宇宙大尺度分形结构的一阶Kohmoto熵

已有观测证据表明宇宙大尺度结构是自相似或自仿射的分形分布，并已求出表片这两类分形的结构分数维。多分形热力学中提出的Ｋｏｈｍｏｔｏ熵函数建立了多重分形和热力学的形式类式。本文在三维球对称坐标系中求取了无标度区间ｒ０≤ｒ≤Ｒ范围内宇宙大尺度自相似分形分布的一阶Ｋｏｈｍｏｔｏ熵函数，它对应于信息论中的信息熵。     

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。     

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。     

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.     

两点相关函数,关联分维及IRAS星系大尺度分布的典型尺度

本对两点相关函数及关联分维间的关系进行了讨论，以ＩＲＡＳ星系红移天样本作为例子进行分析。分析结果表明，在大尺度上，ＩＲＡＳ星系的分布既不能用简单幂律形式的两点关函数，也不能用简单分形来描写，它可以用多级分形来更好地描写，多级分形结构的主要特征之一是存在典型尺度，即相邻分形间的转变尺度，用非归一计数方法可以有效耐 准确地确定这些典型尺度。存在典型尺度对目前已有的结构形成模型提出了挑战。     

宇宙大尺度分形结构的上限

本文给出了用几种达到不同极限星等的星系表确定宇宙分形结构上限截止尺度的公式.利用Zwicky星系表、Shane-Wirtanen星系表和Jagellonian天区的星系表的数据,可以估计这一截止尺度R_c至少为60—70Mpc,且R_c随着自相似分布所占比例f的减小而增大,或可大到约270Mpc的尺度.     

两点相关函数、关联分维及IRAS星系大尺度分布的典型尺度

本文对两点相关函数及关联分维间的关系进行了讨论，以ＩＲＡＳ星系红移巡天样本作为例子进行分析，分析结果表明，在大尺度（≥１５─２０ｈＭｐｃ）上，ＩＲＡＳ星系的分布既不能用简单幂律形式的两点相关函数，也不能用简单分形来描写。它可以用多级分形来更好地描写。多级分形结构的主要特征之一是存在典型尺度，即相邻分形级间的转变尺度，用非归一计数方法可以有效而准确地确定这些典型尺度，存在典型尺度对目前已有的结构形成模型提出了挑战。     

星系团二维分布的分形特征

本文采用分形分析法分别研究了全天区富星系团表中北银纬和南银纬不同深度和不同富性的子样本的二维分布规律，结果发现星系团的二维分布是一个多级分形结构，在Ｄ≤４和Ｄ＝５＋６类子样本中，不同分形级之间的转变尺度所对应的投影尺度均为～４２ｈ~（－１）Ｍｐｃ。在整个尺度范围内，北银纬、南银纬样本星系团的分布规律很相似。     

星系团二维分布的分形特征

本采用分形分析法分别研究了全天区富星系团表中北银纬和南银纬不同深度和不同富性的子样本的二维分布规律，结果发现星系团的二维分布是一个多级分形结构，在Ｄ≤４和Ｄ＝５＋６类子样本中，不同分形级之间的转变尺度所对应的投影尺度均为￣４２ｈ＾－１Ｍｐｃ。在整个尺度范围内，北银纬、南银纬样本星系团的分布规律很相似。     

宇宙的大尺度结构

在宇宙的已观测的范围内,从尺度10~(10)cm直到10~(26)cm可视物质的分布是不均匀的。对星系三维分布的研究结果表明,绝大多数的星系集中在由星系的带、群和团组成的超星系团中;而在超星系团之间是几乎没有可视天体的巨洞。宇宙的大尺度结构(在尺度10Mpc—10~2Mpc上星系分布不均匀性的特征)似乎是网状的。对类星体红移分布的统计分析结果表明,在大尺度结构中可能有周期性分布的成分。周期尺度是10~2Mpc的数量级。 在另一方面,关于微波背景辐射的温度起伏的观测(δT/T 10~(-5),在角尺度10′—180°的范围)表明,宇宙中的物质在更大尺度(10~3Mpc)上的分布是均匀的。 大尺度结构是怎样从早期均匀的背景宇宙中增长起来的?这是在宇宙学中最重要也是最困难的问题上一;要解决这个问题需要有关于宇宙的完善的模型。目前所流行的、关于大尺度结构的理论,基本上是以膨胀宇宙论和密度扰动的理论为基础的理论。 在绝热密度扰动(假定初始扰动是绝热的)的方案中,有两种观念特别值得注意: 1,宇宙密度波的观念。在早期宇宙中的扰动有可能在氢复合前形成有物理意义的相干波列;这种波——“宇宙密度波”在氢复合之后有可能影响物质的分布。作为宇宙密度波的可观测遗迹,可以解释已观测的星系分布不均匀性的上限尺度,以及在类星     

On the theory of the oblateness of the Sun

In this paper we first emphasize why it is important to know the successive zonal harmonics of the Sun's figure with high accuracy: mainly fundamental astrometry, helioseismology, planetary motions and relativistic effects. Then we briefly comment why the Sun appears oblate, going back to primitive definitions in order to underline some discrepancies in theories and to emphasize again the relevant hypotheses. We propose a new theoretical approach entirely based on an expansion in terms of Legendre's functions, including the differential rotation of the Sun at the surface. This permits linking the two first spherical harmonic coefficients (J ₂ and J ₄) with the geometric parameters that can be measured on the Sun (equatorial and polar radii). We emphasize the difficulties in inferring gravitational oblateness from visual measurements of the geometric oblateness, and more generally a dynamical flattening. Results are given for different observed rotational laws. It is shown that the surface oblateness is surely upper bounded by 11 milliarcsecond. As a consequence of the observed surface and sub-surface differential rotation laws, we deduce a measure of the two first gravitational harmonics, the quadrupole and the octopole moment of the Sun: J ₂=−(6.13±2.52)×10⁻⁷ if all observed data are taken into account, and respectively, J ₂=−(6.84±3.75)×10⁻⁷ if only sunspot data are considered, and J ₂=−(3.49±1.86)×10⁻⁷ in the case of helioseismic data alone. The value deduced from all available data for the octopole is: J ₄=(2.8±2.1)×10⁻¹². These values are compared to some others found in the literature. Supplementary material to this paper is available in electronic form at http://dx.doi.org/10.1023/A:1005238718479     

Accounting for the viscosity of the fluid core in the problem of the physical libration of the moon

A two-component theoretical model of the physical libration of the Moon in longitude is constructed with account taken of the viscosity of the core. In the new version, a hydrodynamic problem of motion of a fluid filling a solid rotating shell is solved. It is found that surfaces of equal angular velocity are spherical, and a velocity field of the fluid core of the Moon is described by elementary functions. A distribution of the internal pressure in the core is found. An angular momentum exchange between the fluid core and solid mantle is described by a third-order differential equation with a right-hand side. The roots of a characteristic equation are studied and the stability of rotation is proved. A libration angle as a function of time is found using the derived solution of the differential equation. Limiting cases of infinitely large and infinitely small viscosity are considered and an effect of lag of a libration phase from a phase of action of an external moment of forces is ascertained. This makes it possible to estimate the viscosity and sizes of the lunar fluid core from data of observations.     

Rotation of the elastic Earth: the role of the angular-velocity-dependence of the elasticity-caused perturbation

We calculate the so-called convective term, which shows up in the expression for the angular velocity of the elastic Earth, within the Andoyer formalism. The term emerges due to the fact that the elasticity-caused perturbation depends not only on the instantaneous orientation of the Earth but also on its instantaneous angular velocity. We demonstrate that this term makes a considerable contribution into the overall angular velocity. At the same time the convective term turns out to be automatically included into the correction to the nutation series due to the elasticity, if the series is defined by the perturbation of the figure axis (and not of the rotational axis) in accordance with the current IAU resolution. Hence it is not necessary to take the effect of the convective term into consideration in the perturbation of the elastic Earth as far as the nutation is related to the motion of the figure axis.     

Impact of the Quadrupole Moment of the Sun on the Dynamics of the Earth-Moon System

Range of values of the Sun's mass quadrupole moment of coefficient J₂ arising both from experimental and theoretical determinations enlarge across literature on two orders of magnitude, from around 10^-7 until to 10^-5. The accurate knowledge of the Moon's physical librations, for which the Lunar Laser Ranging data reach an outstanding precision level, prove to be appropriate to reduce the interval of J₂ values by giving an upper bound of J₂. A solar quadrupole moment as high as 1.1 10^-5 given either from the upper bounds of the error bars of the observations, or from the Roche's theory, is not compatible with the knowledge of the lunar librations accurately modeled and observed with the LLR experiment. The suitable values of J₂ have to be smaller than 3.0 10^-6. As a consequence, this upper bound of 3.0 10^-6 is accepted to study the impact of the Sun's quadrupole moment of mass on the dynamics of the Earth-Moon system. Such as effect (with J₂ = 5.5±1.3 × 10^-6) has been already tested in 1983 by Campbell & Moffat using analytical approximate equations, and thus for the orbits of Mercury, Venus, the Earth and Icarus. The approximate equations are no longer sufficient compared with present observational data and exact equations are required. As if to compute the effect on the lunar librations, we have used our BJV relativistic model of solar system integration including the spin-orbit coupled motion of the Moon. The model is solved by numerical integration. The BJV model stems from general relativity by using the DSX formalism for purposes of celestial mechanics when it is about to deal with a system of n extended, weakly self-gravitating, rotating and deformable bodies in mutual interactions. The resulting effects on the orbital elements of the Earth have been computed and plotted over 160 and 1600 years. The impact of the quadrupole moment of the Sun on the Earth's orbital motion is mainly characterized by variations of , , and . As a consequence, the Sun's quadrupole moment of mass could play a sensible role over long time periods of integration of solar system models. This revised version was published online in July 2006 with corrections to the Cover Date.     

On the role of the motion of the photospheric footpoints of the magnetic field lines

By means of a simple relation between the velocity v of the fluid particle and the velocity v_f of the photospheric footpoint of the magnetic field line v_z and B_z being respectively the components of v and the magnetic field B normal to the photospheric surface, it is shown formally that through the phtospheric surface the transport of all the quantities attributed to the magnetic field, such as the magnetic flux, the magnetic energy and the helicity, is independent of v_z, and v_f is the only kinematical quantity on which the transport depends. In addition, in the neighborhood of the neutral line the velocity v_l of the moving curve of constant B_z is found to be equal approximately to the component of v or v_f in the direction of v_l. Since v_l can be measured or extimated, so can the components of v and v_f near the neutral line.     

Determination of the temperature of the solar corona from the spectrum of the electron-scattering continuum

When the K-corona is formed by the scattering of photospheric radiation from free electrons, the Fraunhofer lines are greatly broadened by the thermal motions of the hot electrons. This paper discusses the possibility of measuring the coronal electron temperature from the residual depressions in the K-coronal spectrum. If the ratio of the intensities at 4100 Å and 3900 Å can be measured to an accuracy of ±1%, the coronal temperature can be inferred to an accuracy of ±0.2 MK. The temperature of a coronal inhomogeneity may also be measured by this method, provided the position angle is known.Now at Fraunhofer Institute, Freiburg, Germany.     

Calculation of the global system of the field-aligned currents on the dayside of the magnetosphere

Using the well-known equation for the normal component of the current which exist near the tangential discontinuity in the plasma in the case of the frozen-in magnetic field, and supposing that the current closes in the ionosphere in the auroral oval in the region 1, one calculates and compares with the data of observations the dependence of the density of the field-aligned current at the level of the ionosphere on the local time.     

On the systematic errors of the determinations of the absolute orientation of the meridian marks

The classical method of determination of the absolute azimuth (or Bessel's parameter n) can secure sufficiently precision for RA from observations of stars at high geographical latitudes during polar night only.