 � k � 0.6hMpc 1 . The slope of the power spectrum for k > 0.1hMpc 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 �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 � = 2�/k � 80h 1 Mpc. On scales larger than this we find good agreement with the power measured from the Stromlo-APM Survey (Tadros & Efstathiou), but find more power than estimated from the Las Campanas Redshift Survey (Lin et al). 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 infra-red selected samples of brel = 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 is in very good agreement with the power spectrum of the Durham/UKST Survey. This implies � = 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 � = 320 ± 140kms 1 . We compare the Durham/UKST power spectrum with Cold Dark Matter 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 normalisation, 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 20h 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.

THE DURHAM/UKST GALAXY REDSHIFT SURVEY - III. LARGE-SCALE STRUCTURE VIA THE TWO-POINT CORRELATION FUNCTION

ABSTRACT We have investigated the statistical clustering properties of galaxies by calculating the2-point galaxy correlation function from the Durham/UKST Galaxy Redshift Survey.This survey is magnitude limited to b J ∼ 17, contains ∼2500galaxiessampled at a rateof one on three and surveysa ∼4×10 6 (h −1 Mpc) 3 volume of space. We have empiricallydetermined the optimalmethod ofestimatingthe 2-point correlationfunction from justsuch a magnitude limited survey. Applying our methods to this survey,we find that ourredshift space results agreewell with those from previous optical surveys.In particular,we confirm the previously claimed detections of large scale power out to ∼40h −1 Mpcscales. We compare with two common models of cosmological structure formationand find that our 2-point correlation function has power significantly in excess of thestandard cold dark matter model in the 10-30h −1 Mpc region. We therefore supportthe observational results of the APM galaxy survey. Given that only the redshift spaceclustering can be measured directly we use standard modelling methods and indirectlyestimate the real space 2-point correlation function. This real space 2-point correlationfunction has a lower amplitude than the redshift space one but a steeper slope.Key words: galaxies: clusters – galaxies: general – cosmology: observations – large-scale structure of Universe.