On the Large-Scale Structure of the Universe as given by the Voronoi Diagrams

The size distributions of 2D and 3D Voronoi cells and of cells of Vp(2,3),-2D cut of 3D Voronoi diagram-are explored, with the single-parameter (re-scaled) gamma distribution playing a central role in the analytical fitting. Observational evidence for a cellular universe is briefly reviewed. A simulated Vp(2,3) map with galaxies lying on the cell boundaries is constructed to compare, as regards general appearance, with the observed CfA map of galaxies and voids, the parameters of the simulation being so chosen as to reproduce the largest observed void size.     

类星体L_α森林吸收线密度与发射红移的相关性

本文对16个高红移类星体的L_α森林吸收线密度N(z_(abs))统计分析的结果,表明它明显地依赖于类星体自身的发射红移z_(em)。这不仅表现在z(em)越大的类星体其全部L_α吸收线的平均数密度N(z_(abs))也越大;更重要的是,对于相同的吸收红移值z_(abs),而言,N(z_(abs))在统计意义上明显地随着类星体z_(em)的增大而增大。另一方面,本文也在“吸收体源自类星体抛射”的框架下作了统计,结果仍表明z_(em)对L_α森林吸收线密度有显著影响,但抛射速度却对被抛射体的数目无显著影响。最后,对所得的结果以及可能影响N(z_(abs))的若干因素作了讨论。     

Basal heating in the atmospheres of cool stars

Summary This paper reviews observational evidence concerning the existence of so-calledbasal heating that occurs in the outer atmospheres of all stars with convective envelopes. Effects of basal heating depend primarily on the effective temperature, with little sensitivity to surface gravity or elemental abundances. Basal heating occurs predominantly in the chromosphere, possibly in the (lower) transition region, but not at an observable level in coronae (except perhaps in early F-type and in M-type dwarf stars). Basal fluxes are observed in the slowest rotators where it shows no significant modulation. The basal flux level is observed directly on the Sun only over regions void of intrinsically strong photospheric fields. There is substantial quantitative observational and theoretical evidence that the basal emission from stellar outer atmospheres is caused by the dissipation of acoustic waves generated by turbulent convection. The magnetic canopy turns out to be of little consequence, but effects of intrinsically weak fields on the basal mechanism cannot be entirely ruled out. Solar observations constrain the spatio-temporal character of the basal atmosphere and the acoustic flux levels as a function of height, resulting in a model in which intermittent wave dissipation causes emission characteristic of both cool and warm atmospheric areas, in which — at least in the solar case — a time-averaged chromospheric temperature rise may not even exist.     

Abell团相关性-富度关系的统计研究

本文对D≤4,R≥0的Abell团样品和整个R≥3的Abell团样品的空间两点相关函数做了统计分析,结果表明R≥0,R=0和R≥3的Abell团的相关函数分别为175r~(-1.8),150r~(-1.8)和1900r~(-1.8)利用已有的R≥1和R≥2团的相关函数的统计结果,我们得到了Abell团的相关性幅度α与富度N之间的关系:α∝N~(1.6)。在相关性幅度的统计误差所允许的范围内,α与N之间的关系可以在宇宙弦理论中得到解释。     

Recovering the topology of the initial density fluctuations using the IRAS Point Source Catalogue Redshift Survey

We apply the reconstruction technique of Nusser & Dekel to the recently available Point Source Catalogue Redshift Survey (PSCz) in order to subtract the non-Gaussianities that are expected to develop in the mild non-linear regime of gravitational evolution. We study the evolution of isodensity contours defined using an adaptive smoothing algorithm, in order to minimize the problems derived from the non-commutativity of the smoothing operator and the time-evolution operator. We study the topology of these isodensity contours and concentrate on the evolution of the amplitude drop of the genus compared to a Gaussian field with an identical power spectrum, in order to quantify the level of phase-correlation present in the field. In order to test the method and to quantify the level of statistical uncertainty, we apply the method to a set of mock PSCz catalogues derived from the N -body simulations of two standard cold dark matter (CDM) models, kindly granted to us by the Virgo consortium. We find the method to be reliable in recovering the correct amplitude drops. When applied to PSCz, the level of phase correlations observed is very low on all scales ranging from 5 to 60  h ⁻¹ Mpc, providing support to the theory that structure originated from Gaussian initial conditions.     

Recovery of the cosmological peculiar velocity from the density field in the weakly non-linear regime

Using third-order perturbation theory, we derive a relation between the divergence of the peculiar velocity and the density. Specifically, we compute the expectation value of the divergence given density. Our calculations assume Gaussian initial conditions and are valid for Gaussian filtering of the evolved density and velocity fields. The mean velocity divergence turns out to be a third-order polynomial in the density contrast. We test the power-spectrum dependence of the coefficients of the polynomial for scale-free and standard CDM spectra and find it rather weak. Over scales larger than about 5  h ⁻¹ Mpc, the scatter in the relation is small compared with that introduced by random errors in the observed density and velocity fields. The relation can be useful for recovering the peculiar velocity from the associated density field, and also for non-linear analyses of the anisotropies of structure in redshift surveys.     

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.     

Accurate masses and radii of normal stars

Summary Binary stars are the main source of fundamental data on stellar masses and radii (M, R). Considerable progress has been made in recent years in the quality and quantity of such data, and stellar masses and radii of high accuracy have led to a number of qualitatively new and interesting results on the properties and evolution of normal stars. This paper reviews the current status of fundamentalM andR determinations which (i) have errors 2%, the limit for non-trivial results in many applications, and (ii) can be presumed valid for single stars. These two conditions limit the discussion to data fromdetached, doublelined eclipsing binary systems.After a brief discussion (Sect. 2) of the main tests for accuracy and consistency which must be met for observational data to be included in the sample, data for 45 binary systems (90 single stars) are presented in Sect. 3 (Table 1 and Figs. 2–5). Spectral types are O8-M1 on the main sequence, with only two stars clearly in the red-giant region. From the review by Popper (1980), data for only 6 systems survive unchanged in the present list, while improved data are given for 18 systems; 21 systems are new additions. Broadband colours, effective temperatures, and luminosities are also given, but are scale-dependent and considerably less reliably determined thanM andR.The observed ranges inM andR for a given colour far exceed the observational errors, primarily due to evolutionary effects within the main sequence. For this reason, single-parameter relations used to predictM andR for single stars are limited to an accuracy of some ±15% inM and ±50% inR, basically independent of the number and accuracy of the data used to establish the relations. Two-parameter calibrations are discussed (Sect. 4) which can eventually reduce these errors to & 5% in bothM andR. At this level, abundance effects become significant and presumably account for the residual scatter.Comparison of the data with stellar evolution models is the topic of Sect. 5. Characteristic features of the data which are crucial in such work are emphasized, rather than attempts to prove the validity of any particular set of models. Already fromM andR alone, some significant constraints can be derived (Fig. 4). When bothM, R, andT _e are known, the initial helium abundanceY can be estimated if the metal-abundance parameter Z is assumed or determined. Studies in which binaries with accurate values ofM, R, and Z are fit by models calculated for the precise observed masses, and withY and mixing length constrained to solar values, provide the most stringent tests of the models. Probing further model refinements such as convective overshooting requires full use of the potential of the data. For example, models may yield general main-sequence limits which are consistent with the observations, but still be unable to fit any single system to the precision of the data. Conditions for critical, informative tests are discussed. Tidal effects in binaries are briefly discussed in Sect. 6. As tidal forces are extremely sensitive to the dimensions and internal structure of the stars, the present sample is well suited for such studies. Recent success in matching computed and observed apsidal-motion parameters for early-type binaries is mentioned. Finally, main priorities for future work are outlined.     

星系形成与宇宙大尺度结构

宇宙大尺度结构的形成与星系形成密切相关,前者的研究把星系基本上视为一质点,而星系形成研究涉及到其内部结构,宇宙大尺度结构形成有两种模式,由小到大与由大到小,这两种模式被交替使用（当然不同简单的重复）很重要的一个原因是星系形成研究的推动。     

Concerning the instantaneous mass and the extent of an expanding universe

In this article we want to answer the cosmologically relevant question what, with some good semantic and physical reason, could be called the massM _u of an infinitely extended, homogeneously matter‐filled and expanding universe. To answer this question we produce a space‐like sum of instantaneous cosmic energy depositions surrounding equally each spacepoint in the homogeneous universe. We calculate the added‐up instantaneous cosmic energy per volume around an arbitrary space point in the expanding universe. To carry out this sum we use as basic metrics an analogy to the inner Schwarzschild metric applied to stars, but this time applied to the spacepoint‐related universe. It is then shown that this leads to the added‐up proper energy within a sphere of a finite outer critical radius defining the point‐related infinity. As a surprise this radius turns out to be reciprocal to the square root of the prevailing average cosmic energy density. The equivalent mass of the universe can then also be calculated and, by the expression which is obtained here, shows a scaling with this critical radius of this universe, a virtue of the universe which was already often called for in earlier works by E. Mach, H. Thirring and F. Hoyle and others. This radius on the other hand can be shown to be nearly equal to the Schwarzschild radius of the so‐defined mass M _u of the universe. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Power-spectrum normalization from the local abundance of rich clusters of galaxies

The number density of rich galaxy clusters still provides the most robust way of normalizing the power spectrum of dark matter perturbations on scales relevant to large-scale structure. We revisit this constraint in the light of several recent developments: (1) the availability of well-defined samples of local clusters with relatively accurate X-ray temperatures; (2) new theoretical mass functions for dark matter haloes, which provide a good fit to large numerical simulations; (3) more accurate mass–temperature relations from larger catalogues of hydrodynamical simulations; (4) the requirement to consider closed as well as open and flat cosmologies to obtain full multiparameter likelihood constraints for CMB and SNe studies. We present a new sample of clusters drawn from the literature and use this sample to obtain improved results on σ ₈, the normalization of the matter power spectrum on scales of 8  h ⁻¹ Mpc, as a function of the matter density and cosmological constant in a universe with general curvature. We discuss our differences with previous work, and the remaining major sources of uncertainty. Final results on the normalization, approximately independent of power spectrum shape, can be expressed as constraints on σ at an appropriate cluster normalization scale R _Cl. We provide fitting formulas for R _Cl and σ ( R _Cl) for general cosmologies, as well as for σ ₈ as a function of cosmology and shape parameter Γ. For flat models we find approximately σ ₈≃(0.495_−0.037^+0.034)Ω_M^−0.60 for Γ=0.23, where the error bar is dominated by uncertainty in the mass–temperature relation.     

Dark energy and the evolution of spherical overdensities

We use the non-linear spherical model in cold dark matter (CDM) cosmologies with dark energy to investigate the effects of dark energy on the growth of structure and the formation of virialized structures. We consider dark energy models with a constant equation-of-state parameter w . For  −1 < w < −1/3  , clusters form earlier and are more concentrated in quintessence than in ΛCDM models, but they form later and are less concentrated than in the corresponding open model with the same matter density and no dark energy. We point out some confusion in the literature around the expression of the collapse factor (ratio of the radius of the sphere at virialization to that at turnaround) derived from the virial theorem. We use the Sheth & Tormen extension of the Press–Schechter framework to calculate the evolution of the cluster abundance in different models and show the sensitivity of the cluster abundance to both the amplitude of the mass fluctuations, σ₈, and the σ₈– w normalization, selected to match either the cosmic microwave background observations or the abundance of X-ray clusters.