Searching for the scale of homogeneity

We introduce a statistical quantity, known as the K function, related to the integral of the two-point correlation function. It gives us straightforward information about the scale where clustering dominates and the scale at which homogeneity is reached. We evaluate the correlation dimension, D ₂, as the local slope of the log–log plot of the K function. We apply this statistic to several stochastic point fields, to three numerical simulations describing the distribution of clusters and finally to real galaxy redshift surveys. Four different galaxy catalogues have been analysed using this technique: the Center for Astrophysics I, the Perseus–Pisces redshift surveys (these two lying in our local neighbourhood), the Stromlo–APM and the 1.2-Jy IRAS redshift surveys (these two encompassing a larger volume). In all cases, this cumulant quantity shows the fingerprint of the transition to homogeneity. The reliability of the estimates is clearly demonstrated by the results from controllable point sets, such as the segment Cox processes. In the cluster distribution models, as well as in the real galaxy catalogues, we never see long plateaus when plotting D ₂ as a function of the scale, leaving no hope for unbounded fractal distributions.     

Observational biases in Lagrangian reconstructions of cosmic velocity fields

Lagrangian reconstruction of large-scale peculiar velocity fields can be strongly affected by observational biases. We develop a thorough analysis of these systematic effects by relying on specially selected mock catalogues. For the purpose of this paper, we use the Monge–Ampère–Kantorovitch (MAK) reconstruction method, although any other Lagrangian reconstruction method should be sensitive to the same problems. We extensively study the uncertainty in the mass-to-light assignment due to incompleteness (missing luminous mass tracers), and the poorly determined relation between mass and luminosity. The impact of redshift distortion corrections is analysed in the context of MAK and we check the importance of edge and finite-volume effects on the reconstructed velocities. Using three mock catalogues with different average densities, we also study the effect of cosmic variance. In particular, one of them presents the same global features as found in observational catalogues that extend to 80 h ⁻¹ Mpc scales. We give recipes, checked using the aforementioned mock catalogues, to handle these particular observational effects, after having introduced them into the mock catalogues so as to quantitatively mimic the most densely sampled currently available galaxy catalogue of the nearby Universe. Once biases have been taken care of, the typical resulting error in reconstructed velocities is typically about a quarter of the overall velocity dispersion, and without significant bias. We finally model our reconstruction errors to propose an improved Bayesian approach to measure Ω_m in an unbiased way by comparing the reconstructed velocities to the measured ones in distance space, even though they may be plagued by large errors. We show that, in the context of observational data, it is possible to build a nearly unbiased estimator of Ω_m using MAK reconstruction.     

Boundary corrections in fractal analysis of galaxy surveys

The analysis of redshift surveys with fractal tools requires one to apply some form of statistical correction for galaxies lying near the geometric boundary of the sample. In this paper we compare three different methods of applying such a correction to estimates of the correlation integral in order to assess the extent to which estimates may be biased by boundary terms. We apply the corrections to illustrative examples, including a simple fractal set (Lévy flight), a random β -model, and a subset of the CfA2 Southern Cap survey. This study shows that the new 'angular' correction method we present is more generally applicable than the other methods used to date: the conventional 'capacity' correction imposes a bias towards homogeneity, and the 'deflation' method discards large-scale information, and consequently reduces the statistical usefulness of data sets. The 'angular' correction method is effective at recovering true fractal dimensions, although the extent to which boundary corrections are important depends on the form of fractal distribution assumed as well as the details of the survey geometry. We also show that the CfA2 Southern sample does not show any real evidence of a transition to homogeneity. We then revisit the IRAS PSC z survey and 'mock' PSC z catalogues made using N -body simulations of two different cosmologies. The results we obtain from the PSC z survey are not significantly affected by the form of boundary correction used, confirming that the transition from fractal to homogeneous behaviour reported by Pan & Coles is real.     

Large-scale cosmic homogeneity from a multifractal analysis of the PSCz catalogue

We investigate the behaviour of galaxy clustering on large scales using the PSC z catalogue. In particular, we ask whether there is any evidence of large-scale fractal behaviour in this catalogue. We find the correlation dimension in this survey varies with scale, consistent with other analyses. For example, our results on small and intermediate scales are consistent those obtained from the QDOT sample, but the larger PSC z sample allows us to extend the analysis out to much larger scales. We find firm evidence that the sample becomes homogeneous at large scales; the correlation dimension of the sample is D ₂=2.992±0.003 for r >30  h ⁻¹ Mpc. This provides strong evidence in favour of a universe that obeys the cosmological principle.     

Mock LAMOST galaxy redshift surveys: I. Methodology

For a wide range of cold dark matter models of galaxy formation, we present a general method for constructing mock LAMOST galaxy redshift surveys using cosmological N-body simulation. We use the two-parameter Lagrangian biased model for the construction, take into account the radial selection and survey geometry and use a local morphology-density relation to assign morphological types to the galaxies. We test the mock samples by comparing their angular correlation functions both for the whole catalogue and for different morphological types with those of the APM bright galaxy catalogue. The result shows an excellent agreement between the mock catalogue as a whole and the observations; but the E/S0 galaxies of the mock sample are unable to reproduce the overall amplitude of the observed correlation. The mock catalogue should be useful when designing redshift surveys and provide a valuable aid in developing new statistical estimators and algorithm for quantifying the large scale structure of the universe.     

LAMOST星系红移巡天的数值模拟研究:(Ⅰ)理论模型及模拟样本构造

基于N体数值模拟技术,给出在各种宇宙学模型框架下,产生LAMOST红移巡天的模拟样本的方法．在模拟样本构造中,采用双参数的tagrange偏袒模型,并结合LAMOST的设计,考虑了径向选择效应及巡天几何的限制;同时还根据星系形态和环境的关系,进一步对模拟样本的星系形态进行分类．选择APM的亮星系样本对模型进行检验,并通过计算其角相关函数和模型进行比较．计算结果表明,对包括所有形态的星系样本,模拟样本给出了和观测相符的结果,而对基于Postman和Geller的形态一环境关系所得到的不同形态的模拟星系分布,模拟样本中的椭圆星系和透镜星系不足以解释APM亮星系样本中的成团强度,即强偏袒效应．最后,从实测角度出发,对采用的模拟方法和样本进行评估．     

MoMaF: the Mock Map Facility

We present the Mock Map Facility, a powerful tool for converting theoretical outputs of hierarchical galaxy formation models into catalogues of virtual observations. The general principle is straightforward: mock observing cones can be generated using semi-analytically post-processed snapshots of cosmological N -body simulations. These cones can then be projected to synthesize mock sky images. To this end, the paper describes in detail an efficient technique for creating such mock cones and images from the galaxies in cosmological simulations ( galics ) semi-analytic model, providing the reader with an accurate quantification of the artefacts it introduces at every step. We show that replication effects introduce a negative bias on the clustering signal – typically peaking at less than 10 per cent around the correlation length. We also thoroughly discuss how the clustering signal is affected by finite-volume effects, and show that it vanishes at scales larger than approximately one-tenth of the simulation box size. For the purpose of analysing our method, we show that number counts and redshift distributions obtained with galics / momaf compare well with K -band observations and the two-degree field galaxy redshift survey. Given finite-volume effects, we also show that the model can reproduce the automatic plate measuring machine angular correlation function. The momaf results discussed here are made publicly available to the astronomical community through a public data base. Moreover, a user-friendly Web interface ( http://galics.iap.fr ) allows any user to recover her/his own favourite galaxy samples through simple SQL queries. The flexibility of this tool should permit a variety of uses ranging from extensive comparisons between real observations and those predicted by hierarchical models of galaxy formation, to the preparation of observing strategies for deep surveys and tests of data processing pipelines.     

Simulations of deep pencil-beam redshift surveys

We create mock pencil-beam redshift surveys from very large cosmological N -body simulations of two cold dark matter (CDM) cosmogonies, an Einstein–de Sitter model ( τ CDM) and a flat model with Ω₀=0.3 and a cosmological constant (ΛCDM). We use these to assess the significance of the apparent periodicity discovered by Broadhurst et al. Simulation particles are tagged as 'galaxies' so as to reproduce observed present-day correlations. They are then identified along the past light-cones of hypothetical observers to create mock catalogues with the geometry and the distance distribution of the Broadhurst et al. data. We produce 1936 (2625) quasi-independent catalogues from our τ CDM (ΛCDM) simulation. A couple of large clumps in a catalogue can produce a high peak at low wavenumbers in the corresponding one-dimensional power spectrum, without any apparent large-scale periodicity in the original redshift histogram. Although the simulated redshift histograms frequently display regularly spaced clumps, the spacing of these clumps varies between catalogues and there is no 'preferred' period over our many realizations. We find only a 0.72 (0.49) per cent chance that the highest peak in the power spectrum of a τ CDM (ΛCDM) catalogue has a peak-to-noise ratio higher than that in the Broadhurst et al. data. None of the simulated catalogues with such high peaks shows coherently spaced clumps with a significance as high as that of the real data. We conclude that in CDM universes, the regularity on a scale of ∼130  h ⁻¹ Mpc observed by Broadhurst et al. has a priori probability well below 10⁻³.     

The three-dimensional power spectrum of dark and luminous matter from the VIRMOS-DESCART cosmic shear survey

We present the first optimal power spectrum estimation and three-dimensional deprojections for the dark and luminous matter and their cross-correlations. The results are obtained using a new optimal fast estimator, deprojected using minimum variance and Singular Value Decomposition (SVD) techniques. We show the resulting 3D power spectra for dark matter and galaxies, and their covariance for the VIRMOS-DESCART weak lensing shear and galaxy data. The survey is most sensitive to non-linear scales   k _NL∼ 1 h Mpc⁻¹  . On these scales, our 3D power spectrum of dark matter is in good agreement with the RCS 3D power spectrum found by Tegmark & Zaldarriaga. Our galaxy power is similar to that found by the 2MASS survey, and larger than that of SDSS, APM and RCS, consistent with the expected difference in galaxy population.
We find an average bias   b = 1.24 ± 0.18  for the I -selected galaxies, and a cross-correlation coefficient   r = 0.75 ± 0.23  . Together with the power spectra, these results optimally encode the entire two point information about dark matter and galaxies, including galaxy–galaxy lensing. We address some of the implications regarding galaxy haloes and mass-to-light ratios. The best-fitting 'halo' parameter   h ≡ r / b = 0.57 ± 0.16  , suggesting that dynamical masses estimated using galaxies systematically underestimate total mass.
Ongoing surveys, such as the Canada–France–Hawaii Telescope Legacy Survey, will significantly improve on the dynamic range, and future photometric redshift catalogues will allow tomography along the same principles.     

Clustering of galaxies in a hierarchical universe – III. Mock redshift surveys

This is the third paper in a series which combines N -body simulations and semi-analytic modelling to provide a fully spatially resolved simulation of the galaxy formation and clustering processes. Here we extract mock redshift surveys from our simulations: a cold dark matter model with either Ω₀=1 ( τ CDM) or Ω₀=0.3 and Λ=0.7 (ΛCDM). We compare the mock catalogues with the northern region (CfA2N) of the Center for Astrophysics (CfA) Redshift Surveys. We study the properties of galaxy groups and clusters identified using standard observational techniques, and also the relation of these groups to real virialized systems. Most features of CfA2N groups are reproduced quite well by both models with no obvious dependence on Ω₀. Redshift‐space correlations and pairwise velocities are also similar in the two cosmologies. The luminosity functions predicted by our galaxy formation models depend sensitively on the treatment of star formation and feedback. For the particular choices of Paper I they agree poorly with the CfA survey. To isolate the effect of this discrepancy on our mock redshift surveys, we modify galaxy luminosities in our simulations to reproduce the CfA luminosity function exactly. This adjustment improves agreement with the observed abundance of groups, which depends primarily on the galaxy luminosity density, but other statistics, connected more closely with the underlying mass distribution, remain unaffected. Regardless of the luminosity function adopted, modest differences with observation remain. These can be attributed to the presence of the 'Great Wall' in the CfA2N. It is unclear whether the greater coherence of the real structure is a result of cosmic variance, given the relatively small region studied, or reflects a physical deficiency of the models.     

A submillimetre survey of the star formation history of radio galaxies

We present the results of the first major systematic submillimetre survey of radio galaxies spanning the redshift range 1< z <5. The primary aim of this work is to elucidate the star formation history of this sub class of elliptical galaxies by tracing the cosmological evolution of dust mass. Using SCUBA on the JCMT, we have obtained 850-μm photometry of 47 radio galaxies to a consistent rms depth of 1 mJy, and have detected dust emission in 14 cases. The radio galaxy targets have been selected from a series of low-frequency radio surveys of increasing depth (3CRR, 6CE, etc.), in order to allow us to separate the effects of increasing redshift and increasing radio power on submillimetre luminosity. Although the dynamic range of our study is inevitably small, we find clear evidence that the typical submillimetre luminosity (and hence dust mass) of a powerful radio galaxy is a strongly increasing function of redshift; the detection rate rises from ≃15 per cent at z <2.5 to ≳75 per cent at z >2.5, and the average submillimetre luminosity rises at a rate ∝(1+ z )³ out to z ≃4. Moreover, our extensive sample allows us to argue that this behaviour is not driven by underlying correlations with other radio galaxy properties such as radio power, radio spectral index, or radio source size/age. Although radio selection may introduce other more subtle biases, the redshift distribution of our detected objects is in fact consistent with the most recent estimates of the redshift distribution of comparably bright submillimetre sources discovered in blank field surveys. The evolution of submillimetre luminosity found here for radio galaxies may thus be representative of massive ellipticals in general.     

Topology and geometry of the CfA2 redshift survey

We analyse the redshift space topology and geometry of the nearby Universe by computing the Minkowski functionals of the Updated Zwicky Catalogue (UZC). The UZC contains the redshifts of almost 20 000 galaxies, is 96 per cent complete to the limiting magnitude m _Zw=15.5, and includes the Center for Astrophysics (CfA) Redshift Survey (CfA2). From the UZC we can extract volume-limited samples reaching a depth of 70  h ⁻¹ Mpc before sparse sampling dominates. We quantify the shape of the large-scale galaxy distribution by deriving measures of planarity and filamentarity from the Minkowski functionals. The nearby Universe shows a large degree of planarity and a small degree of filamentarity. This quantifies the sheet-like structure of the Great Wall, which dominates the northern region (CfA2N) of the UZC. We compare these results with redshift space mock catalogues constructed from high-resolution N -body simulations of two cold dark matter (CDM) models with either a decaying massive neutrino ( τ CDM) or a non-zero cosmological constant (ΛCDM). We use semi-analytic modelling to form and evolve galaxies in these dark matter‐only simulations. We are thus able, for the first time, to compile redshift space mock catalogues which contain galaxies, along with their observable properties, rather than dark matter particles alone. In both models the large-scale galaxy distribution is less coherent than the observed distribution, especially with regard to the large degree of planarity of the real survey. However, given the small volume of the region studied, this disagreement can still be a result of cosmic variance, as shown by the agreement between the ΛCDM model and the southern region of CfA2.     

Building a control sample for galaxy pairs

Several observational works have attempted to isolate the effects of galaxy interactions by comparing galaxies in pairs with isolated galaxies. However, different authors have proposed different ways to build these so-called control samples (CS). By using mock galaxy catalogues of the Sloan Digital Sky Survey Data Release 4 buildup from the Millennium Simulation, we explore how the way of building a CS might introduce biases which could affect the interpretation of results. We make use of the fact that the physics of interactions are not included in the semi-analytic model, to infer that any difference between the mock control and pair samples can be ascribed to selection biases. Thus, we find that galaxies in pairs artificially tend to be older and more bulge dominated, and to have less cold gas and different metallicities than their isolated counterparts. Also because of a biased selection, galaxies in pairs tend to live in higher density environments and in haloes of larger masses. We find that imposing constraints on redshift, stellar masses and local densities diminishes the selection biases by  ≈70 per cent  . Based on these findings, we suggest observers how to build a unique and unbiased CS in order to reveal the effect of galaxy interactions.     

Is the universe homogeneous? (On large scales)

I critically discuss in a pedagogical and phenomenological way a few crucial tests challenging the recent claims by Pietronero and collaborators that there is no evidence from available galaxy catalogues that the Universe is actually homogeneous above a certain scale. In a series of papers, these authors assert that observations are consistent with a fractal distribution of objects extending to the limit of the present data. I show that while galaxies are indeed clustered in a scale-free (fractal) way on small and intermediate scales, this behaviour does not continue indefinitely. Although the specific wavelength at which the galaxy distribution apparently turns to homogeneity is dangerously close to the size of the largest samples presently available, there are serious hints suggesting that this turnover is real and that its effects are detected in the behaviour of statistical estimators. The most recent claims of a continuing fractal hierarchy up to scales of several hundreds Megaparsecs seem to be ascribable to the use of incomplete samples or to an improper treatment of otherwise high-quality data sets. The fractal perspective, nevertheless, represents a fruitful way to look at the clustering properties of galaxies, when properly coupled to the traditional gravitational instability scenario. In the last part of this paper I will try to clarify, at a very simple level, some of the confusion existing on the actual scaling properties of the galaxy distribution, and discuss how these can provide hints on the evolution of the large-scale structure of the Universe.     

The 2dF Galaxy Redshift Survey: a targeted study of catalogued clusters of galaxies

We have carried out a study of known clusters within the 2dF Galaxy Redshift Survey (2dFGRS) observed areas and have identified 431 Abell, 173 APM and 343 EDCC clusters. Precise redshifts, velocity dispersions and new centroids have been measured for the majority of these objects, and this information is used to study the completeness of these catalogues, the level of contamination from foreground and background structures along the cluster's line of sight, the space density of the clusters as a function of redshift, and their velocity dispersion distributions. We find that the Abell and EDCC catalogues are contaminated at the level of about 10 per cent, whereas the APM catalogue suffers only 5 per cent contamination. If we use the original catalogue centroids, the level of contamination rises to approximately 15 per cent for the Abell and EDCC catalogues, showing that the presence of foreground and background groups may alter the richness of clusters in these catalogues. There is a deficiency of clusters at     that may correspond to a large underdensity in the Southern hemisphere. From the cumulative distribution of velocity dispersions for these clusters, we derive a space density of     clusters of     This result is used to constrain models for structure formation; our data favour low-density cosmologies, subject to the usual assumptions concerning the shape and normalization of the power spectrum.     

The clustering of galaxy clusters in cosmological models with non-Gaussian initial conditions: predictions for future surveys

We predict the biasing and clustering properties of galaxy clusters that are expected to be observed in the catalogues produced by two forthcoming X-ray and Sunyaev–Zel'dovich effect surveys. We study a set of flat cosmological models where the primordial density probability distribution shows deviations from Gaussianity in agreement with current observational bounds form the background radiation. We consider both local and equilateral shapes for the primordial bispectrum in non-Gaussian models. The two catalogues investigated are those produced by the e ROSITA wide survey and from a survey based on South Pole Telescope observations. It turns out that both the bias and observed power spectrum of galaxy clusters are severely affected in non-Gaussian models with local shape of the primordial bispectrum, especially at large scales. On the other hand, models with equilateral shape of the primordial bispectrum show only a mild effect at all scales, that is difficult to be detected with clustering observations. Between the two catalogues, the one performing better is the e ROSITA one, since it contains only the largest masses that are more sensitive to primordial non-Gaussianity.     

Searching for large-scale structure in deep radio surveys

We calculate the expected amplitude of the dipole and higher spherical harmonics in the angular distribution of radio galaxies. The median redshift of radio sources in existing catalogues is z  ∼ 1, which allows us to study large-scale structure on scales between those accessible to present optical and infrared surveys, and that of the cosmic microwave background (CMB). The dipole is a result of two effects which turn out to be of comparable magnitude: (i) our motion with respect to the CMB, and (ii) large-scale structure, parametrized here by a family of cold dark matter power-spectra. We make specific predictions for the Green Bank 1987 (87GB) and Parkes–MIT–NRAO (PMN) catalogues, which in our combined catalogue include ∼ 40 000 sources brighter than 50 mJy at 4.85 GHz, over about 70 per cent of the sky. For these relatively sparse catalogues both the motion and large-scale structure dipole effects are expected to be smaller than the Poisson shot noise. However, we detect dipole and higher harmonics in the combined 87GB–PMN_raw catalogue which are far larger than expected. We attribute this to a 2 per cent flux mismatch between the two catalogues. Ad hoc corrections made in an effort to match the catalogues may suggest a marginal detection of a dipole. To detect a dipole and higher harmonics unambiguously, a catalogue with full sky coverage and ∼ 10⁶ sources is required. We also investigate the existence and extent of the supergalactic plane in the above catalogues. In a strip of ± 10° of the standard supergalactic equator, we find a 3 σ detection in PMN_raw, but only 1 σ in 87 GB_raw. We briefly discuss the implications of ongoing surveys such as FIRST and NVSS and follow-up redshift surveys.     

Recovering the real-space correlation function from photometric redshift surveys

Measurements of clustering in large-scale imaging surveys that make use of photometric redshifts depend on the uncertainties in the redshift determination. We have used light-cone simulations to show how the deprojection method successfully recovers the real-space correlation function when applied to mock photometric redshift surveys. We study how the errors in the redshift determination affect the quality of the recovered two-point correlation function. Considering the expected errors associated with the planned photometric redshift surveys, we conclude that this method provides information on the clustering of matter useful for the estimation of cosmological parameters that depend on the large-scale distribution of galaxies.