由SLOAN观测数据测试大尺度结构的均匀性

宇宙学的基本假设之一是宇宙在大尺度上均匀各向同性.为了验证星系分布在大尺度上的均匀性,分别计算观测样本和观测空间几何体的分形维数,得到SDSS-DR4中星系分布的分形维数.观测空间几何体的分形维数用随机样本来确定.样本中的星系红移z的范围为0.01-0.26.当尺度持续增加至几十个Mpc时,星系分布的分形维数一致地趋向于3.所有的样本均显示了明显的转变尺度,当尺度大于此转变尺度时,星系分布的分形维数D<,G>～3,星系的分布转变为均匀分布.结果支持了宇宙学的基本原理关于宇宙大尺度均匀的假设.样本的转变尺度随着样本的光度增强而变大,说明小尺度上星系的分布不是简单的分形分布,而是多维分形分布.高光度星系的转变尺度非常大,直到100h-1Mpc左右才变得均匀.     

宇宙在大尺度上是均匀的吗?

宇宙中的物质在大尺度上是均匀分布的,还是保持着分形分布的特点,成为近年来观测宇宙学中争论的一个热点。Ｐｉｅｔｒｏｎｅｒｏ等人认为直到目前观测到的最大尺度（≈１０００ｈ＾－１Ｍｐｃ）星系的分布仍保持Ｄ≈２的分形结构,而大多数坚持标准模型的宇宙学家都认为宇宙在大尺度上是均匀分布的。宇宙物质在大尺度上是否均匀分布,将由下一代的红移巡天的结果来判断。     

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.     

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.     

Statistical properties of the spatial distribution of galaxies

The methods of determining the fractal dimension and irregularity scale in simulated galaxy catalogs and the application of these methods to the data of the 2dF and 6dF catalogs are analyzed. Correlation methods are shown to be correctly applicable to fractal structures only at the scale lengths from several average distances between the galaxies, and up to (10 ? 20)% of the radius of the largest sphere that fits completely inside the sample domain. Earlier the correlation methods were believed to be applicable up to the entire radius of the sphere and the researchers did not take the above restriction into account while finding the scale length corresponding to the transition to a uniform distribution. When an empirical formula is applied for approximating the radial distributions in the samples confined by the limiting apparent magnitude, the deviation of the true radial distribution from the approximating formula (but not the parameters of the best approximation) correlate with fractal dimension. An analysis of the 2dF catalog yields a fractal dimension of 2.20 ± 0.25 on scale lengths from 2 to 20 Mpc, whereas no conclusive estimates can be derived by applying the conditional density method for larger scales due to the inherent biases of the method. An analysis of the radial distributions of galaxies in the 2dF and 6dF catalogs revealed significant irregularities on scale lengths of up to 70 Mpc. The magnitudes and sizes of these irregularities are consistent with the fractal dimension estimate of D =2.1–2.4.     

不同光度星系大尺度分布的交叉相关分析

在对不同光度星系大尺度分布进行空间两点相关函数分析的基础上,仍以CfA红移巡天资料为样本,对不同光度星系分布进行了交叉相关分析。结果表明,不同光度星系间的交叉相关函数仍可近似地以幂函数表示,说明不同光度星系在空间是一起成团的。但在较小尺度上((?)4—6Mpc),光度较高的星系间相关更强,而在更大一些尺度上光度较高的星系间相关减弱更快,甚至变得比与光度较低星系间的相关更弱。结合前面对自相关函数分析的结果可以看到,统计上看来,星系分布形成群和团。群或团中亮的星系形成更致密的分布而较暗的星系则在这些群和团中分布较弥散。此结果表明星系光度和其环境(密度)有关,从而从观测上为Biased星系形成理论提供了一个可能的证据。     

Fractal structure in the large scale distribution of galaxies

We study the large scale structure of galaxy distribution from the fractal point of view using the CfA survey data. Main results are as follows: 1. Within certain ranges, the galaxy distribution is fractal with fractal dimension about 2.0. This result is different fron the value 1.2 – 1.4, expected from the galaxy two-point correlation function. 2. Galaxies of different luminosities show somewhat different fractal dimensions. This result indicates that they may correspond to different perturbation ranges in the early universe, in apparent agreement with thepredictions of biased galaxy formation theory. 3. Scales smaller and greater than 10 Mpc seem to have different fractal dimensions. A preliminary analysis of these results is included.     

The method of a two-point conditional column density for estimating the fractal dimension of the distribution of galaxies

We suggest a new method for estimating the fractal dimension of the spatial distribution of galaxies: the method of selected cylinders. We show the capabilities of this method by constructing a two-point conditional column density for galaxies with known redshifts from the LEDA database. The fractal dimension of a sample of LEDA and EDR SDSS galaxies has been estimated to be 2.1±0.1 for cylinder lengths of 200 Mpc. A major advantage of the suggested method is that it allows scales comparable to the catalog depth to be analyzed for galaxy surveys in the form of conical sectors and small fields in the sky.     

Properties of voids in the 2dFGRS galaxy survey

A method for detecting voids in the galaxy distribution is presented. Using this method, we have identified 732 voids with a radius of the seed sphere R _seed > 4.0h ^?1 Mpc in a volume-limited sample of galaxies from the southern part of the 2dFGRS survey. 110 voids with R _seed > 9.0h ^?1 Mpc have a positive significance. The mean volume of such voids is ～19 × 10³ h ^?3 Mpc³. Voids with R _seed > 9.0h ^?1 Mpc occupy 55% of the sample volume. We construct a dependence of the volumes of all the identified voids on their ranks and determine parameters of the galaxy distribution. The dependence of the volume of voids on their rank is consistent with a fractal model (Zipf’s power law) of the galaxy distribution with a fractal dimension D ≈ 2.1 (given the uncertainty in determining the dimension using our method and the results of a correlation analysis) up to scales of ～25h ^?1 Mpc with the subsequent transition to homogeneity. The directions of the greatest elongations of voids and their ellipticities (oblateness) are determined from the parameters of equivalent ellipsoids. The directions of the greatest void elongations have an enhanced concentration to the directions perpendicular to the line of sight.     

Galaxy Evolution in Groups and Clusters: Workshop Summary

The study of galaxy clusters and groups covers a large range of physical scales, from cosmology to large scale structure, to individual galaxies. This workshop on the evolution of galaxies in clusters and groups provided a rich assembly of subjects. Brief summaries are given in some of these topics, including: the applications of clusters to cosmology, the evolution of cluster galaxies in the context of the Butcher-Oemler effect, the galaxy populations in clusters – from dwarfs to the cD galaxy, the interplay between cluster/group environment and the evolution of clusters, the infalling cluster members and the galaxy luminosity function. This revised version was published online in July 2006 with corrections to the Cover Date.     

Galaxy–dark matter correlations applied to galaxy–galaxy lensing: predictions from the semi-analytic galaxy formation models

We use semi-analytic models of galaxy formation combined with high-resolution N -body simulations to make predictions for galaxy–dark matter correlations and apply them to galaxy–galaxy lensing. We analyse cross-power spectra between the dark matter and different galaxy samples selected by luminosity, colour or star formation rate. We compare the predictions with the recent detection by the Sloan Digital Sky Survey (SDSS). We show that the correlation amplitude and the mean tangential shear depend strongly on the luminosity of the sample on scales below 1  h ⁻¹ Mpc, reflecting the correlation between the galaxy luminosity and the halo mass. The cross-correlation cannot, however, be used to infer the halo profile directly because different halo masses dominate on different scales and because not all galaxies are at the centres of the corresponding haloes. We compute the redshift evolution of the cross-correlation amplitude and compare it with those of galaxies and dark matter. We also compute the galaxy–dark matter correlation coefficient and show that it is close to unity on scales above 1  h ⁻¹ Mpc for all considered galaxy types. This would allow one to extract the bias and the dark matter power spectrum on large scales from the galaxy and galaxy–dark matter correlations.     

Scale-dependent galaxy bias in the Sloan Digital Sky Survey as a function of luminosity and colour

It has been known for a long time that the clustering of galaxies changes as a function of galaxy type. This galaxy bias acts as a hindrance to the extraction of cosmological information from the galaxy power spectrum or correlation function. Theoretical arguments show that a change in the amplitude of the clustering between galaxies and mass on large scales is unavoidable, but cosmological information can be easily extracted from the shape of the power spectrum or correlation function if this bias is independent of scale. Scale-dependent bias is generally small on large scales,   k < 0.1  h  Mpc⁻¹  , but on smaller scales can affect the recovery of  Ω_m h   from the measured shape of the clustering signal, and have a small effect on the Baryon Acoustic Oscillations. In this paper, we investigate the transition from scale-independent to scale-dependent galaxy bias as a function of galaxy population. We use the Sloan Digital Sky Survey Data Release 5 sample to fit various models, which attempt to parametrize the turn-off from scale-independent behaviour. For blue galaxies, we find that the strength of the turn-off is strongly dependent on galaxy luminosity, with stronger scale-dependent bias on larger scales for more luminous galaxies. For red galaxies, the scale dependence is a weaker function of luminosity. Such trends need to be modelled in order to optimally extract the information available in future surveys, and can help with the design of such surveys.     

The signature of dark energy on the local Hubble flow

Using N -body simulations of flat, dark energy-dominated cosmologies, we show that galaxies around simulated binary systems resembling the Local Group (LG) have low peculiar velocities, in good agreement with observational data. We have compared results for LG-like systems selected from large, high-resolution simulations of three cosmologies: a ΛCDM model, a ΛWDM model with a 2-keV warm dark matter candidate, and a quintessence (QCDM) model with an equation-of-state parameter   w =−0.6  . The Hubble flow is significantly colder around LGs selected in a flat, Λ-dominated cosmology than around LGs in open or critical models, showing that a dark energy component manifests itself on the scales of nearby galaxies, cooling galaxy peculiar motions. Flows in the ΛWDM and QCDM models are marginally colder than in the ΛCDM one.
The results of our simulations have been compared to existing data and to a new data set of 28 nearby galaxies with robust distance measures (Cepheids and surface brightness fluctuations). The measured line-of-sight velocity dispersion is given by  σ_H= (88 ± 20  km s⁻¹) × ( R /7 Mpc)  . The best agreement with observations is found for LGs selected in the ΛCDM cosmology in environments with  −0.1 < δρ/ρ < 0.6  on scales of 7 Mpc, in agreement with existing observational estimates on the local matter density. These results provide new, independent evidence for the presence of dark energy on scales of a few megaparsecs, corroborating the evidence gathered from observations of distant objects and the early Universe.     

Normal galaxies in the all-sky survey by the eROSITA X-ray telescope of the Spectrum-X-Gamma observatory

We analyze the statistical properties of normal galaxies to be detected in the all-sky survey by the eROSITA X-ray telescope of the Spectrum-X-Gamma observatory. With the current configuration and parameters of the eROSITA telescope, the sensitivity of a 4-year-long all-sky survey will be ≈10^?14 erg s^?1 in the 0.5–2 keV band. This will allow ～(1.5–2) × 10⁴ normal galaxies with approximately the same contribution of star-forming and elliptical galaxies to be detected. All galaxies of the X-ray survey are expected to enter into the existing far-infrared (IRAS) or near-infrared (2MASS) catalogs; the sample of star-forming galaxies will be approximately equivalent in sensitivity to the sample of star-forming galaxies in the IRAS catalog of infrared sources. Thus, a large homogeneous sample of normal galaxies with measured X-ray, near-infrared, and far-infrared fluxes will be formed. About 90% of the galaxies in the survey are located within ～200–400 Mpc. A typical (most probable) galaxy will have a luminosity log L _X ～ 40.5–41.0, will be located at a distance of ～70–90 Mpc, and will be either a star-forming galaxy with a star formation rate of ～20M _⊙ yr^?1 whose X-ray emission is produced by ultraluminous X-ray sources (ULXs) or an elliptical galaxy with amass log M _* ～ 11.3 emitting through to a hot interstellar gas. The galaxies within 35 Mpc will collectively contain ～10² ULXs with luminosities log L _X > 40, ～80% of whichwill be the only luminous source in the galaxy. Thus, although the angular resolution of the eROSITA telescope is too low for the luminosity function of compact sources in galaxies to be studied in detail, the survey data will allow one to investigate its bright end and, possibly, to impose constraints on the maximum luminosity of ULXs.     

Correlation properties of galaxies from the Main Galaxy Sample of the SDSS survey

The apparatus of correlation gamma function (Γ^*(r)) is used to analyze volume-limited samples from the DR4 Main Galaxy Sample of the SDSS survey with the aim of determining the characteristic scales of galaxy clustering. Up to 20h ^?1 Mpc (H ₀ = 65 km s^?1 Mpc^?1), the distribution of galaxies is described by a power-law density—distance dependence, Γ^*(r) ∝ r ^?γ , with an index γ ≈ 1.0. A change in the state of clustering (a significant deviation from the power law) was found on a scale of (20–25) h ^?1 Mpc. The distribution of SDSS galaxies becomes homogeneous (γ ～ 0) from a scale of ～60h ^?1 Mpc. The dependence of γ on the luminosity of galaxies in volume-limited samples was obtained. The power-law index γ increases with decreasing absolute magnitude of sample galaxies M _abs. At M _abs ～ ?21.4, which corresponds to the characteristic value M _r ^* of the SDSS luminosity function, this dependence exhibits a break followed by a more rapid increase in γ.     

基于红移畸变测量宇宙结构增长率的进展

星系红移巡天的一个主要目标是依据光谱红移测距,详细刻画宇宙中星系的三维空间分布。由于星系本动速度的存在,红移空间的星系分布存在着严重畸变,在大小尺度上有着不同模式的各向同性偏离。通过对红移畸变的观测研究,人们可从中获取速度场的信息,因此,红移畸变已成为暗能量探测的重要探针之一,为检验宇宙学尺度上的引力模型提供帮助。当前星系红移巡天项目已经取得了非凡成功,为人们提供了详细的星系空间分布数据。人们据此测量了星系的相关函数和功率谱,提取了精确的红移畸变信号,并通过模型拟合限制出了一批不同红移处宇宙结构增长率的估值,为探索宇宙尺度的引力模式提供了数据支持。主要介绍红移畸变模型、星系红移巡天观测和宇宙结构增长率测量等研究进展。     

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 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.     

The G3 non-isomorphic clustering graph and the problem of the physical reality of the clustering tendency

Chains ofnormal galaxies dominate small-scale clustering. This filamentary structure has nothing to do with large-scale filaments between clusters; and the revelation of short galaxy chains among normal galaxies was not expected by Arp, who investigated chains ofpeculiar galaxies. The nature of revealed chains cannot be explained in terms of so-called filaments observed in a scale of 100 Mpc: there is no continuation between 100 kpc and 100 Mpc chains of galaxies. Three sorts of clustering modes, corresponding toG ₁,G ₂ andG ₄ non-isomorphic graphs withthree vertices, are free of the time paradox. Chains (the clustering mode corresponding to theG ₃ graph) are stable on a time scale less (tens and sometimes a hundred times) than the conventional age ofnormal galaxies. Why do the chains dominate small scales?     

The clustering of colour-selected galaxies

We present measurements of the angular correlation function of galaxies selected from a B _J ∼23.5 multicolour survey of two 5°×5° fields located at high galactic latitudes. The galaxy catalogue of ∼4×10⁵ galaxies is comparable in size to catalogues used to determine the galaxy correlation function at low redshift. Measurements of the z ∼0.4 correlation function at large angular scales show no evidence for a break from a power law, although our results are not inconsistent with a break at ≳15 h⁻¹ Mpc. Despite the large fields-of-view, there are large discrepancies between the measurements of the correlation function in each field, possibly caused by dwarf galaxies within z ∼0.11 clusters near the South Galactic Pole.
Colour selection is used to study the clustering of galaxies from z ∼0 to z ∼0.4. The galaxy correlation function is found to depend strongly on colour, with red galaxies more strongly clustered than blue galaxies by a factor of ≳5 at small scales. The slope of the correlation function is also found to vary with colour, with γ∼1.8 for red galaxies and γ∼1.5 for blue galaxies. The clustering of red galaxies is consistently strong over the entire magnitude range studied, although there are large variations between the two fields. The clustering of blue galaxies is extremely weak over the observed magnitude range, with clustering consistent with r ₀∼2 h⁻¹ Mpc. This is weaker than the clustering of late-type galaxies in the local Universe, and suggests that galaxy clustering is more strongly correlated with colour than morphology. This may also be the first detection of a substantial low-redshift galaxy population with clustering properties similar to faint blue galaxies.