On the fairness of the main galaxy sample of SDSS

Flux-limited and volume-limited galaxy samples are constructed from the Sloan Digital Sky Survey(SDSS)data releases DR4,DR6 and DR7 for statistical analysis.The two-point correlation functionsξ(s),monopole of three-point correlation functionsζ0,projected two-point correlation function wp and pairwise velocity dispersionσ12 are measured to test if galaxy samples are fair for these statistics.We find that with the increment of sky coverage of subsequent data releases in SDSS, ξ(s)of the flux-limited sample is...     

SDSS galaxy clustering: luminosity and colour dependence and stochasticity

Differences in clustering properties between galaxy subpopulations complicate the cosmological interpretation of the galaxy power spectrum, but can also provide insights about the physics underlying galaxy formation. To study the nature of this relative clustering, we perform a counts-in-cells analysis of galaxies in the Sloan Digital Sky Survey in which we measure the relative bias between pairs of galaxy subsamples of different luminosities and colours. We use a generalized  χ²  test to determine if the relative bias between each pair of subsamples is consistent with the simplest deterministic linear bias model, and we also use a maximum likelihood technique to further understand the nature of the relative bias between each pair. We find that the simple, deterministic model is a good fit for the luminosity-dependent bias on scales above  ∼2  h ⁻¹ Mpc  , which is good news for using magnitude-limited surveys for cosmology. However, the colour-dependent bias shows evidence for stochasticity and/or non-linearity which increases in strength towards smaller scales, in agreement with previous studies of stochastic bias. Also, confirming hints seen in earlier work, the luminosity-dependent bias for red galaxies is significantly different from that of blue galaxies: both luminous and dim red galaxies have higher bias than moderately bright red galaxies, whereas the biasing of blue galaxies is not strongly luminosity dependent. These results can be used to constrain galaxy formation models and also to quantify how the colour and luminosity selection of a galaxy survey can impact measurements of the cosmological matter power spectrum.     

Power spectrum analysis of the ESO Slice Project galaxy redshift survey

We measure the power spectrum of the galaxy distribution in the ESO Slice Project (ESP) galaxy redshift survey. We develop a technique to describe the survey window function analytically, and then deconvolve it from the measured power spectrum using a variant of the Lucy method. We test the whole deconvolution procedure on ESP mock catalogues drawn from large N -body simulations, and find that it is reliable for recovering the correct amplitude and shape of P ( k ) at k >0.065  h  Mpc⁻¹. In general, the technique is applicable to any survey composed of a collection of circular fields with an arbitrary pattern on the sky, as typical of surveys based on fibre spectrographs. The estimated power spectrum has a well-defined power-law shape k ⁿ with n ≃−2.2 for k ≥0.2  h  Mpc⁻¹, and a smooth bend to a flatter shape ( n ≃−1.6) for smaller k . The smallest wavenumber where a meaningful reconstruction can be performed ( k ∼0.06  h  Mpc⁻¹) does not allow us to explore the range of scales where other power spectra seem to show a flattening and hint at a turnover. We also find, by a direct comparison of the Fourier transforms, that the estimate of the two-point correlation function ξ ( s ) is much less sensitive to the effect of a problematic window function, such as that of the ESP, than the power spectrum. Comparison with other surveys shows an excellent agreement with estimates from blue-selected surveys. In particular, the ESP power spectrum is virtually indistinguishable from that of the Durham–UKST survey over the common range of k , an indirect confirmation of the quality of the deconvolution technique applied.     

The basic properties of galaxy groups from the volume-limited main galaxy sample of SDSS DR6

Using the Berlind et al. algorithm and the Davis et al. algorithm, we find that the mean velocity dispersion, virial radius, and virial mass of the group catalogs identified in the volume-limited sample are much smaller than those identified in the flux-limited sample. Our study shows that these properties of groups are heavily influenced by the relative values of the linking parameters and that there may be no values for the linking lengths that will work perfectly for every sample. In addition, we note that the luminosity distribution of member galaxies of groups identified by different algorithms is nearly the same, but member galaxies of groups identified using the linking lengths b_⊥ = 0.14, b_∥ = 0.75 have a higher proportion of blue galaxies and a lower proportion of red galaxies than member galaxies of groups identified using the linking length b = 0.2, and the early-type fraction of member galaxies of groups identified using the linking length b = 0.2 is higher than that of member galaxies of groups identified using the linking lengths b_⊥ = 0.14, b_∥ = 0.75. Published in Astrofizika, Vol. 51, No. 4, pp. 555–566 (August 2008).     

The origin of scaling in the galaxy distribution

I present an analytic model for non‐linear clustering of the luminous (baryonic) material in a universe in which the gravitational field is dominated by dark matter. The model is based on a two-component generalization of the adhesion approximation in which the gravitational potential of the dark component is determined by the standard Zel'dovich approximation or one of its variants, or by an N ‐body simulation. The baryonic matter flow is dissipative and is driven by this dark matter gravitational potential. The velocity potential of the matter is described by a generalization of the Burgers equation: the random heat equation ('RH equation') with a spatially correlated Gaussian driving potential.
The properties of the RH equation are well understood: it is closely related to the equation for the Anderson model and to Brownian motion in a random potential: the solution can be expressed in terms of path integrals. Using this it is possible to derive the scaling properties of the solution and, in particular, those of the resultant velocity field. Even though the flow is non‐linear, the velocity field remains Gaussian and inherits its scaling properties from the gravitational potential. This provides an underlying dynamical reason why the density field in the baryonic component is lognormally distributed and manifests multifractal scaling.
By explicitly putting dark and luminous matter on different footings, the model provides an improved framework for considering the growth of large‐scale cosmic structure. It provides a solution for the velocity potential of the baryonic component in closed form (albeit a path integral) from which the statistical properties of the baryonic flow can be derived.     

Estimating β from redshift-space distortions in the 2dF galaxy survey

Given the failure of existing models for redshift-space distortions to provide a highly accurate measure of the β -parameter, and the ability of forthcoming surveys to obtain data with very low random errors, it becomes necessary to develop better models for these distortions. Here we review the failures of the commonly used velocity dispersion models and present an empirical method for extracting β from the quadrupole statistic that has little systematic offset over a wide range of β and cosmologies. This empirical model is then applied to an ensemble of mock 2dF southern strip surveys, to illustrate the technique and see how accurately we can recover the true value of β . We compare this treatment with the error we expect to find caused only by the finite volume of the survey. We find that non-linear effects reduce the range of scales over which β can be fitted, and introduce covariances between nearby modes in addition to those introduced by the convolution with the survey window function. The result is that we are only able to constrain β to a 1 σ accuracy of 25 per cent ( β =0.55±0.14 for the cosmological model considered). We explore one possible means of reducing this error, that of cluster collapse, and show that accurate application of this method can greatly reduce the effect of non-linearities, improving the determination of β . We conclude by demonstrating that, when the contaminating effects of clusters are dealt with, this simple analysis of the full 2dF survey yields β =0.55±0.04. For this model, this represents a determination of β to an accuracy of 8 per cent and hence an important constraint on the cosmological density parameter Ω₀.     

Approaching a homogeneous galaxy distribution: results from the Stromlo–APM redshift survey

Recent results from a number of redshift surveys suggest that the Universe is well described by an inhomogeneous, fractal distribution on the largest scales probed. This distribution has been found to have fractal dimension, D , approximately equal to 2.1, in contrast to a homogeneous distribution in which the dimension should approach the value 3 as the scale is increased. In this paper we demonstrate that estimates of D , based on the conditional density of galaxies, are prone to bias from several sources. These biases generally result in a smaller measured fractal dimension than the true dimension of the sample. We illustrate this behaviour in application to the Stromlo–APM redshift survey, showing that this data set in fact provides evidence for fractal dimension increasing with survey depth. On the largest scale probed, r ≈60  h ⁻¹ Mpc, we find evidence for a distribution with dimension D =2.76±0.10. A comparison between this sample and mock Stromlo–APM catalogues taken from N -body simulations (which assume a CDM cosmology) reveals a striking similarity in the behaviour of the fractal dimension. Thus we find no evidence for inhomogeneity in excess of that expected from conventional cosmological theory. We consider biases affecting future large surveys and demonstrate, using mock SDSS catalogues, that this survey will be able to measure the fractal dimension on scales at which we expect to see full turn-over to homogeneity, in an accurate and unbiased way.     

Voids in the Las Campanas Redshift Survey versus cold dark matter models

We analysed the distribution of void sizes in the two-dimensional slices of the Las Campanas Redshift Survey (LCRS). Fourteen volume-limited subsamples were extracted from the six slices to cover a large part of the survey and to test the robustness of the results against cosmic variance. Thirteen samples were randomly culled to produce homogeneously selected samples. We then studied the relationship between the cumulative area covered by voids and the void size as a property of the void hierarchy. We found that the distribution of void sizes scaled with the mean galaxy separation, λ . In particular, we found that the size of voids covering half of the area is given by D _med≈ λ +(12±3)  h ⁻¹ Mpc. Next, by employing an environmental density threshold criterion to identify mock galaxies, we were able to extend this analysis to mock samples from dynamical N -body simulations of cold dark matter (CDM) models. To reproduce the observed void statistics, overdensity thresholds of δ _th≈0,…,1 are necessary. We compared standard (SCDM), open (OCDM), vacuum energy dominated (ΛCDM) and broken scale invariant CDM models (BCDM): we found that both the void size distribution and the two-point correlation function provided important and complementary information on the large-scale matter distribution. The dependence of the void statistics on the threshold criterion for the mock galaxy identification showed that the galaxy biasing was more crucial for the void size distribution than were differences between the cosmological models.     

The clustering evolution of the galaxy distribution

We follow the evolution of the galaxy population in a ΛCDM cosmology by means of high-resolution N -body simulations in which the formation of galaxies and their observable properties are calculated using a semi-analytic model. We display images of the spatial distribution of galaxies in the simulations that illustrate its evolution and provide a qualitative understanding of the processes responsible for the various biases that develop. We consider three specific statistical measures of clustering at     and     : the correlation length (in both real and redshift space) of galaxies of different luminosity, the morphology–density relation and the genus curve of the topology of galaxy isodensity surfaces. For galaxies with luminosity below L ∗, the     correlation length depends very little on the luminosity of the sample, but for brighter galaxies it increases very rapidly, reaching values in excess of 10  h ⁻¹ Mpc. The 'accelerated' dynamical evolution experienced by galaxies in rich clusters, which is partly responsible for this effect, also results in a strong morphology–density relation. Remarkably, this relation is already well-established at     . The genus curves of the galaxies are significantly different from the genus curves of the dark matter, however this is not a result of genuine topological differences but rather of the sparse sampling of the density field provided by galaxies. The predictions of our model at     will be tested by forthcoming data from the 2dF and Sloan galaxy surveys, and those at     by the DEEP and VIRMOS surveys.