Testing the Homogeneity of Large-scale Structure with the SDSS Data

One of the basic assumptions in cosmology is that the universe is homogeneous and isotropic on large scales. This assumption is the most important keystone of modern cosmology. In order to verify the homogeneity of galaxy distribution on large scales, we have computed the fractal dimensionality of the galaxy distribution in SDSS-DR4. The fractal dimensionality of the observed spatial geometric bodies is determined with random samples. The redshifts of sample galaxies are in the range 0.01～0.26. When the scale grows continuously to dozens of Mpc, the fractal dimensionality of the galaxy distribution approaches to 3 consistently. All the 6 samples exhibit obviously a transition scale. For scales larger than the transition scale, the fractal dimensionality D_G of the galaxy distribution is very close to 3, the galaxy distribution is homogeneous. This result supports the assumption that the universe is homogeneous on large scales. The transition scale of the sample increases with the luminosity of the sample. This means that the galaxy distribution on small scales is not a of simple fractal distribution, but a multi-fractal distribution. The transition scale of high-luminosity galaxies is very large, the distribution will not become homogeneous till about 100 h^?1Mpc.     

光学亮星系大尺度分布中的多级结构

本文在Wen等人工作的基础上,对CfA红移巡天样本中银道以北和以南天区中星系的大尺度分布分别进行了分维计算并比较其所得结果。分析表明,这两个区域内星系的大尺度分布存在显著差异。说明CfA样本还不能构成代表宇宙大尺度结构的好样本。另一方面,两个区域中样本分析结果又存在着一些明显的共同点:它们都表现出明显的多级分形特征。结合对IRAS星系红移巡天样本和星系分立小天区红移巡天样本的分析结果。我们认为,多级分形很可能是宇宙大尺度结构的一个普遍和重要的特征。本文对这一特征的含义也作了简略的讨论。     

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.     

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.     

GALICS: capturing the panchromaticity of galaxies

This contribution describes results obtained with the GALICS model (for Galaxies In Cosmological Simulations), which is a hybrid model for hierarchical galaxy formation studies, combining the outputs of large cosmological N-body simulations with simple, semi-analytic recipes to describe the fate of the baryons within dark matter halos. Designed to predict the overall statistical properties of galaxies, with special emphasis on the panchromatic spectral energy distribution emitted by galaxies in the UV/optical and IR/submm wavelength ranges, such an approach can be used to predict the galaxy luminosity function evolution from the ultraviolet to far infrared, along with individual galaxies star formation histories. This revised version was published online in September 2006 with corrections to the Cover Date.     

GHASP: an Hα kinematic survey of spiral and irregular galaxies – V. Dark matter distribution in 36 nearby spiral galaxies

The results obtained from a study of the mass distribution of 36 spiral galaxies are presented. The galaxies were observed using Fabry–Perot interferometry as part of the GHASP survey. The main aim of obtaining high-resolution Hα 2D velocity fields is to define more accurately the rising part of the rotation curves which should allow to better constrain the parameters of the mass distribution. The Hα velocities were combined with low resolution H  i data from the literature, when available. Combining the kinematical data with photometric data, mass models were derived from these rotation curves using two different functional forms for the halo: an isothermal sphere (ISO) and a Navarro–Frenk–White (NFW) profile. For the galaxies already modelled by other authors, the results tend to agree. Our results point at the existence of a constant density core in the centre of the dark matter haloes rather than a cuspy core, whatever the type of the galaxy from Sab to Im. This extends to all types the result already obtained by other authors studying dwarf and low surface brightness galaxies but would necessitate a larger sample of galaxies to conclude more strongly. Whatever model is used (ISO or NFW), small core radius haloes have higher central densities, again for all morphological types. We confirm different halo scaling laws, such as the correlations between the core radius and the central density of the halo with the absolute magnitude of a galaxy: low-luminosity galaxies have small core radius and high central density. We find that the product of the central density with the core radius of the dark matter halo is nearly constant, whatever the model and whatever the absolute magnitude of the galaxy. This suggests that the halo surface density is independent from the galaxy type.     

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.     

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。     

Head-on Collision of Disk–Sphere Galaxies

Numerical simulations are performed to study the tidal effects of non-merging rapid head-on collision between a disk galaxy and a spherical galaxy. The disk consists of three components – a disk, a bulge and a halo – and the spherical galaxy is a Plummer model. The galaxies have the same dimensions with different mass ratios viz., 2, 1 and 0.5. They move in a rectilinear orbit with a relative velocity of 1000 km s⁻¹. None of the simulations leads to the merger of the galaxies by tidal capture. The results of our simulations indicate that although tidal effects are sensitive to both the mass ratio and the inclination of the disk to the orbital plane, it is the mass ratio which is more important in producing tidal damage to the less massive galaxy. The spherical galaxy undergoes considerable tidal effects if the mass of the disk is same or larger. On the other hand the collisions in which the mass of the spherical galaxy is more, result in the formation of a ring structure after the closest approach and the structure disappears by the end of the simulations.     

Gas dynamic stripping and X-ray emission of cluster elliptical galaxies

Detailed three-dimensional numerical simulations of an elliptical galaxy orbiting in a gas-rich cluster of galaxies indicate that gas dynamic stripping is less efficient than the results from previous, simpler calculations by Takeda et al. and Gaetz et al. implied. This result is consistent with X-ray data for cluster elliptical galaxies. Hydrodynamic torques and direct accretion of orbital angular momentum can result in the formation of a cold gaseous disc, even in a non-rotating galaxy. The gas lost by cluster galaxies via the process of gas dynamic stripping tends to produce a colder, chemically enriched cluster gas core. A comparison of the models with the available X-ray data of cluster galaxies shows that the X-ray luminosity distribution of cluster galaxies may reflect hydrodynamic stripping, but also that a purely hydrodynamic treatment is inadequate for the cooler interstellar medium near the centre of the galaxy.     

Fractal properties of outflows from Venusian impact craters

This article presents fractal analyses of 28 outflow margins from 18 Venusian impact craters. The fractal dimensions of the second parts of R-plots of the outflow outlines were measured by a three-step method. The fractality values for the same outflow measured from images which have only a small difference in resolution are very similar, while large differences in image resolution may result in differences in fractality, possibly due to the fact that we are actually studying geological processes on different scales. The outflows were classified into three general categories: single outflows, multiple outflows and outflow fields. Three conclusions were drawn on the relations between fractality and crater diameter, which may be related to the greater effects caused by the immediate local environment on the outflows from small craters than on those from larger craters. Investigation of the relations between the regional topography and fractality indicates that there are substantially less effects on outflows originating from large craters than on those from small craters. The smooth bending in the R-plot and the higher D-value for the multiple outflows could result from the mixing of various fractal or non-fractal units. When comparing our results with the fractality of terrestrial lava flows, outflows from craters of diameter greater than 50 km seem to resemble aa-type lava flows in their fractal dimensions and outflows from craters of diameter below 50 km tend to be more pahoehoe-like. This preliminary result is based on 28 outflows, however, and the pattern should be investigated more carefully by further more extensive work.     

3D spectroscopy of merger Seyfert galaxy Mrk 334: nuclear starburst, superwind and the circumnuclear cavern

We are presenting new results on kinematics and structure of the Mrk 334 Seyfert galaxy. Panoramic (3D) spectroscopy is performed at the 6-m telescope of the Special Astrophysical Observatory of the Russian Academy of Sciences using the integral-field Multi-Pupil Fiber Spectrograph (MPFS) and scanning Fabry–Pérot interferometer. The deep images have revealed that Mrk 334 is observed during the final stage of its merging with a massive companion. A possible mass ratio ranges from 1/5 to 1/3. The merger has triggered mass redistribution in the disc resulting in an intensification of nuclear activity and in a burst of star formation in the inner region of the galaxy. The circumnuclear starburst is so intense that its contribution to the gas ionization exceeds that contribution of the active galactic nuclei (AGN). We interpret the nuclear gas outflow with velocities of  ∼200 km s⁻¹  as a galactic superwind that accompanies the violent star formation. This suggestion is consistent with the asymmetric X-ray brightness distribution in Mrk 334. The trajectory of the fragments of the disrupted satellite in the vicinity of the main galaxy nucleus can be traced. In the galaxy disc, a cavern is found that is filled with a low-density ionized gas. We consider this region to be the place where the remnants of the companion have recently penetrated through the gaseous disc of the main galaxy.     

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.     

Projected bispectrum in spherical harmonics and its application to angular galaxy catalogues

We present a theoretical and exact analysis of the bispectrum of projected galaxy catalogues. The result can be generalized to evaluate the projection in spherical harmonics of any 3D bispectrum and therefore has applications to cosmic microwave background and gravitational lensing studies.
By expanding the 2D distribution of galaxies on the sky in spherical harmonics, we show how the three-point function of the coefficients can be used in principle to determine the bias parameter of the galaxy sample. If this can be achieved, it would allow a lifting of the degeneracy between the bias and the matter density parameter of the Universe, which occurs in linear analysis of 3D galaxy catalogues. In previous papers, we have shown how a similar analysis can be done in three dimensions, and we show here through an error analysis and by implementing the method on a simulated projected catalogue that ongoing three-dimensional galaxy redshift surveys (even with all the additional uncertainties introduced by partial sky coverage, redshift-space distortions and smaller numbers) will do far better than all-sky projected catalogues with similar selection function.     

Kinematics of an Anaemic Cluster Galaxy

We present new HI and CO data including velocity information of NGC 4548, an anaemic galaxy in the Virgo Cluster. The distribution of the atomic gas shows a ring-like structure. The HI rotation curve is deduced and can be extrapolated inwards with the help of the CO data. The derived molecular fraction decreases continuously up to a radius of about 40″ showing a rather sharp transition between the molecular and the atomic disc. A three-dimensional visualization of the data cube permits us to detect a perturbation of the velocity field in the northern part of the galaxy. In a first approach we reconstruct the possible sites of HI emission with the help of a simple kinematical model in three dimensions. The reconstructed model shows a ridge which is believed to be due to ram-pressure stripping. In addition, we show first results of a dynamical model to simulate the interaction between the intra-cluster medium and the galaxy. This revised version was published online in July 2006 with corrections to the Cover Date.     

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。     

Geometry of Spiral Galaxy Arms

The previous work (He, 2001) on image analysis of over one hundred nearby galaxies indicates that for any spiral galaxy image of small inclination there is evidence of two sets of iso-ratio curves in different scales which, like curvilineal coordinate lines, expand over different galaxy components. This result sets constraint on galaxy patterns and a general equation which carries this constraint is presented in the current paper. The equation has clear geometrical meaning. Its much simplified version which applies to galaxy arms, when solved, may be a guidance to understanding galaxy patterns. This revised version was published online in July 2006 with corrections to the Cover Date.     

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.     

河外IRAS暗源大尺度分布的二维分析

本文对ＩＲＡＳ暗源表中４个选区内的ＩＲＡＳ星系的两点角相关函数，关联分维进行了计算。结果表明，所有选区内的星系呈现小角尺度上的成团。在较大角尺度上，分布可以用多级分形很好地表示。在更大角尺度上，用非归一星系对计数可以探测到密度分布中可能存在的典型尺度。当取４个选区的平均值作为ＩＲＡＳ星系在宇宙中分布情况的代表时，所得结果与用全天ＩＲＡＳ点源表和其他巡天资料得到的结果一致。     

The global structure of galactic discs

A statistical study of global galaxy parameters can help to improve our understanding of galaxy formation processes. In this paper we present the analysis of global galaxy parameters based on optical and near-infrared observations of a large sample of edge-on disc galaxies. We found a correlation between the ratio of the radial to vertical scale parameter and galaxy type: galaxies become systematically thinner when going from type S0 to type Sc, whereas the distribution seems to level off for later types. The observed scalelength ratios (and thus the radial colour gradients) largely represent the dust content of the galaxies. On average, the colour gradients indicated by the scalelength ratios increase from type Sa to at least type Sc. For galaxy types later than Sc, the average colour gradient seems to decrease again. The distribution of K -band (edge-on) disc central surface brightnesses is rather flat, although with a large scatter. However, the latest-type sample galaxies ( T  > 6) show an indication that their average disc central surface brightnesses may be fainter than those of the earlier types. This effect is probably not the result of dust extinction.