The Durham/UKST Galaxy Redshift Survey – III. Large-scale structure via the two-point correlation function

We have investigated the statistical clustering properties of galaxies by calculating the two-point galaxy correlation function from the optically selected Durham/UKST Galaxy Redshift Survey. This survey is magnitude-limited to b _J∼17, contains ∼2500 galaxies sampled at a rate of one-in-three and surveys a ∼4×10⁶ ( h ⁻¹ Mpc)³ volume of space. We have empirically determined the optimal method of estimating the two-point correlation function from just such a magnitude-limited survey. Applying our methods to this survey, we find that our redshift-space results agree well with those from previous optical surveys. In particular, we confirm the previously claimed detections of large-scale power out to ∼40 h ⁻¹ Mpc scales. We compare with two common models of cosmological structure formation and find that our two-point correlation function has power significantly in excess of the standard cold dark matter model in the 10–30 h ⁻¹ Mpc region. We therefore support the observational results of the APM galaxy survey. Given that only the redshift-space clustering can be measured directly, we use standard modelling methods and indirectly estimate the real-space two-point correlation function from the projected two-point correlation function. We then invert this projected correlation function to obtain an estimate of the spatial two-point correlation function in real space. This correlation function in real space has a lower amplitude than that in redshift space, but a steeper slope.     

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 two-point galaxy correlation function perpendicular and parallel to the observer's line of sight, ξ(σ, π). On small, non-linear scales we observe an elongation of the constant ξ(σ, π) contours in the line-of-sight direction. This is a result of 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 〈 w ²〉^1/2=416±36 km s⁻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 ξ(σ, π) contours in the line-of-sight direction. This is caused by the infall of galaxies into overdense regions, and the Durham/UKST data favours a value of (Ω^0.6/ b )∼0.5, where Ω is the mean mass density of the Universe and b is the linear bias factor that relates the galaxy and mass distributions. Comparison with other optical estimates yields consistent results, with the conclusion that the data do not favour an unbiased critical-density universe.     

The Durham/UKST Galaxy Redshift Survey — V. The catalogue

We present the radial velocities and blue, optical magnitudes for all of the galaxies within the Durham/UKST Galaxy Redshift Survey. This catalogue consists of ∼2500 galaxy redshifts to a limiting apparent magnitude of B _J⋍17 mag, covering a ∼1500-deg² area around the South Galactic Pole. The galaxies in this survey were selected from the Edinburgh/Durham Southern Galaxy Catalogue and were sampled, in order of apparent magnitude, at a rate of one galaxy in every three. The spectroscopy was performed at the 1.2-m UK Schmidt Telescope in Australia using the FLAIR multi-object spectrograph. We show that our radial velocity measurements made with this instrument have an empirical accuracy of ±150 km s⁻¹. The observational techniques and data reduction procedures used in the construction of this survey are also discussed. This survey demonstrates that the UKST can be used to make a three-dimensional map of the large-scale galaxy distribution, via a redshift survey to b _J⋍17 mag, over a wide area of the sky.     

Large-scale galaxy distribution in the Las Campanas Redshift Survey

We make use of three-dimensional clustering analysis, inertia tensor methods, and the minimal spanning tree technique to estimate some physical and statistical characteristics of the large-scale galaxy distribution and, in particular, of the sample of overdense regions seen in the Las Campanas Redshift Survey (LCRS). Our investigation provides additional evidence for a network of structures found in our core sampling analysis of the LCRS : a system of rich sheet-like structures, which in turn surround large underdense regions criss-crossed by a variety of filamentary structures.
We find that the overdense regions contain ∼40–50 per cent of LCRS galaxies and have proper sizes similar to those of nearby superclusters. The formation of such structures can be roughly described as a non-linear compression of protowalls of typical cross-sectional size ∼ 20–25  h ⁻¹ Mpc; this scale is ∼5 times the conventional value for the onset of non-linear clustering – to wit, r ₀, the autocorrelation length for galaxies.
The comparison with available simulations and theoretical estimates shows that the formation of structure elements with parameters similar to those observed is presently possible only in low-density cosmological models, Ω_m h ∼0.2–0.3, with a suitable large-scale bias between galaxies and dark matter.     

The topology of the IRAS Point Source Catalogue Redshift Survey

We investigate the topology of the new Point Source Catalogue Redshift Survey (PSCz) of IRAS galaxies by means of the genus statistic. The survey maps the local Universe with approximately 15 000 galaxies over 84.1 per cent of the sky, and provides an unprecedented number of resolution elements for the topological analysis. For comparison with the PSCz data we also examine the genus of large N -body simulations of four variants of the cold dark matter (CDM) cosmogony. The simulations are part of the Virgo project to simulate the formation of structure in the Universe. We assume that the statistical properties of the galaxy distribution can be identified with those of the dark matter particles in the simulations. We extend the standard genus analysis by examining the influence of sampling noise on the genus curve and introducing a statistic able to quantify the amount of phase correlation present in the density field, the amplitude drop of the genus compared to a Gaussian field with identical power spectrum. The results for PSCz are consistent with the hypothesis of random-phase initial conditions. In particular, no strong phase correlation is detected on scales ranging from 10 to 32 h ⁻¹ Mpc, whereas there is a positive detection of phase correlation at smaller scales. Among the simulations, phase correlations are detected in all models at small scales, albeit with different strengths. When scaled to a common normalization, the amplitude drop depends primarily on the shape of the power spectrum. We find that the constant-bias standard CDM model can be ruled out at high significance, because the shape of its power spectrum is not consistent with PSCz. The other CDM models with more large-scale power all fit the PSCz data almost equally well, with a slight preference for a high-density τCDM model.     

The 2dF Galaxy Redshift Survey: luminosity dependence of galaxy clustering

We investigate the dependence of the strength of galaxy clustering on intrinsic luminosity using the Anglo-Australian two degree field galaxy redshift survey (2dFGRS). The 2dFGRS is over an order of magnitude larger than previous redshift surveys used to address this issue. We measure the projected two-point correlation function of galaxies in a series of volume-limited samples. The projected correlation function is free from any distortion of the clustering pattern induced by peculiar motions and is well described by a power law in pair separation over the range     . The clustering of     galaxies in real space is well-fitted by a correlation length     and power-law slope     . The clustering amplitude increases slowly with absolute magnitude for galaxies fainter than M *, but rises more strongly at higher luminosities. At low luminosities, our results agree with measurements from the Southern Sky Redshift Survey 2 by Benoist et al. However, we find a weaker dependence of clustering strength on luminosity at the highest luminosities. The correlation function amplitude increases by a factor of 4.0 between     and −22.5, and the most luminous galaxies are 3.0 times more strongly clustered than L * galaxies. The power-law slope of the correlation function shows remarkably little variation for samples spanning a factor of 20 in luminosity. Our measurements are in very good agreement with the predictions of the hierarchical galaxy formation models of Benson et al.     

Void statistics and void galaxies in the 2dF Galaxy Redshift Survey

In the 2dF Galaxy Redshift Survey, we study the properties of voids and of fainter galaxies within voids that are defined by brighter galaxies. Our results are compared with simulated galaxy catalogues from the Millennium simulation coupled with a semi-analytical galaxy formation recipe. We derive the void size distribution and discuss its dependence on the faint magnitude limit of the galaxies defining the voids. While voids among faint galaxies are typically smaller than those among bright galaxies, the ratio of the void sizes to the mean galaxy separation reaches larger values. This is well reproduced in the mock galaxy samples studied. We provide analytic fitting functions for the void size distribution. Furthermore, we study the galaxy population inside voids defined by galaxies with   B _J− 5 log  h < −20  and diameter larger than  10  h ⁻¹ Mpc  . We find a clear bimodality of galaxies inside voids and in the average field but with different characteristics. The abundance of blue cloud galaxies inside voids is enhanced. There is an indication of a slight blueshift of the blue cloud. Furthermore, galaxies in void centres have slightly higher specific star formation rates as measured by the η parameter. We determine the radial distribution of the ratio of early- and late-type galaxies through the voids. We find and discuss some differences between observations and the Millennium catalogues.